**1. Introduction**

Since its legendary introduction to the imperial court during the Eastern Han dynasty (25–221 CE),1 Buddhism had a profound impact on every aspect of the Chinese civilization in the following millennium of Medieval China.2 In the physical world, cities and landscapes were transformed by the spread of Buddhist practices and the introduction of new architectural types; in the spiritual world, Buddhism changed the way people perceived human life in terms of both its synchronic relationships with heaven (gods) and earth (societies), and its diachronic relationships with the past (ancestors) and the future (descendants). In the field of architectural history, much scholarship has been dedicated to the translation of Indian and Central Asian Buddhist architecture into Chinese contexts, especially the creation and development of the pagoda, the adoption and evolvement of traditional Chinese courtyard conventions in the construction of monasteries,3 and their influence on the development of traditional Chinese architecture. With great contributions to our knowledge on Chinese architecture, such approaches, however, presume an interpretative model of influence vs. Sinicization that treats Buddhist and Chinese architecture as two separate systems. Buddhism, as would be argued here, not only influenced but also directly participated in the very formation of Chinese architectural conventions.

This article explores the Buddhist ritual and architectural conventions that were incorporated into the Chinese funeral architecture during the period from the 3rd to the 13th centuries. A careful observation of some key types of sacred architecture from ancient East Asia, both before and after the Buddhist introduction, reviews fundamental similarities in their forms and structures. For instance, the early pagodas of West China from the 3rd to 10th centuries share great resemblances with both the sacrificial halls, or *xiangtang* 享堂, in the royal tombs of the Zhongshan kingdom during the Warring States period (476–221 BCE) of the Eastern Zhou dynasty (771–256 BCE), and the tomb mound, or *lingtai* 陵臺, in the royal mausoleums of the Western Xia kingdom (1032–1227), in their concentric plans and the combination of an earth core with the multilayered wooden verandas. Similarly,

**Citation:** Yu, Shuishan. 2021. The Translation of Buddhism in the Funeral Architecture of Medieval China. *Religions* 12: 690. https:// doi.org/10.3390/rel12090690

Academic Editor: Todd Lewis

Received: 19 July 2021 Accepted: 23 August 2021 Published: 27 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the highly architectural elements in the crowns of the funeral jars, or *hunping* 魂 瓶, in the areas of Jiangsu and Zhejiang provinces from the 4th century resemble both the Indian stupa and the Han *mingtang* 明 堂. What is the nature of such resemblances? Rather than using the influence and Sinicization model, I prefer to use the concept of "translation" for the discussion on the interactions among different cultures. Translation is not simply a substitution of words between the original and targeted languages, but a reconstruction of meanings in new contexts based on the understanding of a text in a different cultural and linguistic milieu. Borrowed from the linguistic practice, the translation model in the analysis of cultural exchanges forsakes the static view on a given culture as singular and predefined, thus allowing us to treat both Buddhist and Chinese architecture as multiple and evolving traditions.4 Through the study of the historical contexts from which certain architectural types and imageries were produced and a comparative analysis of their forms and functions, intertwined mutual translations of formal and ritual conventions can be observed between Buddhist and Chinese funeral architecture, which played a significant role in the formations of both architectural traditions in Medieval China.

#### **2. The Shifting Underground:** *Mingqi***,** *Hunping***, Stupa, and the Early Translation of Buddhism in Local Tombs**

Before the introduction of Buddhism to China during the Eastern Han dynasty, the Chinese buried their deceased's bodies without cremation. In the Qin and Western Han period (221 BCE–8 CE), the rich and powerful built enormous aboveground tumuli with elaborate underground chambers. The Mausoleum of the First Emperor of Qin (*Qin Shihuangdi*), for instance, had two layers of rectangular enclosure of walls with gates on the cardinal directions, which measured 2165 m north–south and 940 m east–west for the outer layer, and within the inner layer, a pyramidal rammed earth mound ( 封 土 *fengtu*) with a base square of 350 m each side and an extant height of 76 m.5 Commoners had much humbler tombs, buried with at least several specially made objects or utensils they once had during their lifetimes to accompany their afterlives. Buddhists, on the other hand, cremated the remains of the deceased, especially the venerated ones, to create the relics known as *sharila*, which was believed to be a confirmation of *nirvana*, the ultimate enlightenment. On such occasions, such as in the case of Shakyamuni Buddha, structures such as the stupa would be built to honor such a spiritual achievement.6 During the early Medieval period of the 3rd to 6th centuries, with the progressive Buddhist conversion and the gradual establishment of Buddhist communities and monasteries, pagodas were built to honor both relics of Buddha and the remains of great Buddhist masters.7 Burial customs of common Buddhists also started to bear the imprints of the new faith.

The reception of Buddhism was incorporated into the Chinese funeral tradition by the substitution of the previous Confucian and Daoist imageries with Buddhist deities and forms. The images of Buddha appeared in Chinese tombs as early as the late 2nd century. In the cave-tomb from Mahao in Sichuan province, for instance, a seated Buddha carved on the lintel carries the unmistakable Buddhist iconographic marks of *ushnisha* and *abhaya mudra* (see Figure 1).

Among other narrative carvings of Confucian ideology and morality, such as the famous Jing Ke's attempted assassination of the First Emperor of Qin, it occupies a place previously occupied by the Daoist gods of Dong Wanggong 東 王 公 and Xi Wangmu 西 王 母. Although the icon is Buddhist, the concept and functionality behind the Buddha image is Daoist, as Professor Wu Hung pointed out that "this holy image is no longer an object of worship on public occasion, but is a symbol of the deceased individual who had hoped to attain immortality after his death".8 Buddhism was translated into the Chinese architectural context of the 2nd to 3rd centuries through the substitution of traditional Chinese deities with the Buddha. Such an understanding of the foreign god was also confirmed by the contemporary intellectual discourse on Buddhism. In the famous monograph *Lihuolun* 理 惑 論, Mu Rong, the late 2nd-century Buddhist scholar, frequently cited Confucius and Laozi in the defense of Buddhism and argued that Buddha is an honorary title for the enlightened one, much like the title of *Shen* 神 for the Three *Huang* 三皇, the title *Sheng* 聖 for the Five *Di* 五帝, and the supreme origin of *Dao* and *De* 道德之元祖.9 Deities and saints of both Confucianism and Daoism were evoked to help for a translation of Buddha into the Chinese religious contexts.

**Figure 1.** Mahao tomb, front chamber, lintel carved with a Buddha image, Leshan, Sichuan province, later 2nd century CE. (Drawing by author, after Figure 1 in Wu Hung, "Buddhist Elements in Early Chinese Art".)

Grave goods of the early Medieval China experienced a similar Buddhist translation. The previously mentioned specially made objects buried to serve the afterlife of the tomb masters are known as *mingqi* 明器, which literally means the "bright utensils". Since the Han dynasty, a type of *mingqi* made in the form of house model became increasingly popular. Archaeologists discovered such architectural *mingqi* in large quantities, especially from the tombs of the Eastern Han dynasty and after.10 Some *mingqi* house models feature multi-story towers with painted or sculpted details of wooden structure, such as postand-lintel frames and the *dougong* 斗拱 brackets. These multi-story tall buildings were either interpreted as the watchtowers for defensive purpose and scenery enjoyment11 or the reference to the dwelling of immortals.12 The former fulfills the Confucian filial service of the deceased in the similar way as they were alive, while the latter was deeply imbedded

in the Daoist practice aiming for immortality. A house model from Xiangyang in Hubei province, on the other hand, features Buddhist architectural details (see Figure 2).

**Figure 2.** *Mingqi* from Xiangyang, collection of the Xiangyang municipal Museum, Hubei province, Eastern Han to Three Kingdoms period, 2nd–3rd centuries CE. (Drawing by author, after Figure 1 in Luo Shiping, "Xianren hao louju: Xiangyang xin chutu xianglun taolou yu Zhongguo futuci leizheng".)

This house shares with other Eastern Han and Three Kingdoms period *mingqi* model in the combination of a main tower with a walled and gated courtyard. Both the tower and the gate have wooden frames supporting tiled roofs. The main tower is a two-story structure. The first story has a rectangular plan and an overhanging two-slope roof, supporting a wooden platform on brackets, above which the second story with a square plan and a four-slope roof sits. The unique feature is a pole with seven umbrellas, rising from the center of the four-slope roof, which clearly resembles the vertical axis and *chatras* in Indian stupa such as the one from the Great Stupa at Sanchi.

The typical roofs of *mingqi* houses from this period often have sculpted birds standing the tops and ends of the ridges. Here, in the Xiangyang model, while the center of the top horizontal ridge supports a Buddhist axis, the ends of both the horizontal and slanting ridges turn into a leaf-like shape. According to Luo Shiping from the Centra Academy of Fine Arts in Beijing, these leaves represent the bodhi tree, under which Shakyamuni Buddha meditated and became enlightened.13 Thus, the Buddhist concepts of enlightenment and *nirvana* were both translated into the Chinese funeral practice through the incorporation of iconic imageries from the life of Buddha and the features of the stupa into the *mingqi* house. The terminal of the axis in the Xiangyang model is a crescent, which is neither a Chinese nor an Indian architectural feature. Rather, some stupa images from Central Asia bare crescent forms on the railing poles. The formal translation of Buddhist architecture into the Chinese funeral practice was not direct and straightforward. Given the great distance and diverse cultures in between China and the original land of the Buddha, it might had gone through many mediating stages.14

Another type of funeral object that yields rich architectural images is called *hunping* 魂 瓶, the bottle of the soul. Though made in ceramic with a body shaped like a jar, *hunping* was not made to be used as a container. Small holes often appear in the middle part of the body and the round mouth is often sealed with a highly sculptural complex of additional decorations. The sculptural forms forming the crown of *hunping* are often tall, concentric in plan, and quite architectural, featuring a two to three-story tower-pavilion amid a crowd of animal and human figures of both real and mythical, birds, lions, phoenixes, musicians, dancers, singers, etc. The appearance of *hunping* was in the 3rd century, much later than the architectural *mingqi*, and spread in the following centuries of the early Medieval period mainly in the lower Yangtze provinces of Jiangsu and Zhejiang. Wu Hung argued that an important prototype of the *hunping* jar might be the reliquary used in the Indian world such as the famous Reliquary of Kanishka from the 2nd century.15 He suggested that *hunping* was primarily used by the northern Chinese exiled to the southern Yangtse area during the catastrophic collapse of the Western Jin dynasty, who had lost the bodies of the deceased and adopted the local tradition to provide the resting places for their souls using such vessels. *Hunping*, thus, became the embodiment of a specific funeral practice amalgamating the Confucian filial rites, the ancient shamanistic soul-calling (*zhaohun* 招 魂) of the southern (Chu and Wu) areas, and the Buddhist belief in the separation of the physical remains and the true self.16

The tangible Buddhist decorative motifs are human figures on some *hunping* jars that can be identified as Buddha or bodhisattvas through their attributes such as the *ushnisha*, halo, or *mudras*. While many previous discussions focus on the stylistic and iconographic analysis of imageries, this article pays special attention to the architectural elements in the *hunping*. A typical crown structure of the *hunping* has a concentric plan with a pyramidal three-dimensional form. In a 3rd-century Western Jin dynasty *hunping* jar from the Museum of Fine Arts Boston, the peaking center is an urn with a wide circular opening, surrounded by four smaller urns of similar shape and proportion (see Figure 3).

The four small urns form the corners of a square, defining the four cardinal directions. On one direction, four layers of sloping roofs create a façade of a wooden tower, under which a square opening serves as the only entrance hidden behind a mounted figure, who is seemingly emerging from the gate of the tower, defined by two solid pillars. Two additional mounted figures frame on the outer sides of the pillars, seemingly guarding the gate. On both sides of the four-story tower are singers and musicians playing various instruments, divided into four groups by three flocks of birds. All the birds are heading up with widely open wings, creating a strong soaring momentum. The base of the crown complex and the openings of the top central urn are both circular, while the four corner urns define a square set in between the larger lower circle of the base and the smaller upper circle of the central urn (see Figure 4).

**Figure 3.** *Hunping*, collection of the Museum of Fine Arts Boston, Western Jin dynasty, late 3rd century CE (photo by author).

While the urns and the architectural, anthropomorphic, and zoomorphic figures are typical decorative motifs on *hunping* jars, the entrance tower in the MFA Boston item strongly resembles a later pagoda in East Asia, and the combination of square and circle, as well as the emphasis on both the cardinal directions and the axial centrality, share much in common with the Indian stupa. Like a tower-pavilion style pagoda (*lougeshi-ta* 樓閣式塔), the MFA *hunping* tower has multiple layers of tiled roofs diminishing in size and width toward the top. Attached to the wall of the jar, it especially resembles the wooden edifice added to make a façade for a large Buddhist cave, for instance, the Nine-Story Pagoda (*jiucengta* 九層塔) at the Mogao Caves in Dunhuang, Gansu province (see Figure 5).

**Figure 4.** *Hunping*, view from above, collection of the Museum of Fine Arts Boston, Western Jin dynasty, late 3rd century CE (photo by author).

The cave behind the pagoda façade was created during the early Tang dynasty (618–907), much later than the Boston *hunping*, and the wooden structure has been rebuilt many times. It was also unlikely that the Dunhuang pagoda copied the images of the Eastern Jin dynasty *hunping*. The resemblance must be a reflection of a common architectural prototype they both shared, such as the context for the generation of meanings in a linguistic translation to which both the original and targeted languages refer.

The grouping of a large central stupa surrounded by four smaller ones on the corners can be traced back to the stupa at the Mahabodhi Temple in Bodhgaya, the place where historical Buddha attained enlightenment. The stupa with a tall *shikara* tower surrounded by four smaller one elevated on a square platform had undergone much rebuilding and repairs, but the original construction was at least since the Gupta dynasty (c. 319–467), and its prototype might even be earlier. The Diamond Throne, *vajrasana*, covered by the Bodhi tree, under which Buddha was believed to have meditated, was said to be established by King Ashoka (r. c. 268 to 232 BCE).17 It is still a popular style in Theravada stupas of Southeastern Asia. Additionally, some scenes in Dunhuang murals from the Northern dynasties period (386–577) contain pagoda-like structures with similar assemblage. In late imperial China, such an assemblage in the Buddhist relics structure can be found in the Vajrayana school (*Mizong* 密宗) known as *Jingangbaozuo-ta* 金剛寶座塔, the Diamond Throne Pagoda, which became especially popular among the monasteries related to the Tibetan practice since the Yuan dynasty.18

A *hunping* jar in the National Museum in Beijing from the same region and period, indeed, has the five urns replaced by five pavilions, with the central one elevated on a tower (see Figure 6). *Hunping* jars with five pavilions arranged in similar concentric plan can also be found in other museum collections, for instance, the one from the Museum of the Six Dynasties in Nanjing.19 With the *que* gates added to mark the entrance and axiality, the whole complex strongly resembles a *Jingangbaozuo-ta* such as the one from the Ming dynasty Zhenjue Monastery in Beijing or the one from the Qing dynasty Five Pagodas Monastery in Hohhot, Inner Mongolia (see Figure 7).

**Figure 5.** The Nine-Story Pagoda (*jiucengta*) at the Mogao Caves, Dunhuang, Gansu province (photo by author).

**Figure 6.** *Hunping*, Celadon Hunping (Soul Jar), Western Jin dynasty (Creative Commons: https: //commons.wikimedia.org/wiki/File:Western\_Jin\_Celadon\_Hunping\_(Soul\_Jar).jpg; accessed on 23 May 2021).

**Figure 7.** *Jingangbaozuo-ta* from the Five Pagodas Monastery, Hohhot, Inner Mongolia, Qing dynasty, 18th century (photo by author).

#### **3. The Transformed Passage:** *Que* **Gate,** *Mubiao***, and the Ashoka Column**

The early incorporation of Buddhist ideas and imageries in Chinese funeral architecture, in the 2nd to 3rd centuries as discussed in the previous section, concerns mostly the afterlife of the deceased, remains on objects that were not meant to be engaged by the livings, and concentrates largely underground. In the following 4th to 6th centuries, the translation of Buddhist architecture into the Chinese funeral context became more psychological, life engaging, ritually related, and manifests mainly along the aboveground passage.20 While objects discussed in the previous section were mostly from tombs of common well-to-do families, relatively of humble origins, cases sampled in this section can be related to the funeral practice of the imperial rulers.21 Compared to those of the previous Han dynasty, imperial mausoleums from the Eastern Jin (266–420) and the Southern Dynasties (420–589) were much smaller in terms of both the aboveground mounds and the underground chambers.22 The sculptural scheme framing the spirit path leading from the entrance to the tomb mound, however, became more refined and elaborate with concentrated Buddhist translation of architectural elements.

The sculptures framing a typical Southern Dynasties spirit path *shendao* 神道 for the imperial mausoleum start with the chimerical creature combining the body of a lion and a pair of wings, a mythical animal known as *qilin* 麒麟 or *pixie* 辟邪. They are followed in a certain distance by a pair of free-standing columns and ended with a pair of stone steles on turtle bases23 (see Figure 8).

The stone column often bears a rectangular tablet inscribed with the name and titles of the tomb master, thus known as *mubiao* 墓表, the sign of the tomb. The *mubiao* pillars are rich in details of European, Indian, or West Asian origins (see Figure 9).

**Figure 8.** Spirit path in a typical plan of a Southern Dynasties royal tomb (drawing by author, after Figure 5.1 in Wu Hung, *Monumentality in Early Chinese Art and Architecture*, 252).

**Figure 9.** Prince Xiao Jing (477–523) *mubiao*, Nanjing, Jiangsu province, Liang Dynasty (Creative Commons: https://commons.wikimedia.org/wiki/File:Tomb\_of\_Xiao\_Jing\_-\_P1200017.JPG; accessed on 29 May 2021).

The Prince Xiao Jing (477–523) *mubiao* from the Liang Dynasty, for instance, has a fluted shaft similar to that of an ionic column in classical Greco-Roman architecture. The earliest fluted column shaft came from the Eastern Han dynasty, such as the *mubiao* of the Cleric Qin of the You Prefecture 東漢幽州書佐秦君墓表 from the modern-day Beijing area24 (see Figure 10).

**Figure 10.** Cleric Qin of the You Prefecture *mubiao*, Shijingshan District, Beijing, Eastern Han dynasty, 105 CE (Creative Commons: https://upload.wikimedia.org/wikipedia/commons/f/fe/%E5%B9 %BD%E5%B7%9E%E6%9B%B8%E4%BD%90%E7%A7%A6%E5%90%9B%E7%9F%B3%E9%97%95 \_03.jpg; accessed on 19 June 2021).

The round details at the end of the fluting resemble the egg-and-dart in a classical ionic capital. The twin animal figures framing the neck connecting the fluted shaft below and the inscribed tablet above resemble the incorporation of symmetrical animal figures in the carved capitals from the Persian Persepolis.25

The framing of a passageway with free-standing columns can be considered a Buddhist translation of the Chinese *que* 闕 gate.26 A standard spirit path of an Eastern Han cemetery often starts with a pair of stone *que* towers, followed by mythical animals and stelae and ending at the shrine in front of the pyramidal rammed earth tumulus (see Figure 11).

**Figure 11.** Standard plan of an Eastern Han dynasty tomb (drawing by author, after Figure 4.1 in Wu Hung, *Monumentality in Early Chinese Art and Architecture*, 191).

The *mubiao* of the Cleric Qin of the You Prefecture, for instance, was originally part of a *que* gate complex. Fragments of Eastern Han funeral *que* had been discovered in different areas, especially from the southeastern Sichuan province.27 The stone *que* used in the funeral complex was already a translation of its counterpart with wooden structure serving in the living quarters. In an actual wooden *que* gate, the two towers framing the passageway are often connected in the middle above the path with roofs and sometimes verandas, such as the ones in the crown complex of the *hunping* jar from the museum in Nanjing. They might also be connected with enclosing walls thus serve the function of an actual gate. In the tombs from the period of Eastern Jin and the Southern Dynasties (266–589), however, the free-standing stone *que* towers preceding the mythical animal sculptures largely disappeared and the *mubiao* columns were added following them.

These *mubiao* pillars bear great similarities with the Ashoka columns in India from the 3rd century BCE.28 The combination of animal sculptures at the summit, a slender shaft with inscriptions planted on the ground, and a seat decorated with lotus petals in-between is a characteristic feature for the columns ordered to be founded by Ashoka (r. 268–232 BCE), the model king for Buddhist sponsorship and the quintessential example of *chakravarti*, a religious universal ruler. Known as Ayuwang 阿 育 王 in Chinese, many monasteries in his name were established in his honor in early Medieval China, including the one rebuilt by Emperor Wu of Liang 梁 武 帝, the cousin of Prince Xiao Jing.29 The Xiao Jing *mubiao* has a sculpture of a winged chimerical creature standing on the top of a large disk with lotus petal decoration. A comparison of the Xiao Jing *mubiao* (early 6th century) with the Ashoka pillar (3rd century BCE) (see Figure 12), the Persepolis columns (5th–4th centuries BCE), and the Naxos Sphinx pillar (6th century BCE) (see Figure 13) clearly indicates the cognate relationships among them and the possible transmission of the chimerical column from the West to the East. Buddhism served as a very important medium for the formal translation in this monumental construction.

**Figure 12.** Lauria Nandangarh pillar of Ashoka, India (photo date: 27 June 2018; photo author: M. Vidyut Prakash Maurya; Creative Commons: https://commons.wikimedia.org/wiki/File:Lauria\_ Nandangarh\_pillar\_of\_Ashoka\_side\_view.jpg; accessed on 19 June 2021).

**Figure 13.** Reconstructed view of the Naxian Sphinx on its 12.5 m Ionic column, erected next to the Temple of Apollo in Delphi, Greece, 560 BCE, collection of the Delphi Archaeological Museum (Creative Commons: https://www.wikiwand.com/en/Sphinx\_of\_Naxos; accessed on 19 June 2021).

While the major formal features of the Xiao Jing *mubiao* were mainly of foreign origins, the tablets inscribed with the tomb master's name and official titles, a traditional Confucian ritual for honoring the deceased ancestors, also went through the Buddhist translation. With spirit path running from south to north, two *mubiao* pillars used to stand on the east and west sides of the passage. Today, only the one on the west side survived. The inscriptions on its tablet, however, would be unreadable to any literate Chinese on the first sight. The twenty-three Chinese characters were written in mirror-image, or *fanshu* 反書, exactly symmetrical stroke by stroke with those on the tablet of the missing east *mubiao* pillar. In traditional Chinese cosmology, the east, which is associated with the element wood in the circle of Five Elements *wuxing* 五行, symbolizes life, while the west is the

direction associated with death and afterlife. The mirror-image of standard legible Chinese characters on the west *mubiao* of the Xiao Jing tomb, thus, was not meant for the living—the visitors who pass through the spirit path to pay homage to the deceased, but for the very tomb master who was buried behind. Wu Hung argued that the mirror-image inscriptions suggest a transparent stone slab and presume a vision from the direction of the tomb, the perspective of the deceased.30

The resurrection of the vision of the dead in funeral architecture was the result of a revised understanding about life and death brought by the new faith of Buddhism. Buddhists believe death was not the end of life but a necessary step to transcend life toward enlightenment. Buddhism gained enormous popularity in south China during the Liang dynasty, whose ruling classes include the imperial Xiao clan. Xiao Jing's cousin, Emperor Wu of Liang, was the famous Buddhist emperor who had founded numerous monasteries and personally served in Buddhist temples only to be ransomed by his courtiers to return to throne.31 Xiao Jing himself also wrote letters in support of Buddhism.32 In discussion of the mirror-image in the *mubiao* inscriptions, Wu Hung argued, "The important point is that this reading/viewing process forces the mourner to go through a psychological dislocation from this world to the world beyond it ... The discovery of the mirror relationship between the two inscriptions forges a powerful metaphor for the opposition between life and death ... More important, to completely fulfill the ritual transformation, the material existence of the gate has to be rejected".33

Indeed, the Buddhist translation of funeral architecture in China during this period made more tangible transformation of the physical structure engaging ritual activities aboveground. The *mubiao* pillars were no longer replicas of timber towers in the Chinese palace, as the stone carved *que* gates did in previous funeral complexes. Rather, they derived their forms from foreign Buddhist architecture. In terms of decorative motifs, sacred figures and historic scenes representing Confucian ideologies and morality were replaced by chimerical creatures both guarding the ground and soaring in the sky; architectural details imitating palatial edifices were replaced by the symbolic Buddhist image of the lotus flower. As Wu Hung observed, "a funerary gate no longer related itself to a counter-image in the living world and derived its meaning from this opposition; rather, it directly expressed the idea of transcendence and enlightenment. Most important, the mirror inscriptions on the gate completely alter the relationship between a monument and its audience: instead of presenting readable texts confirming the shared values of filial piety, they 'reverse' the conventional way of writing and challenge the viewer's perception, forcing him to reinterpret a funerary monument and to view it with fresh eyes".34 The new monumentality after the Buddhist translation blurred the boundaries between life and death, highlighting the active process of the funeral rites rather than simply providing a static familiar living environment for the afterlife. The inscriptions along the spirit path were written for both the eyes of the living and the soul of the deceased, making a spiritual transformation for the stone and earth of the tomb structure. It is a powerful metaphor about transcendence and enlightenment.

#### **4. The Shared Superstructure:** *Lingtai***,** *Xiangtang***,** *Mingtang***, and the Pagodas**

The most characteristic architectural symbol of Buddhism in East Asian is the pagoda. Translating the Buddhist relics structure into the Chinese timber building context, the *Louge* 樓 閣 (tower-pavilion) style35 wooden pagoda features a multi-story tower, often with an odd number of levels each with a sloping tiled roof diminishing in both heights and width toward the top. The number of bays for each level often remain the same with the intercolumnar distances diminish as the height rises. Completing the submit of such a pagoda is the wooden axis with *chatras*. Originated in China, such wooden pagodas are popular in all East Asian countries, including Korea and Japan, for instance, the 7th-century five-story pagoda from Horyuji in Nara,36 which is the oldest extant wooden pagoda in the world (see Figure 14). In China, three-dimensional images of early Louge style pagoda can be found in Buddhist grottoes, for instance, the 5th-century Yungang caves.37 Although the

oldest extant wooden pagoda in China, the Wooden Pagoda of Yingxian (see Figure 15) is from the 11th century, some masonry pagodas from the Tang dynasty also mimic wooden frames in decorative details on the walls.38

**Figure 14.** Five-story pagoda, Horyuji, Nara, Japan, 7th–8th centuries (photo by author).

Buddhist relics structures first appeared in China in the western regions along the ancient Silk Road. The region, known as *Xiyu* 西域, the Western Realm, refers to a vast area west of the Hexi Corridor in today's Gansu province, including Xinjiang in modern China and areas in many other Central Asian countries. Buddhism was first introduced to China from India via Central Asia through the ancient Silk Road.39 In the early 20th century, Buddhist ruins were discovered by Western exploders40 such as Marc Aurel Stein (1862–1943).41 Since the 1950s, Chinese archaeologists made systematic surveys of Buddhist sites in Xinjiang, excavating and documenting ancient structures including stupas. These early stupas in Western China, for instance, the Mauri-tim stupa near Kashgar,42 were often constructed with adobe. Sharing with the Indian stupa in features such as the solid core and a tripartite vertical division, however, they often had a square plan with an emphasis on the continuity from the base to the upper axis, shapes taping gradually toward the top instead of featuring a large hemispherical main body (*anda*) in the middle part. They share more in common with the Central Asian, especially the Gandara region stupa from the Kushan period (1st to 4th centuries).43 A 3rd-century stupa from the Subash monastery near Kuche has a tall square base, on top of which a cylindrical middle drum supports a domical top similar to the *anda* in Indian stupa44 (see Figure 16). Small holes appear on different levels in the square base, the cylindrical drum, and the domical top, which suggest there might be additional wooden or ceramic surface materials attached. Compared to the Sanchi stupa, the tomb mound feature was played down and the soaring verticality was highlighted. The square base has an arch opening on one side, clearly defining a frontal façade and giving the concentric plan an axial orientation. The plan and architectural image

give equal emphasis on the geometric motifs of square and circle.45 All these features make the *Xiyu* stupas closer to the ritual architecture of China and further differentiated from the Indian prototype. Similar stupas had also been discovered in other *Xiyu* sites such as Miran and Khotan.46

**Figure 15.** Wooden Pagoda of Yingxian, Ying county, Shanxi province, Liao dynasty, 11th century (photo by author).

**Figure 16.** Subash monastery stupa, Kuche, Xinjiang (Creative Commons: https://commons. wikimedia.org/wiki/File:Subashi\_BLP472\_PHOTO1125\_16\_671.jpg; accessed on 28 June 2021).

In China Proper, the earliest wooden pagodas in the Louge Style were constructed around a rammed earth core. Professor Fu Xinian suggested that the pre-Buddhist *taixie* 臺榭 tradition in Chinese architecture made it natural for the Chinese Buddhists to adopt the forms of the *Xiyu* earth stupa and combine them with the Chinese wooden construction.47 *Taixie* is a construction method in early Chinese architecture for building multi-level monumental structures combining rammed earth platforms with surrounding wooden

structures. Wrapping wooden verandas around the lower levels of platforms and elevating wooden towers on the top, the *taixie* method created an appearance of great scale and height without the actual creation of multiple-story interior space.48 Widely discovered in archaeological sites of the Zhou (1046-221 BCE), Qin (221-206 BCE), and Han (206 BCE to 220 CE) periods, they gradually disappeared since the Medieval time.49 Like Luo Shiping and many other scholars, Fu also believes that the high wooden towers were built for the hope to achieve immortality. The Daoist belief that immortals favored tower dwellings had contributed to the creation of the Louge Style pagoda.50

The famous nine story pagoda of the Yongning Monastery from the Northern Wei capital Luoyang was constructed with such a *taixie* method. After excavation, archaeologists discovered on the site of the Yongning Monastery pagoda rammed earth platform of 20 by 20 m on top of a rammed earth base of 38.2 by 38.2 m. The upper inner platform should be the earth core for the first floor of the pagoda, which was originally surrounded by a wooden veranda; the wider lower platform should be the base of the pagoda. Based on historical records such as the *Water Classics* (*Shuijingzhu* 水 經 註), contemporary pagoda images from the Northern Wei Buddhist caves such as those form Yungang and Dunhuang, and the archaeological data, scholars reconstructed the plan, elevation, and section of this famous early wooden pagoda. Fu Xinian's reconstruction is a nine-story pagoda with a square plan and a central pillar within a rammed earth core with wooden reinforcement. The lower seven stories are wooden verandas around earth platforms and the upper two stories are pure wooden structures. Each floor has a nine-bay façade on each side with both a sloping roof and a wooden balcony51 (see Figure 17).

**Figure 17.** Reconstructed section of the Yongning Monastery pagoda (drawing by author, after Figure 2-7-24 in Fu Xinian, *Zhongguo gudai jianzhushi di 2 juan: Liangjin, Nanbeichao, Sui, Tang, Wudai jianzhu*, 188).

The Yongning Monastery pagoda was built in 516 and burned down in 534. Half a millennium later, rulers of a regional regime in Northwestern China, the Western Xia Kingdom, built the main structures of their mausoleums in a way similar to both the pagoda in Luoyang and the stupas along the Silk Road. In today's Ningxia Hui Autonomous Region of northwest China, at the foot along the eastern slopes of the Helan Mountain, an area of some 50 square kilometers provides the resting places for nine rulers of the Western Xia kingdom from the late 10th to the early 13th centuries. It was not entirely clear about the identity for each of the nine royal tombs, which share the same basic plan and the same north–south orientation. Each mausoleum has two layers of walls with corner towers, defining an inner court and an outer court such as in the living cities. The outer layer has only one gate located at the center of the south wall while the inner layer has gates on all four cardinal directions. The plan has a strong axiality and is highly symmetrical. The north and south gates are located on the main north–south axis and other key elements, such as the corner towers, *quetai* 雀 臺 platforms, and stele pavilions, symmetrically frame the central axis on both sides (see Figure 18). The main tomb structures, the sacrificial hall *xiandian* 獻 殿 and the tomb mound *lingtai* 陵 臺, however, are deliberately off the main axis on the west side.52 The geometric center for the inner court is the central platform *zhongxintai* 中 心 臺.53

**Figure 18.** Model of a Western Xia royal tomb in the Mausoleum Museum, Ningxia (photo by author).

Most structures in the Western Xia royal tombs were constructed with rammed earth, with the additions of bricks, paints, and glazed tiles for protection and decoration. The Tomb No. 1, which was believed to be the mausoleum for the founding ruler Taizu (Li Jiqian 李 繼 遷), for instance, has an octagonal rammed earth platform of nine steps, the sizes of which reduce progressively toward the top. On the base level, each of the eight sides of the octagon measures approximately 12 to 14 m. Horizontal lines of holes appear on each side of every level. The holes measure approximately 20 cm in diameter for each, which must have been the traces left by the wooden rafters supporting a tiled roof. During the archaeological excavations, large number of ceramic tiles, tile ends, animal sculptures for roof decoration, charcoal, and rotten wood were discovered on the upper steps of the rammed earth platform, as well as on the ground near the *lingtai*.54 Thus, it is highly possible that the steps of the earth platform were surrounded by wooden verandas with tiled roof, transforming the exterior of the earth platform into a wooden pagoda (see Figure 19). Like the Yongning Monastery pagoda, the structure of wooden façades around

an earth core in the Western Xia royal tombs is basically a *taixie* method. Seen from the exterior, the *lingtai* mound used to be a multi-story tower, with all levels featuring a sloping tiled roof diminishing in both heights and width toward the top. In a similar way as the system of Louge style Buddhist pagodas, the number of levels for each *lingtai* is always an odd number, either 9, 7, or 5. The *lingtai* for emperor Taizu, for example, is the highest nine story, same as the Yongning Monastery pagoda.

**Figure 19.** *Lingtai* and the inner walls, Western Xia royal tomb, Ningxia (photo by author).

Unlike the pre-Buddhist Chinese tombs such as the Mausoleum for the First Emperor of Qin, the *lingtai* mound in the Western Xia mausoleum is not built on top of the underground tomb chambers *mushi* 墓室. Due to the damage made by earlier tomb robbers, the tomb chambers for Tomb No. 6 were revealed and archaeologists followed to make excavation and documentation.  Symmetrically planned with a north–south axis, the central chamber is framed by two smaller side chambers on the east and west sides, and connected with another group of chambers to its south through a corridor. South of the tomb chambers is sloping passageway *mudao* 墓道, linking the floor of the underground chambers with the ground surface, which is approximately 25 m above.55 (Figure 20) The sacrificial hall *xiandian* is very close to the entrance of the *mudao* passageway. The three central parts from south to north, *xiandian*, the underground *mudao* and *mushi*, and the *lingtai*, all follow the same north–south axis, which is to the west of the main north–south axis established by the walls and gates, parallel but not overlapped. Without covering the coffins of the tomb masters in the underground tomb chambers, the functionality of the *lingtai* mound is purely symbolic. Like the pagoda in Buddhism, *lingtai* in the Western Xia royal tomb is not a structure to protect the physical remains of a reincarnated sentient body, but a timeless monument dedicated to the hope for a future enlightenment.

**Figure 20.** Plan and section of the tomb chambers, Western Xia royal tomb No. 6 (drawing by author, after Figures 5–60 in Guo Daiheng, *Zhongguo gudai jianzhushi di 3 juan: Song, Liao, Jin, Western Xia jianzhu*, 223).

According to *Xixiaji* 西夏紀, the Records of the Western Xia, the rulers of the Western Xia were descendants of the Tuoba clans of the Northern Dynasties, the imperial clan of the Northern Wei empire who built the Yongning Monastery in the 6th century.56 Like their remote ancestors, the imperial families of the Western Xia were also Buddhists. In 1007, after his mother Wangshi 罔氏 died, King Taizong (Li Deming 李德明) sent envoys to the Song court, asking for permission to repair the ten great temples in Mount Wutai.57 Mount Wutai was located at the border area among Song, Liao, and Western Xia then under the Song jurisdiction. It is one of the four sacred Mountains in China and revered as the seat of bodhisattva Manjushri, the Bodhisattva of Wisdom. By the Tang dynasty (618–907), Mount Wutai had become one of the most important Buddhist centers in China and an international pilgrimage site, drawing Buddhist pilgrims from such faraway places as Japan and India.58 The Song emperor responded to Li's request by sending mourning envoys as well as sacrificial items to Mount Wutai, contributing to the religious rituals performed for Wangshi's afterlife.59 The Repairing or making monetary contribution for the repair of statues and buildings in temples and monasteries is a major merit for Buddhists to build up good *karma* 業 for desirable future reincarnations and the eventual enlightenment. Such religious contributions were part of the funeral service for Buddhists in East Asia. The adoption of the form of Buddhist pagoda for the construction of *lingtai* in Western Xia royal tombs was the result of the same intention for desirable *karmic* retribution in honor of the deceased.

The Yongning Monastery pagoda is not the only prototype for the *lingtai* from the Western Xia royal tombs. There was an even more remote model in Chinese funeral architecture. During the Warring States period (476–221 BCE), the kings of the Zhongshan state also built their mausoleums within two layers of rectangular walls, gated by the que towers in the middle of the southern wall. *Zhaoyutu* 兆域圖, the map of the entire mausoleum complex carved in a bronze plate discovered from the very archaeological site, indicates that within the inner court, five multi-story structures were elevated on top of a shared platform (see Figure 21). Each of the five structures features two additional concentric layers of rammed earth platforms surrounded by wooden verandas. The lower layer measures 92 by 110 m, a near square rectangle. The upper layer recedes from the lower platforms. The sacrificial hall, or *xiangtang* 享堂, is built on top of the upper layer rammed earth platform. The pointed roof of the *xiangtang* and the single slope roofs of the two verandas expand in size toward the lower base, forming a pyramidal profile for the tomb structure60 (see Figure 22) The concentric plan and multilayered verticality of the *xiangtang* shared much in common with the *lingtai* from the Western Xia Royal tombs, which were built more than a thousand years later. Combining a supporting earth core with a wooden frame wrapping, they were both manifestations of the *taixie* structure that had been widely used for the construction of monumentality since the Zhou dynasty.

**Figure 21.** The inscribed plan with inscriptions on the bronze plate discovered on the site of the Zhongshan Mausoleum, Pingshan county, Hebei province (Creative Commons: https://commons. wikimedia.org/wiki/File:Zhongshan\_Zhaoyutu.jpg; accessed on 27 May 2021).

**Figure 22.** Reconstructed drawing for the Royal Mausoleum of the Zhongshan state (drawing by author, after Figures 3–101 in Liu Xujie, *Zhongguo gudai jianzhushi di 1 juan: Yuanshi shehui, Xia, Shang, Zhou, Qin, Han jianzhu*, 268).

#### **5. Buddhism and the Transformation of Chinese Funeral Architecture**

The Yongning Monastery pagoda was chronologically sandwiched in-between the mausoleums for the kings of the Zhongshan state and the Western Xia royal tombs. A common feature for the three types of monumental constructions as represented by these three complexes is a ritual hierarchical order that all Chinese monumentality subscribes to. The ritual hierarchy may be expressed in the size of the walled area, the scale of the central monument, the number of buildings and gates for a complex, or the number of stories for the main tower. The Yongning Monastery pagoda has nine layers, the Great Wild Geese pagoda in Tang capital Changan has seven, and the wooden pagoda in the Ying county from the Liao dynasty has five.61 Among the Western Xia royal tombs, the *lingtai* mounds for Taizu and Taizong were nine-story tall, and the rest of them were either seven- or five-story tall, depending on the posthumous evaluations of the tomb masters by their decedents. According to the *Book of Rites*, or *Liji* 禮 記, the Son of Heaven *Tianzi* 天 子 can have seven ancestral temples, a ruler of a local state *Zhuhou* 諸 侯 five, a minister *Dafu* 大夫 three, a common aristocrat *Shi* 士 one; for the elevation above the ground of the main ceremonial hall's floor, the Son of Heaven nine feet (*chi* 尺), a local state ruler seven feet, a minister five, and a common aristocrat three.62 The legendary architecture for such a ritual system is *mingtang* 明 堂, the building complex where the Son of Heaven was supposed to make sacrifice to Heaven and the royal ancestors, performed the monthly rituals in different halls to harmonize the world according to the seasons, met homage-paying local rulers and court subjects, and delivered the most important edicts and lectures.63 The structure of the Han dynasty *mingtang* was also of the *taixie* type, a combination of a stepped rammed earth core with an envelope of wooden frame and sloping tiled roofs.64 Legitimizing the regime as holding the Mandate of Heaven, the construction of *mingtang* is one of the most significant architectural projects a Confucian dynastic ruler would have embarked on, including the non-Chinese speaking rulers of the Northern Wei and Western Xia.65

The translation of Buddhist concepts and forms into East Asian architecture was deeply imbedded in the Confucian context. It was a process operating upon the vocabularies and grammars of various local building traditions, for which the Medieval Chinese funeral architecture bears one of the most tangible fruits. The transformation started from underground, substituting local motifs in the tomb chambers with Buddhist symbols without altering the funeral space and structures. As Buddhist concepts further incorporated into the Chinese thoughts, revised views on life and death brought new elements to the spirit path, the passageway framing active funeral rites. When, finally, the main funeral structures were given Buddhist touches, it was already hard to tell whether the Buddhist became Chinese or the Chinese became Buddhist. Like the translation of Buddhist sutras that had created new vocabularies and brought new meanings to the Chinese language, the translation of Buddhism in the built environments had also participated in the very formation of architectural traditions in China. It blurred the boundaries between Buddhist architecture and other architectural typological divisions, which were largely based on the differentiation of functionality, the "content" of architecture.

In his 1939 article "Iconography and Iconology: An Introduction to the Study of Renaissance Art", Erwin Panofsky discussed the relationship between form and subject matter in European art and argued that on the deepest level, there is no "form as such" but just a continuous series of multilayered "contents". He argued that "in whichever stratum we move, our identifications and interpretations will depend on our subjective equipment, and for this very reason will have to be supplemented and corrected by an insight into historical processes the sum total of which may be called tradition".66 In the field of architectural history, the content is often understood as the functionality of a building, practical or symbolic. The application of a split between form and content in the discussion of traditional Chinese architecture obscures the profound impact Buddhism made to the Chinese architectural tradition, in which formal consistency often overshadows the differences in content, just like the power of the Chinese characters have done to every textual translation. On the other hand, Buddhist architecture, or *fojiao jianzhu* 佛 教 建 築, and funeral architecture, or *lingmu jianzhu* 陵 墓 建 築, are often categorized as two different types in the discipline of Chinese architectural history. An uncomfortable subtype within these two categories is the pagoda, which is obviously of funeral origin but often strictly

discussed under the Buddhist umbrella. The other side of the dilemma, those classified as funeral architecture but primarily constructed and decorated within the Buddhist contexts, is often neglected, remaining a blind spot unable to be recognized as a discomfort at all. The uncovering of such categorical discomfort as imbedded in Buddhist vs. funeral architecture is meaningful for a fuller understanding of Chinese architecture as, like what Panofsky said, the "historical processes" and "the sum total of which may be called tradition". It is an index of the great impact that the introduction of Buddhism had on Chinese architecture, like Xuanzang's translation of the *Prajnaparamita Sutra* 波若心經, which has become inseparably Buddhist and Chinese.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The author declares no conflict of interest.


**8. Simulation of fuzzy temperature control**

Normally, before proceeding with the implementation of the controller, a simulation is performed to evaluate its performance. The results of the simulation can aid in improving the design of the fuzzy controller and in verifying that it will work correctly when it is implemented. Such a simulation is shown below, implemented using Matlab (Sivanandam et al., 2007), specifically Simulink to simulate the control loop and fuzzy toolbox to implement the fuzzy controller.

The controller designed earlier is defined using the fuzzy toolbox in Matlab, yielding the fuzzy system shown in Figure 10. The fuzzy partition of the inputs and output is shown in Figure 11. As for the output surface, it is shown in Figure 12.

With this tool, we can see how the inference process is carried out, Figure 13.

The next step is to carry out a simulation with the temperature system to check the control system's performance. To do this, we will use the simulation tool Simulink, which allows us to implement the control loop in blocks and to use the fuzzy system made with the fuzzy toolbox as the controller. The diagram of the control system, then, is as shown in Figure 14.

equal their measured value. We also avoid the calculations that would be required if another membership function were used, such as Gaussian fuzzification, which requires constructing a Gaussian-shaped membership function to represent the exact value being

In order to define the inference mechanism, we have to determine how to carry out the basic operations. Since we are using Mandani's model, we have decided to implement the T-norm

The last step is to define the defuzzification process. For this temperature control case, we

Normally, before proceeding with the implementation of the controller, a simulation is performed to evaluate its performance. The results of the simulation can aid in improving the design of the fuzzy controller and in verifying that it will work correctly when it is implemented. Such a simulation is shown below, implemented using Matlab (Sivanandam et al., 2007), specifically Simulink to simulate the control loop and fuzzy toolbox to

The controller designed earlier is defined using the fuzzy toolbox in Matlab, yielding the fuzzy system shown in Figure 10. The fuzzy partition of the inputs and output is shown in

The next step is to carry out a simulation with the temperature system to check the control system's performance. To do this, we will use the simulation tool Simulink, which allows us to implement the control loop in blocks and to use the fuzzy system made with the fuzzy toolbox as the controller. The diagram of the control system, then, is as shown in Figure 14.

Fig. 9. Fuzzification process for the controller's input variable.

as the minimum and the S-norm as the maximum.

**8. Simulation of fuzzy temperature control**

Figure 11. As for the output surface, it is shown in Figure 12.

With this tool, we can see how the inference process is carried out, Figure 13.

will use the center of gravity.

implement the fuzzy controller.

provided by the sensor.

Fig. 10. Fuzzy controller for the temperature system.

Fig. 11. Fuzzy partition of the fuzzy controller inputs (error and error-variation) and output (increase command).

Control Application Using Fuzzy Logic: Design of a Fuzzy Temperature Controller 393

A prerequisite step to studying the results of the fuzzy controller is to adjust its parameters. In other words, we used fuzzy partitions that were normalized between -1 and 1, and yet the error, the error variation and the commanded increase have to take on values within a different range. To do this, we use gains that scale these variables within the design range of the fuzzy controller, adjusting these gains to achieve the desired specifications. These gains

2. If gs > 1, then the membership functions are uniformly contracted by a factor of 1/gs. 3. If gs < 1, then the membership functions are uniformly expanded by a factor of 1/gs.

Fig. 14. Fuzzy temperature control.

are called gains of scale (gs) and their effect is as follows:

Fig. 15. Output of fuzzy temperature controller.

1. If gs = 1, there is no effect on the membership functions.

Fig. 12. Control surface.

Fig. 13. Inference process for LP error (0.9) and LN error-variation (-0.8).

Fig. 14. Fuzzy temperature control.

Fig. 13. Inference process for LP error (0.9) and LN error-variation (-0.8).

Fig. 12. Control surface.

A prerequisite step to studying the results of the fuzzy controller is to adjust its parameters. In other words, we used fuzzy partitions that were normalized between -1 and 1, and yet the error, the error variation and the commanded increase have to take on values within a different range. To do this, we use gains that scale these variables within the design range of the fuzzy controller, adjusting these gains to achieve the desired specifications. These gains are called gains of scale (gs) and their effect is as follows:

Fig. 15. Output of fuzzy temperature controller.

Control Application Using Fuzzy Logic: Design of a Fuzzy Temperature Controller 395

In this chapter we have presented the steps required to implement fuzzy controllers. Such controllers, when integrated into systems that handle precise values, require a translation process before and after the reasoning method is applied. Hence the three-step structure of

The different stages were explained using an example involving temperature control. This is a trivial, academic problem that can be solved using many techniques, such as with a classical PI controller; in this chapter, however, we used this example to illustrate the design

Babuška R. (1998). *Fuzzy Modeling for Control*, Kluwer Academic Publishers, ISBN 978-0-

Cai X.-Z. (1997). Intelligent Control: Principles, Techniques and Applications, World Scientific Publishing Company, ISBN<PHONE_NUMBER>643, Singapore-New Jersey Chen G. & Joo Y. H. (2009). Introduction to Fuzzy Control Systems, In: *Encyclopedia of*

Horváth L. & Rudas I. J. (2004). *Modeling and Problem Solving Methods for Engineers*, Elsevier,

Jang J. S. R., Sun C. T. & Mizutani E. (1997). *Neuro-Fuzzy and Soft Computing*, Prentice Hall,

Li H. X. & Tong S.C. (2003). A hybrid adaptive fuzzy control for a class of nonlinear mimo

Passino K. M. & Yurkovich S. (1998). *Fuzzy Control*, Addison Wesley Longman, Inc., ISBN

Pedrycz W. (1993). *Fuzzy Control and Fuzzy Systems*, Research Studies. Press/John Wiley,

Sala A., Guerra T. M. & Babuška R. (2005). Perspectives of Fuzzy Systems and Control.

Sala J., Picó J. & Bondia J. (2000) Tratamiento de la incertidumbre en modelado y control

Sivanandam S.N., Sumathi S. & Deepa S.N. (2007). *Introduction to Fuzzy Logic using*

Tanaka K. & Sugeno M. (1992). Stability Analysis and Design of Fuzzy Control Systems,

Tanaka K. & Wang H. O. (2001). *Fuzzy control systems design and analysis. A linear matrix inequality approach*, John Wiley & Sons, ISBN<PHONE_NUMBER>242, New York

*MATLAB*, Ed. Springer, ISBN<PHONE_NUMBER>803, Berlín, New York

systems. *IEEE Trans. Fuzzy Systems*, Vol.11, No.1, (February 2003), pp. 24–34, ISSN

*Fuzzy Sets and Systems*, Vol.156, No.3, (December 2005), pp. 432-444, ISSN 0165-

borrosos, *Revista Iberoamericana de Inteligencia Artificial*. Vol.4, No 10, (Summer

*Fuzzy Sets and Systems*, Vol.45, No.2, (January 2002), pp. 135-156, ISSN 0165-0114,

Jantzen J. (2007). *Foundations of Fuzzy Control,* Wiley, ISBN<PHONE_NUMBER>633, New York Klir G. & Yuan B. (1995). *Fuzzy Sets and Fuzzy Logic*, Prentice Hall, ISBN<PHONE_NUMBER>717,

*Artificial Intelligence*, J. R. Rabul, J. Dorado, and A. Pazos (Eds.), 688-695, Hersh,

fuzzy controllers: fuzzification, inference and defuzzification.

of a fuzzy controller, as well as its mode of operation.

ISBN<PHONE_NUMBER>499, La Coruña, España

ISBN<PHONE_NUMBER>667, New York

Upper Saddle River, NJ

0114, North-Holland

North-Holland

0–201–18074–X, California

ISBN O-471-93475-5, Taunton, New York

2000), pp. 119-126, ISSN 1137-3601, España

1063-6706

Academic Press, ISBN<PHONE_NUMBER>506, New York

7923-8154-9, Boston, USA

**10. References**

For the temperature controller, we have selected a gain of scale for the controller's error input of Ke=0.0238, of Kev=1 for the error variation and of Kci=5000 for the command increase. The values Ke and Kev are needed to keep the error and the error variation bounded in the same margins. The Kci value is used to match up the maximum command to the maximum value of resistance (2000 watts). The values used in the gains of scale have been selected through an adaptive method based on the results of successive simulations.

The results yielded by this system are as shown in Figure 15. By applying the maximum command (2000 watts), we can reach the setpoint value in 1000 seconds. The rules that are applied at first (trigger force equal to 0 is shown in black, with the brightness increasing to white as we progress to a trigger force equal to 1) correspond to rules 27-31, which involve LP. Then the 20-22 group takes over, these rules controlling MP errors and small error variations. Next to activate are those rules for dealing with SP errors. Lastly, rule 7, with trigger force 1, is activated for dealing with ZE error and ZE error variation.

If the setpoint is changed at t=2,200 seconds, the result is as shown in Figure 16. When the setpoint is changed, a new command is output since the MP and SP error rules are activated.

Fig. 16. Output of fuzzy temperature controller with change at t=2200 seconds.

#### **9. Conclusions**

Fuzzy logic is based on the method of reasoning that is typically used by experts to handle all kinds of systems, from the simplest to the very complex. This method (control) can be formulated with rules of the type if-then applied to inexact magnitudes such as "many", "fast", "cold", etc. Implementing this method of reasoning requires a representation of these vague magnitudes and an associated logic. These are the Theory of Diffuse Groups and Diffuse Logic, respectively.

In this chapter we have presented the steps required to implement fuzzy controllers. Such controllers, when integrated into systems that handle precise values, require a translation process before and after the reasoning method is applied. Hence the three-step structure of fuzzy controllers: fuzzification, inference and defuzzification.

The different stages were explained using an example involving temperature control. This is a trivial, academic problem that can be solved using many techniques, such as with a classical PI controller; in this chapter, however, we used this example to illustrate the design of a fuzzy controller, as well as its mode of operation.

#### **10. References**

394 Fuzzy Inference System – Theory and Applications

For the temperature controller, we have selected a gain of scale for the controller's error input of Ke=0.0238, of Kev=1 for the error variation and of Kci=5000 for the command increase. The values Ke and Kev are needed to keep the error and the error variation bounded in the same margins. The Kci value is used to match up the maximum command to the maximum value of resistance (2000 watts). The values used in the gains of scale have been

The results yielded by this system are as shown in Figure 15. By applying the maximum command (2000 watts), we can reach the setpoint value in 1000 seconds. The rules that are applied at first (trigger force equal to 0 is shown in black, with the brightness increasing to white as we progress to a trigger force equal to 1) correspond to rules 27-31, which involve LP. Then the 20-22 group takes over, these rules controlling MP errors and small error variations. Next to activate are those rules for dealing with SP errors. Lastly, rule 7, with

If the setpoint is changed at t=2,200 seconds, the result is as shown in Figure 16. When the setpoint is changed, a new command is output since the MP and SP error rules are activated.

selected through an adaptive method based on the results of successive simulations.

trigger force 1, is activated for dealing with ZE error and ZE error variation.

Fig. 16. Output of fuzzy temperature controller with change at t=2200 seconds.

Fuzzy logic is based on the method of reasoning that is typically used by experts to handle all kinds of systems, from the simplest to the very complex. This method (control) can be formulated with rules of the type if-then applied to inexact magnitudes such as "many", "fast", "cold", etc. Implementing this method of reasoning requires a representation of these vague magnitudes and an associated logic. These are the Theory of Diffuse Groups and

**9. Conclusions**

Diffuse Logic, respectively.

**19**

*Brazil*

**An Evolutionary Fuzzy Hybrid System for**

Carlos Henrique Valério de Moraes3 and Germano Lambert-Torres3

When the Fuzzy Set Theory was proposed by Lotfi Zadeh in a seminal paper published in 1965, he noted that the technological resources available until then were not able to automate the activities related to industrial, biological or chemical problems. These activities use typically analog data which are inappropriate to be handled in a digital computer that

Using this idea, Fuzzy Logic can be defined as a way to use data from typical analog processes that move through a continuous track in a digital computer that works with discrete values. The use of Fuzzy Logic for solving control problems has tremendously increased over the last few years. Recently the Fuzzy Logic has been used in industrial process control electronic equipment, entertainment devices, diagnose systems and even to control appliances. Thus, the teaching of fuzzy control in engineering courses is becoming a necessity. In a previous work, it has been presented a computational package for students' self-training on fuzzy control theory. The package contains all required instructions for the users to gain the understanding of fuzzy control principles. The training instructions are

Although this approach has proven to be convenient in giving to students an opportunity to appreciate real life like situations, it suffers a serious disadvantage: the type of learning. In fact, students often go through a "trial-and-error" method to select an appropriate control action, such as rule definitions or membership fitting. The problem of this type of learning is a tendency from students to get the erroneous concept that corrective actions are much a matter of guess. The purpose of this chapter is to present a strategy for an automatic membership function fitting using three different evolutionary algorithms, namely: modified genetic algorithms (MGA), particle swarm optimization (PSO) and hybrid particle

The proposed strategies are applied in a computational package for fuzzy logic learning. This computer program was developed for self-training in engineering students in the

works with well-defined numerical data, i.e. , discrete values.

**1. Introduction**

presented via a practical example.

swarm optimization (HPSO).

Ahmed Ali Abadalla Esmin1, Marcos Alberto de Carvalho2,

**Educational Purposes**

*1Lavras Federal University*

*3Itajuba Federal University*

*2José do Rosário Vellano University*


*Article* **Two Pre-Islamic Places of Worship in the Tourism Landscape of the UAE**

**Adriaan De Man**

Department of Tourism and Heritage, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates<EMAIL_ADDRESS>
**Abstract:** As suggested by the title, this paper explores two of the several archaeological sites that configure religious loci in the territory of the current United Arab Emirates. It does so by assessing their relevance, by refining their nature and historical context, and by analyzing their positioning as components of a tourism mix. The core research question is whether or not integration is accomplished. Both structures are quite well known in the academic literature and underwent excavation and conservation investments that allow their proper use and promotion. Discussion and conclusions identify challenges for achieving an appropriate integration with conditioning supply factors.

**Keywords:** archaeology; Abu Dhabi; Umm Al Quwain; heritage tourism; commodification


**4. Improving the Data Distribution over the** *S* **Range of the Data Used for Threshold Calculation**

#### *4.1. Rationale*

While sticking to the choice of [35] of defining *x*% thresholds from 2*x*% subsets of data, we first propose a major modification of the *AR-S* method aimed at optimizing the use of the information available over the entire *S* range. Fundamentally, the data that are now considered for inclusion in the calibration subsets rely no longer on residuals of an often non-significant fit over the whole data set but rather on minimum *AR* values. The best possible distribution of the latter is obtained by stratified sampling, dividing the actual *S* range of the data set in a number of slices from which (as much as possible) equal numbers of minimum *AR* data are selected. The slices are taken of equal size in log(*S*) and their optimal number was fixed at 10 on a trial-and-error basis. As an example, suppose you want to estimate a 10% threshold based on a data set containing 150 landslide events, i.e., 450 event dates (see [35] and A.1 below). Homogeneously distributing over 10 *S* classes the 90 data of

the 20% subset required for this threshold calculation implies to select the nine events with lowest *AR* in each class. Obviously, some classes may contain less than nine data, thus contributing less to the composition of the data subset, whose final size will often be slightly smaller than expected. In addition, when an *S* class does not contain enough data to fully contribute to the subset, all its data will be selected, however far their *AR* values are from minimum. However, tested through down weighting of the data proportionately to the deficit in contribution of their provenance class, this possible bias appeared to insignificantly affect the threshold estimates. The modified method is described in detail hereafter (see also Figure 4). The source code is provided in the Supplementary Material (Code S1).

	- A.1. *AR* values associated with each day of a reported landslide plus the days prior and after these dates are extracted from the *AR* time series of the corresponding pixels calculated according to Equation (1) and the parameterization adopted in [35], i.e., *a* = *b* = 1.2, *n* = 42 days, for which the index is relevant for landslide types ranging from shallow to deep-seated landslides [35,63]. Data with *AR* < 5 mm are discarded from the data set as unlikely to have been triggered by rainfall [35]. The size of the provisional data set *Q* is then *q* ≤ 3*p*, where *p* is the number of landslide events in the raw calibration set.
	- A.2. The data are weighted to account for the event date uncertainty: *w* = 24/36 for the day a landslide was reported, *w* = 6/36 for the days prior and after the landslide was reported. This weighting is implemented by expanding the data set as described in [35]. The expanded set is noted *R*.
	- B.1. The number *tC* of data to be selected per *S* class is determined as

$$t\_{\mathbb{C}} = \frac{2 \times \text{TPE} \times r}{10},\tag{5}$$

where TPE refers to the desired threshold probability of exceedance, *r* is the number of data in *R*, and 10 is the number of log(*S*) classes.

Threshold quality is evaluated through the correspondence between the obtained false negative rate (FNR, actual ratio of data in *R* below the calculated threshold) and the nominal TPE. Differences may result from *t* significantly smaller than (2 × TPE × *r*), large outliers in *T*, and possibly also from bootstrap issues (see Section 5).

**Figure 4.** Workflow of the modified antecedent rainfall (*AR*)–susceptibility (*S*) threshold approach for landslides. The data sets used or derived from the respective part of the workflow are highlighted in red. *RT* refers to the number of data in *R* below the threshold.


**Evaluation**

Right and false reactions are calculated in relation to the presented events (in percentage), the latter being registered as an error. The unfounded (delayed) reactions are given in absolute numbers. The age-and gender-independent cut-off value for the error is 5.75% (SD = 11.3%) after a standardization study with healthy volunteers of Randerath and colleagues (2000). For the unfounded responses and response times are currently no cut-off values. Measurements for the reliability and validity are pending.


**Abstract**

Ferrocene is a good electron donor, and as such has been used to test asymmetric conduction (rectification) in molecules that contain ferrocene. Of the five ferrocene-containing molecules that rectify (structures 11, 15, 19, 20, and 22), the last (22) exhibits a record rectification ratio, which should be a dramatic incentive for searching for more high-efficiency rectifiers.

**Keywords:** ferrocene, unimolecular electronics, rectification ratio, highest occupied molecular orbital, Aviram-Ratner proposal of 1974


**ADVANCES IN CARBON NANOSTRUCTURES**

Edited by **Adrián M.T. Silva** and **Sónia A.C. Carabineiro**

#### **Advances in Carbon Nanostructures**

http://dx.doi.org/10.5772/61730 Edited by Adrian M.T. Silva and Sonia A.C. Carabineiro

#### **Contributors**

Mohammad Ali Ali Mohammad, He Tian, Yi Yang, Tian-Ling Ren, Wen-Tian Mi, Irena Kratochvílová, Boris Kharisov, Oxana V. Kharissova, Beatriz Ortega García, Ubaldo Ortiz Mendez, Saiful Izwan Abd Razak, Nadirul Hasraf Mat Nayan, Nor Syuhada Azmi, Abdul Halim Mohd Yusof, Izzati Fatimah Wahab, Farah Nuuruljannah Dahli, Noor Fadzliana Ahmad Sharif, Youngduck Kim, Myung-Ho Bae, Quan Xu, Wenwen Zhang, Liu Shuan, Hammad Younes, Vesselin Shanov, Seyram Gbordzoe, Rachit Malik, Noe Alvarez, Robert Wolf, Davide Micheli, Roberto Pastore, Antonio Vricella, Mario Marchetti

#### **© The Editor(s) and the Author(s) 2016**

The moral rights of the and the author(s) have been asserted.

All rights to the book as a whole are reserved by INTECH. The book as a whole (compilation) cannot be reproduced, distributed or used for commercial or non-commercial purposes without INTECH's written permission. Enquiries concerning the use of the book should be directed to INTECH rights and permissions department (permissions@intechopen.com).

Violations are liable to prosecution under the governing Copyright Law.

Individual chapters of this publication are distributed under the terms of the Creative Commons Attribution 3.0 Unported License which permits commercial use, distribution and reproduction of the individual chapters, provided the original author(s) and source publication are appropriately acknowledged. If so indicated, certain images may not be included under the Creative Commons license. In such cases users will need to obtain permission from the license holder to reproduce the material. More details and guidelines concerning content reuse and adaptation can be foundat http://www.intechopen.com/copyright-policy.html.

#### **Notice**

Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book.

First published in Croatia, 2016 by INTECH d.o.o. eBook (PDF) Published by IN TECH d.o.o. Place and year of publication of eBook (PDF): Rijeka, 2019. IntechOpen is the global imprint of IN TECH d.o.o. Printed in Croatia

Legal deposit, Croatia: National and University Library in Zagreb

Additional hard and PDF copies can be obtained from<EMAIL_ADDRESS>
Advances in Carbon Nanostructures Edited by Adrian M.T. Silva and Sonia A.C. Carabineiro p. cm. Print ISBN 978-953-51-2642-3 Online ISBN 978-953-51-2643-0 eBook (PDF) ISBN 978-953-51-5080-0


**Abortion and Family Planning**

**Abortion and Family Planning**

#### Affonso Renato Meira Affonso Renato Meira Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71772

#### **Abstract**

Abortion, a procedure by which the dead fetus is removed from the maternal organism and considered as a cultural trait, is found in all cultures of developed societies, as well as in the populations of aboriginal peoples. Moreover, it has long been a concern that has drawn social attention. It was only after in 1798, that the attention was drawn to the relationship between population and the production of goods. This concern has been accentuated by the birth rate and the longevity of human being. Abortion has undoubtedly interfered with population growth, the restriction of abortion advocated for human rights, or religious or economics reasons or by others. Family planning is a set of actions that help men and women plan for the arrival of their children, as well as prevent unwanted pregnancies. It is a project for couples to have offspring per their intentions and also the increase in world population that is worrying everyone has a decrease. For this, the Control of Birth is the method proposed to contain pregnancy. Abortion should only be recommended when a woman cannot or does not wish to give birth to a child or when the method used to control pregnancy has failed.

DOI: 10.5772/intechopen.71772

**Keywords:** family planning, birth control, artificial fertility, abortion, legislation, religion

#### **1. Introduction**

Culture for Edward Tylor "is all that complex that includes knowledge, beliefs, arts, morals, law, customs as well as all the skills acquired by man as a member of a society"[1] "The word culture, therefore, within an approach to the social sciences, includes everything that human beings have invented, built, adapted, or developed to survive and make life at least a satisfying and enjoyable experience, not only materially but also spiritually" [1].

Culture is an indivisible system that determines social behavior through traits, concepts, and patterns. Although it is an abstract process, culture sums up all the processes of reality that are

> Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

learned in a slow but effective way. Being a learning process through communication between people, culture is a process that precedes and succeeds the components of a society. Thus, it is considered a historical phenomenon, but in another view, the cultural aspects being abstract are kept within the people and, in this sense, can be considered a psychological phenomenon.

decrease. For this, the Control of Birth is the method proposed to contain pregnancy. Abortion should only be recommended when a woman cannot or does not wish to give birth to a child

Abortion and Family Planning

281

http://dx.doi.org/10.5772/intechopen.71772

Countries through legislation established by the government punish or liberate abortion. At the same time, the doctrine of various religions considers it to be a totally unwanted behavior. A cultural trait that turned into a medical fact is penalized by jurists and priests. Considered

As a cultural trait, abortion on many occasions is not obeyed and not even penalized by women or society. This is because there are many reasons for women seeking abortion

Among these reasons is rape, that is, the sexual act by violence and without the permission of the woman, which in almost all the countries of the Western world and countless of the Eastern world is considered a reason for the punishment of the man, as well as for allowing the woman to resort to abortion in order not to generate the fetus. In addition to rape, other

Among the biological reasons are life-threatening or health-related injuries, such as the most relevant ones. The current knowledge of medicine is so developed that if abortion is used to save a woman's life, it is almost abandoned. The emergence of diseases produced by viruses leading to the birth of fetuses with abnormalities, such as anencephaly, that will produce harmful effects on the life of the newborn is also considered. In some countries, incest is remembered [2].

On the other hand, many social reasons are forgotten by many societies that consider, with greater weight, the position of several churches, among them more narrowly Catholic.

Among these social reasons, it is possible to enumerate at once the desire of the woman not wanting the birth of a child, which can occur through several factors: the lack of knowledge of the father; the disappearance of the father; the father's attitude in not recognizing the child; the lack of acknowledgment of childbirth by the woman's family, even causing expulsion from her home; the financial impossibility of the family to support another child; the impossibility of giving pause to a livelihood or future improvement activity; and finally the failure

Birth control has always been sought in ancient civilizations for more than 4000 years. In Egypt, the Berlin papyrus refers to fumigation that prevented pregnancy and the Ebers papyrus indicates procedures that prevented a woman from becoming pregnant for 2–3 years. The Old Testament refers to the "coitus interruptus" method adopted in Europe in the nineteenth century and to this day adopted by poorer and less enlightened layers throughout the world. The abandonment of unwanted children was practiced among the Greeks as well as among the Romans. Chinese were organized on farms for the reception of children who remained

or when the method used to control pregnancy has failed.

a medical act of which presents very little risk to the woman.

**3. Generalities**

whether biological or social.

reasons are considered for abortion.

in the process of birth control.

until they were sacrificed [3].

The process of learning culture is a slow, continuous, unconscious process that begins at birth and continues throughout life. The culture of a society leads people to think, feel, and act per cultural standards. Cultural pattern is the orientation provided by the complexities and cultural traits that are valued in different ways. It is also in Piovesan's words the paths followed by the customs, ideas, beliefs, and attitudes of a population group. It is possible to consider that in all cultures, therefore in all societies, there is a standard in relation to health, which is composed of concepts grouped in medical knowledge that are characterized by traits, characterizing the behavior of society, at various levels in relation to health. Concepts are derived from medicine based on scientific learning or on empirical learning based on analogical knowledge.

Cultural trait is the least definable element (Kroeber) or identifiable (Herskovits) of culture [1]. Abortion should be considered a component of the standard of health of all cultures.


**2. The LmPy-GC/MSMS hyphenated system**

LmPy-GC/MSMS is a hyphenated analytical technique composed by: a neodymium-doped yttrium aluminum garnet (Nd-YAG; Nd: Y3Al5O12) laser source, an optical device containing the sample chamber, a transfer line from the optical device to the gas chromatography equipment coupled to a triple quadrupole mass spectrometer (GC/MSMS) with a cryogenic entrapment (Liquid Nitrogen, −80°C) or Cold Trap in the PTV (programmed temperature vaporization) injector. **Figure 1** shows the schematic system of the LmPy-GC/MSMS technique and the Palynofacies and Organic Facies Laboratory (*LAFO*) hyphenated system located at the Federal University of Rio de Janeiro (*UFRJ*), Brazil. CSIRO (Commonwealth Scientific and Industrial Research Organization), Division of Petroleum Resources (Sydney, Australia) assembled this system exclusively for *LAFO/UFRJ* with financial support from *PETROBRAS*/Brazil.

The most common laser type used to emit light in the infrared spectrum (λ = 1064 nm) consists of an yttrium oxide and crystalline aluminum as a "host" doped with neodymium as a "guest." This device is known as the Nd-YAG laser and forms a variety of garnets. In the LmPy-GC/MSMS system, the Nd-YAG laser is the thermal energy source used to degrade large molecular-weight polymer carbon chains present in organic matter into smaller volatile species, under an oxygen-free environment. While the GC/MSMS technique separates and details the composition of molecular pyrolysis products (i.e., molecular fingerprinting). The association of these techniques has been useful to determine the composition or structure of original samples.