**4.2 BPLM process designer – structure and functionality BPLM process designer – structure and functionality – quantitative view**

#### *4.2.1 BP functional view consideration no. 1*

f g ½ � BPF i, j ð Þ ¼ f g ½ � BPF\_TR i, j1 ð Þ , BPF\_TT i, j2 ½ � ð Þ , BPF\_IM i, j3 ½ � ð Þ (1)

[BPF\_TR (i, j1)] - Transformation rule linguistic set – the set elements represent

[BPF\_TT (i, j2)] - Transformation tool linguistic set – the set elements represent closely related to human resources HRs, production technological device resources PDEV and production technological tool resources PTOOL, while formula (2) might

½BPF\_TT i, j2 ð Þ� ¼ ½ðHRs i, j21 ð Þ, PDEV i, j22 ð Þ, PTOOL i, j23 ð Þ ð Þ (2)

(HRs (i, j22), � the linguistic set, which contains data closely related to human

(PDEV (i, j21), � the linguistic set, which contains data closely related to production technological device resources, which participate at transformation

(PTOOL (i, j21), � the linguistic set, which contains data closely related to production technological tool resources, which participate at transformation

[BPF\_IM (i, j3)]} - BP internal metrics linguistic set, the content of which represent subsets, which contain data closely related to operational and technical parameters of to production technological device resources and theoretical knowl-

However, any BP is represented by external metrics items, which are closely related to actual BP inputs and outputs as well. The actual linguistic sets and algorithms concerned with relations among them are described in Section 4.2.2 via

In general, no business process proper and efficient functionality is possible without appropriate information support. At that level, the information support deals with reference database (RDBs) functionality and corresponds with their conceptual, logical and physical model. All linguistic seta related to BPF structure and functionality are stored in those RDBs and are closely related to BPF knowledge based support, while they contain pointers to appropriate semantic networks (SNWs), which create basis of BP knowledge-based support. However, they contain pointers to external data or information support resources (SAP components

The actual linguistic sets and algorithms concerned with relations among them

In a previous section, we have postulated that no business process proper and

efficient functionality is possible without appropriate information support. However, the same is concerned with the BP knowledge-based support. The BP knowledge-based support provides interconnection between the BP process and

i = 1, 2 … n is the index which indicates the BP, which an appropriate BPF is

math rules and algorithms, which regulate the BPF transformation process

*Operations Management - Emerging Trend in the Digital Era*

resources, which participate at transformation operations within actual

where

be postulated

where

BPFfunctionality.

Consideration no. 2.

especially).

**196**

operations within actual BPF functionality.

operations within actual BPF functionality.

edge and practical skills of human resources

*4.1.5 Business process model information support view*

are described in Section 4.2.3 via Consideration no. 3.

*4.1.6 Business process model knowledge-based support view*

beingassigned to.

The functional view deals with the BP vertical structure, which is created by core business processes (CBP), main business processes (MBP), subordinated business processes (SBP) and elementary business processes1 (EBP).

The view on a process as a structured chain of activities has a direct coupling to coordination as defined by Malone & Crowston. Coordination is simply the management of the dependencies between these activities. This implies that coordination is an activity in itself carried out by some actors. The work object of the coordination activity is coordination manifested as various tangible and intangible elements in the organization.

Now, we shall try quantifying those aspects with the use of PBPL Equation [25, 26]. BP Model Functional view quantification with the use of PBPL Equation.

Let us consider a core business process CBP (0, I) Utility Glass Production represented by the {CBP (I, j)} linguistic set being decomposed into CBP (0, 1) Utility Glass Production Preparation denoted as CBP (i', j') represented by {CBP (i', j')} linguistic set i' = 1 … … n' j=1 … ..m1' and CBP (i", j") i' = 1 … .n",j=1 … .m1" Utility Glass Production Management represented by {CBP (i", j")} linguistic set, while the {CBP (i', j')} and {CBP (i", j")} are considered to be the linguistic subsets relating to the {CBP (I, j)}, while formula (3) might be postulated.

$$\{\text{CBP (I,j)}\} = \{ [\text{CBP (i',j')}] \} [\text{, [CBP (i'',j'')]}] \tag{3}$$

However, the CBP (0, I) business process is represented by its own internal and external metrics as well, while formulas (4) and (5) might be postulated.

$$\{\text{CBP (I, j)}\} \equiv \{\text{CBP}\_{\text{m}} \ (\text{I, j})\} \tag{4}$$

$$\{\text{CBP}\_{\text{m}}(\text{I}, \text{j})\} = \{ [\text{CBP}\_{\text{mint}}(\text{I}, \text{j})], [\text{CBP}\_{\text{miert}}(\text{I}, \text{j})] \}\tag{5}$$

Where index i' represents a hierarchic level of BP to be investigated and j' index represents a number subordinated processes relating to the BP investigated.

Now, we shall try to investigate how the superior core business process together with its internal and external metrics should be decomposed related to lower levels of management. With respect to this issue, we shall postulate two important questions.

1 The BP, which cannot be decomposed in other subordinated one or its further decomposition is meaningless from practical point of view is denoted as the elementary process.

(A) How the superior business process C (0, I) represented by {[CB (I, j)]} linguistic set should be decomposed to subordinated core business processes related to lower management levels, it means from strategic to tactic and operational management level and how the superior core business functional model should be created.

At first, we shall try to find an answer related to (A) question. In order to achieve that, we have to define the superior core business process in form of adequate linguistic set {CBP (I, j)} and to assign to that set an appropriate linguistic set {b0I} = {[b0hl], [bnbp],[binm]), denoted as BP Functional View Control Linguistic Set (BP-FWC Linguistic Set), while.

[b0hl] – is a linguistic subset element, which indicates a hierarchic level of BP to be decomposed.

[bnbp] – is a linguistic subset element which indicates a number of business process stored at subordinated level

[binm] – is a linguistic subset element which indicates a serial number of that BP at appropriate hierarchic level, which should be decomposed.

Example:

Let us consider a core business process stored at hierarchic level one [bnbp] = 1, while a serial number of that BP within appropriate hierarchic level is =1 [binm]=1 and that BP should be decomposed in 3 subordinated business processes [bnbp] = 3. For that case, linguistic set {b0I} elements are represented by formula (6).

$$\{\mathbf{b}\_{\rm 0I}\} = \{\mathbf{b}\_{\rm 0I}\} = \{ [\mathbf{b}\_{\rm 0h}], [\mathbf{b}\_{\rm nbp}], [\mathbf{b}\_{\rm inn}] \} = \{\mathbf{b}\_{\rm 0I}\} = \{ [\mathbf{1}], [\mathbf{3}], [\mathbf{1}] \} \tag{6}$$

Now, let us consider the superior core CBP (I, j) business process represented by {CBP (I, j) linguistic set, which should be decomposed in two subordinated core processes2 , which operate at strategic management level, while the {b0I} linguistic set3 elements are postulated via formula (7).

$$\{\mathbf{b}\_{\rm 0I}\} = \{\mathbf{b}\_{\rm 0I}\} = \{ [\mathbf{b}\_{\rm 0h}], [\mathbf{b}\_{\rm nbp}], [\mathbf{b}\_{\rm inn}] \} = \{\mathbf{b}\_{\rm 0I}\} = \{ [\mathbf{1}], [\mathbf{2}], [\mathbf{1}] \} \tag{7}$$

and the {b0I} set elements create basis for {[Petx (I, j)]} linguistic set, while formulas (8) and (9) might be postulated.

$$\{ [\text{Petx}\ (\mathbf{I}, \mathbf{j})] \} = \{ \mathbf{b}\_{01} \} \tag{8}$$

When applying PBPL Equation, the following result might be generated.

*Business Process Linguistic Modeling: Theory and Practice Part II: BPLM Business Process…*

Finally, let us consider the business process no.1 located at hierarchic level 2, which should be decomposed into two subordinated business processes located at hierarchic level 3, while two subordinated processes should be stored at that level and the {b0I} linguistic set elements are postulated with respect two formula (13).

, 2½ � g ⊗ CB 2, i3, j3

f g b0I ¼ f g b0I ¼ f b0hl�, bnbp , b½ �g ¼ inm f g b0I ¼ f g ½ � 3 , 2½ �, 1½ � (13)

When applying PBPL Equation, the following result might be generated {[3], [2],[1]} ⊗ {[CB (2, i2, j2)],[2}]} = {[CB (3, i2, j2)],[1}]} ⊗ {[CB (3, i2, j2)],[2}]} see

The above-mentioned formulas and relations create basis for BP functional view

However, the BPLM Process View deals with BP horizontal structure as well, an

BP Model Process view quantification with the use of PBPL Equation.

appropriate BP to be investigated and modeled, is selected from set of BP with adequate vertical structure (functional view) and the BP internal and external metrics plays a role of principle importance. Furthermore, a significant role plays BP Input Metrics, which creates an integral part of BP External Metrics {BPEXM (i, j4)} as well (see also formula (14). On the other hand, the BP internal metrics

, 3½ � g (12)

f g ½ � 2 , 3½ �, 1½ � ⊗ f CB 1, i1, j1

*4.2.2 Process view consideration no. 2*

¼ CB 2, i1, j1

**Figure 1.**

also **Figure 1.**

**199**

, 1½ � g

without BP internal and external metrics linguistic sets.

, 1½ � ⊗ CB 2, i2, j2

*An example of BP functional model source: The authors.*

*DOI: http://dx.doi.org/10.5772/intechopen.95350*

$$\{\left[\mathbf{P}\mathbf{t}\mathbf{x}\left(\mathbf{I},\mathbf{j}\right)\right]\} = \{\left[\mathbf{b}\_{0\text{hl}}\right], \left[\mathbf{b}\_{\text{nbp}}\right], \left[\mathbf{b}\_{\text{inn}}\right]\}\tag{9}$$

When applying the PBPL Equation formula (10) might be postulated.

$$\begin{aligned} & \left\{ \left[ \text{Petx} \left( \mathbf{I}, \mathbf{j} \right) \right] \right\} \otimes \left\{ \left[ \text{Pe} \left( \mathbf{I}, \mathbf{j} \right) \right] \right. \\ &= \left\{ \left[ \mathbf{b}\_{0\text{hl}} \right], \left[ \mathbf{b}\_{\text{nbp}} \right], \left[ \mathbf{b}\_{\text{inn}} \right] \right\} \otimes \left\{ \text{CBP } \left( \mathbf{I}, \mathbf{j} \right) \right. \\ &= \left\{ \left[ \text{CBP } \left( \mathbf{1}, \mathbf{i}\_{1}, \mathbf{j}\_{1} \right) \right], \left[ \mathbf{1} \right] \right\} \otimes \left\{ \left[ \text{CBP } \left( \mathbf{1}, \mathbf{i}\_{2}, \mathbf{j}\_{2} \right) \right], \left[ \mathbf{2} \right] \right\} \end{aligned} \tag{10}$$

This equation corresponds to the first hierarchic level shown in **Figure 1**.

Subsequently, we shall try to decompose the subordinated BP represented by {[CBP (1, i1, j1)]} into hierarchic level 2, where three subordinated BP should be stored and a number of the BP to be decomposed is 1. The {b0I} = {b0I} = {[b0hl], [bnbp],[binm]}linguistic set content might be postulated as follows:

$$\{\mathbf{b}\_{0\mathbf{l}}\} = \{\mathbf{b}\_{0\mathbf{l}}\}\_{=} \{ [\mathbf{b}\_{0\mathbf{l}\mathbf{l}}], [\mathbf{b}\_{\mathbf{n}\mathbf{p}\mathbf{p}}], [\mathbf{b}\_{\mathbf{l}\mathbf{m}}] \} = \{\mathbf{b}\_{0\mathbf{l}}\} = \{ [2], [3], [1] \} \tag{11}$$

2 The terms business process and process are considered to be equivalent from semantic point of view.

3 The terms linguistic set and set are considered to be equivalent from semantic point of view.

*Business Process Linguistic Modeling: Theory and Practice Part II: BPLM Business Process… DOI: http://dx.doi.org/10.5772/intechopen.95350*

#### **Figure 1.**

(A) How the superior business process C (0, I) represented by {[CB (I, j)]} linguistic set should be decomposed to subordinated core business processes related to lower management levels, it means from strategic to tactic and operational management level and how the superior core business functional model should be created. At first, we shall try to find an answer related to (A) question. In order to achieve that, we have to define the superior core business process in form of adequate linguistic set {CBP (I, j)} and to assign to that set an appropriate linguistic set {b0I} = {[b0hl], [bnbp],[binm]), denoted as BP Functional View Control Linguistic

[b0hl] – is a linguistic subset element, which indicates a hierarchic level of BP to

[binm] – is a linguistic subset element which indicates a serial number of that BP

Let us consider a core business process stored at hierarchic level one [bnbp] = 1, while a serial number of that BP within appropriate hierarchic level is =1 [binm]=1 and that BP should be decomposed in 3 subordinated business processes [bnbp] = 3.

, b½ � inm

, b½ � inm

and the {b0I} set elements create basis for {[Petx (I, j)]} linguistic set, while

f g¼ ½ � Petx I, j ð Þ b0hl ½ �, bnbp

When applying the PBPL Equation formula (10) might be postulated.

, 1½ � ⊗ CBP 1, i2, j2

This equation corresponds to the first hierarchic level shown in **Figure 1**. Subsequently, we shall try to decompose the subordinated BP represented by {[CBP (1, i1, j1)]} into hierarchic level 2, where three subordinated BP should be stored and a number of the BP to be decomposed is 1. The {b0I} = {b0I} = {[b0hl],

, b½ � inm

2 The terms business process and process are considered to be equivalent from semantic point of view. 3 The terms linguistic set and set are considered to be equivalent from semantic point of view.

f g ½ � Petx I, j ð Þ ⊗ f½Pe I, j ð Þ

 , b½ � inm ⊗ fCBP I, j ð Þ

[bnbp],[binm]}linguistic set content might be postulated as follows:

¼ b0hl ½ �, bnbp

f g b0I ¼ f g b0I ¼ b0hl ½ �, bnbp

¼ CBP 1, i1, j1

Now, let us consider the superior core CBP (I, j) business process represented by {CBP (I, j) linguistic set, which should be decomposed in two subordinated core

, which operate at strategic management level, while the {b0I} linguistic

¼ f g b0I ¼ f½ � 1 , 3½ �, 1½ �Þ (6)

¼ f g b0I ¼ f½ � 1 , 2½ �, 1½ �Þ (7)

f g ½ � Petx I, j ð Þ ¼ f g b0I (8)

, 2½ �

¼ f g b0I ¼ f g ½ � 2 , 3½ �, 1½ � (11)

(9)

(10)

, b½ � inm

For that case, linguistic set {b0I} elements are represented by formula (6).

[bnbp] – is a linguistic subset element which indicates a number of business

at appropriate hierarchic level, which should be decomposed.

f g b0I ¼ f g b0I ¼ b0hl ½ �, bnbp

*Operations Management - Emerging Trend in the Digital Era*

f g b0I ¼ f g b0I ¼ b0hl ½ �, bnbp

set3 elements are postulated via formula (7).

formulas (8) and (9) might be postulated.

Set (BP-FWC Linguistic Set), while.

process stored at subordinated level

be decomposed.

Example:

processes2

**198**

*An example of BP functional model source: The authors.*

When applying PBPL Equation, the following result might be generated.

$$\begin{array}{l} \{ [2], [3], [1] \} \otimes \{ [\text{CB } (\mathbf{1}, \mathbf{i}\_1, \mathbf{j}\_1)], [1] \} \\ = \{ [\text{CB } (\mathbf{2}, \mathbf{i}\_1, \mathbf{j}\_1)], [1] \} \otimes \{ [\text{CB } (\mathbf{2}, \mathbf{i}\_2, \mathbf{j}\_2)], [2] \} \} \otimes \{ [\text{CB } (\mathbf{2}, \mathbf{i}\_3, \mathbf{j}\_3)], [3] \} \end{array} \tag{12}$$

Finally, let us consider the business process no.1 located at hierarchic level 2, which should be decomposed into two subordinated business processes located at hierarchic level 3, while two subordinated processes should be stored at that level and the {b0I} linguistic set elements are postulated with respect two formula (13).

$$\{\mathbf{b}\mathbf{o}\mathbf{l}\} = \{\mathbf{b}\mathbf{o}\mathbf{l}\} = \{\left[\mathbf{b}\_{\text{0hl}}, \left[\mathbf{b}\_{\text{nbp}}\right], \left[\mathbf{b}\_{\text{inm}}\right]\right] \} = \{\mathbf{b}\mathbf{o}\mathbf{l}\} = \{\left[\mathbf{3}\right], \left[\mathbf{2}\right], \left[\mathbf{1}\right]\} \tag{13}$$

When applying PBPL Equation, the following result might be generated {[3], [2],[1]} ⊗ {[CB (2, i2, j2)],[2}]} = {[CB (3, i2, j2)],[1}]} ⊗ {[CB (3, i2, j2)],[2}]} see also **Figure 1.**

The above-mentioned formulas and relations create basis for BP functional view without BP internal and external metrics linguistic sets.

#### *4.2.2 Process view consideration no. 2*

BP Model Process view quantification with the use of PBPL Equation.

However, the BPLM Process View deals with BP horizontal structure as well, an appropriate BP to be investigated and modeled, is selected from set of BP with adequate vertical structure (functional view) and the BP internal and external metrics plays a role of principle importance. Furthermore, a significant role plays BP Input Metrics, which creates an integral part of BP External Metrics {BPEXM (i, j4)} as well (see also formula (14). On the other hand, the BP internal metrics

{BPINM (i, j4)} (see also formula (15) is created by those linguistic sets, which make basis for BP Function (BPF) definition.

pre-defined time points, it means they are time dependent and are called BP external

*Business Process Linguistic Modeling: Theory and Practice Part II: BPLM Business Process…*

However, that data are undertaken to an appropriate statistic evaluation and analysis as well, while adequate statistic values are being calculated (average and extend of variation) and a predefined time interval should be respected, when calculating those values. Those values are of an aggregated nature and are called BP external and internal metrics secondary data. In the next sections, we shall discuss

Let us consider the business process, which is of a technological nature4 and operates with selected material inputs5 represented by linguistic set {[Petx (i, j)]}, while that set consists of subsets6 [Petx (i, 1)], [Petx (i, 2)] … … [Petx (i, m1)],

i. is index closely related to BP serial number with set of processes

j1- is index, which represents number subsets, the linguistic set {[Petx (i, j1)]}

However, that BP external metric is represented by adequate outputs as well, while they are quantified via {[Res1 (i, j3,)]} linguistic set, which contains values

With respect to the above-mentioned issues, the PBPL Equation actual version

A fictive data, which create conted of {[Petx (i, j)]} and {[Res1 (i, j3,)]} will be

However, the {[Pe (i, j2,)]} linguistic set contains subsets, which quantify BPFs, the BP quantified via {[Pe (i, j2,)]} linguistic set consist of. When selecting one BPF, we can assign to it the linguistic set {[BPF (i, jf)]}, which consists of three subsets,

Now, let us have a look at {[Pe (i, j2,)]} linguistic set, which represents the business process Pe, while that process provides transfer of material input represented by {[Petx (i, j)]} linguistic set into final products (glass articles)

, BPF\_TT i, jf2

the subset = [BPF\_TR (i, jf1)] = {[BPF\_TR (i, j1)]} and the content might be

the subset = [BPF\_TT (i, jf1)] = {[BPF\_TT1 (i, j1)]} and the content might be

the subset = [BPF\_TM (i, jf1)] = {[BPFEM (i, j1)], [BPFIM(i, j2)]} and the

6 The terms linguistic set and set are considered to be the same from semantic point of view

content might be quantified via formulas (14) and (15).

f g ½ � Petx i, j ð Þ ⊗ Pe i, j2, ¼ Res1 i, j3, (16)

, BPF\_TM i, jf3

(17)

BP external metrics primary data – quantification via linguistic sets.

and internal metrics primary data generated at the first stage.

about that data quantification. Consideration no. 3a.

*DOI: http://dx.doi.org/10.5772/intechopen.95350*

Where

consists of

might be postulated.

discussed within Case study section.

represented by {[Res1 (i, j3,)]} linguistic set.

while formula (17) might be postulated.

f g ½ � BPF i, jf ð Þ ¼ BPF\_TR i, jf 1

quantified via formula (16).

quantified via formula (19)

4 Glass Article Primary Production- GAPP

Where

5 Glass Melt - GM

**201**

which represent one part of BP external metrics.

concerned with **nArtgood, nArtrep,** and **nArtwaste** items.

$$\begin{aligned} \text{?F (i,j2) (j2 = 1 \ldots m2)} &= >[\text{F (i,j2)}] ?[\text{Pexpj2 (i,j1)}] ?[\text{Pexp (i,j1)}] ?[\text{Pexp (i,j1)}] \\ &= >[\text{Pexpj2 (i,j1)}] ?[\text{F (i,j2)}] \\ &= [\text{Resi}j2 (i,j3), !] ?[[\text{Res1 (i,j3)}, )] \end{aligned} \tag{14}$$

$$\begin{aligned} \text{?Pe (i,j2) (j2 = 1 \ldots m2)} &= > >[\text{Pe (i,j2)}] ?[[\text{Pex } (i,j1,)]] \ $ \times \{[\text{Res1 } (i,j3,)]\} \\ &= > > \{[\text{Pex } (i,j1,)]\} \$  \{[\text{Res1 } (i,j3,)]\} ? \{\text{BPEXM (i,j4)}\} \end{aligned} \tag{15}$$

$$\&\quad \{\text{Pe } (i,j2)\} ? \{\text{BPINM (i,j5)}\} \end{aligned} \tag{15}$$

#### *4.2.3 BPM information support view*

In general, a proper and an efficient functionality of any business process depends on an adequate information support, however the question is: What the term BP information support related to BP functionality does mean? In general, any BP functionality and performance are closely related to BP external and internal metrics. However, the problems of BP external and internal metrics theory are discussed within Section 2 as well, while at that place we shall discuss aspects closely related to so called two stage BP external and internal metrics (see also **Figure 2**). What the term two stage BP external and internal metrics does mean?

In general, the implemented and operated BP is running and generates predefined output products (articles) – denoted as the primary products based on appropriated adequate material, information and financial inputs. On the other hand, the investigated BP operates with a set of input and output information generated based on detailed data, e.g. number of good articles nArtgood – a quality of which corresponds to pre-defined requirements, number of repaired articles nArtrep - number of produced articles their quality does not correspond to pre-defined requirements and should be repaired, and number of waste articles nArtwaste - number of produced articles their quality does not correspond to pre-defined requirements – cannot be repaired and should be considered to be a waste. They are considered to be detailed data and have no level of aggregation. The same is concerned with other data closely related to BP external or internal metrics and they are being measured at

**Figure 2.** *Business process horizontal structure source: The authors.*

#### *Business Process Linguistic Modeling: Theory and Practice Part II: BPLM Business Process… DOI: http://dx.doi.org/10.5772/intechopen.95350*

pre-defined time points, it means they are time dependent and are called BP external and internal metrics primary data generated at the first stage.

However, that data are undertaken to an appropriate statistic evaluation and analysis as well, while adequate statistic values are being calculated (average and extend of variation) and a predefined time interval should be respected, when calculating those values. Those values are of an aggregated nature and are called BP external and internal metrics secondary data. In the next sections, we shall discuss about that data quantification.

Consideration no. 3a.

BP external metrics primary data – quantification via linguistic sets.

Let us consider the business process, which is of a technological nature4 and operates with selected material inputs5 represented by linguistic set {[Petx (i, j)]}, while that set consists of subsets6 [Petx (i, 1)], [Petx (i, 2)] … … [Petx (i, m1)], which represent one part of BP external metrics.

Where

{BPINM (i, j4)} (see also formula (15) is created by those linguistic sets, which

?F i, j2 ð Þ ð Þ¼ j2 ¼ 1 … *:*m2 > ½ � F i, j2 ð Þ ?½ � Petxj2 i, j1, ð Þ ?f g ½ � Petx i, j1, ð Þ ¼ > ½ � Petxj2 i, j1, ð Þ ?½ � F i, j2 ð Þ

?Pe ið Þ *;* j2 ðj2 ¼ 1 … *:*m2Þ ¼¼ >f g Pe ið Þ *;* j2 ?f g ½ � Petx ið Þ *;* j1*;* & Res1 i f g ½ � ð Þ *;* j3*;*

& Pe i f g ð Þ *;* j2 ?f g BPINM ið Þ *;* j5

In general, a proper and an efficient functionality of any business process depends on an adequate information support, however the question is: What the term BP information support related to BP functionality does mean? In general, any BP functionality and performance are closely related to BP external and internal metrics. However, the problems of BP external and internal metrics theory are discussed within Section 2 as well, while at that place we shall discuss aspects closely related to so called two stage BP external and internal metrics (see also **Figure 2**).

In general, the implemented and operated BP is running and generates predefined output products (articles) – denoted as the primary products based on appropriated adequate material, information and financial inputs. On the other hand, the investigated BP operates with a set of input and output information generated based on detailed data, e.g. number of good articles nArtgood – a quality of which corresponds to pre-defined requirements, number of repaired articles nArtrep - number of produced articles their quality does not correspond to pre-defined requirements and should be repaired, and number of waste articles nArtwaste - number of produced articles their quality does not correspond to pre-defined requirements – cannot be repaired and should be considered to be a waste. They are considered to be detailed data and have no level of aggregation. The same is concerned with other data closely related to BP external or internal metrics and they are being measured at

What the term two stage BP external and internal metrics does mean?

¼ ½ � Res1j2 i, j3, ð Þ ?f g ½ � Res1 i, j3, ð Þ (14)

¼ >f g ½ � Petx ið Þ *;* j1*;* & Res1 i f g ½ � ð Þ *;* j3*;* ?f g BPEXM ið Þ *;* j4

(15)

make basis for BP Function (BPF) definition.

*Operations Management - Emerging Trend in the Digital Era*

*4.2.3 BPM information support view*

**Figure 2.**

**200**

*Business process horizontal structure source: The authors.*

i. is index closely related to BP serial number with set of processes

j1- is index, which represents number subsets, the linguistic set {[Petx (i, j1)]} consists of

However, that BP external metric is represented by adequate outputs as well, while they are quantified via {[Res1 (i, j3,)]} linguistic set, which contains values concerned with **nArtgood, nArtrep,** and **nArtwaste** items.

With respect to the above-mentioned issues, the PBPL Equation actual version might be postulated.

$$\{\left[\text{Petx (i,j)}\right]\} \otimes \{\left[\text{Pe (i,j\_2, )}\right]\} = \{\left[\text{Res1 (i,j\_3, )}\right]\} \tag{16}$$

A fictive data, which create conted of {[Petx (i, j)]} and {[Res1 (i, j3,)]} will be discussed within Case study section.

Now, let us have a look at {[Pe (i, j2,)]} linguistic set, which represents the business process Pe, while that process provides transfer of material input represented by {[Petx (i, j)]} linguistic set into final products (glass articles) represented by {[Res1 (i, j3,)]} linguistic set.

However, the {[Pe (i, j2,)]} linguistic set contains subsets, which quantify BPFs, the BP quantified via {[Pe (i, j2,)]} linguistic set consist of. When selecting one BPF, we can assign to it the linguistic set {[BPF (i, jf)]}, which consists of three subsets, while formula (17) might be postulated.

$$\{\left[\text{BPF } (\text{i,jf})\right]\} = \{\left[\text{BPF } \text{TR } (\text{i,jf}\_1)\right], \left[\text{BPF } \text{TT } (\text{i,jf}\_2)\right], \left[\text{BPF } \text{TM } (\text{i,jf}\_3)\right]\} \tag{17}$$

Where

the subset = [BPF\_TR (i, jf1)] = {[BPF\_TR (i, j1)]} and the content might be quantified via formula (16).

the subset = [BPF\_TT (i, jf1)] = {[BPF\_TT1 (i, j1)]} and the content might be quantified via formula (19)

the subset = [BPF\_TM (i, jf1)] = {[BPFEM (i, j1)], [BPFIM(i, j2)]} and the content might be quantified via formulas (14) and (15).

4 Glass Article Primary Production- GAPP

5 Glass Melt - GM

6 The terms linguistic set and set are considered to be the same from semantic point of view

$$\{\left[\text{Pe}\left(\mathbf{i}, \mathbf{j}\_2, \right)\right]\}' = \text{II}\left\{\left[\text{BPF}\left(\mathbf{i}, \mathbf{j}\_\mathbf{f}\right)\right]\right\} \tag{18}$$

½ � Petx i, m2a ð Þ , ¼ ½ð Þ mat m2 ð Þ11 t k ð Þ ð Þ , mat m2 ð Þ12 t k ð Þ ð Þ ,ðmat m2 ð Þ 21 tð Þ,

*Business Process Linguistic Modeling: Theory and Practice Part II: BPLM Business Process…*

Now, let us select [Petx (i, 1)] and undertake its content to statistic evaluation7

½ �¼ Petx i, 1b ð Þ ½ðmat 1ð Þ11 mat 1 ð ð Þ12Avg, mat 1 ð � ð Þ12MMin, mat 1 ð Þ ð Þ12MMax , mat 1 ð Þ ð Þ12Vrp

m2a – index, which indicates a serial number of input record within Petx

formula (29) indicates an extension of [Petx (i, 1a)] linguistic set.

m12 – index, which indicates a serial number of item and value input record. Formula (28) indicates statistic values of items assigned to selected input, while

Now let us consider the {[Res1 (i, j3)]} and let us suppose that the **nArtgood, nArtrep nArtwaste** are time dependent, while formulas (30), (31), and (32) might be

With respect to those issues, appropriate statistic values might be calculated.

½Article\_repairst� ¼ nArtrep ¼ nArtrepawg, nArtrepmin, nArtrepmax, nArtrepVrp (34) ½Article\_wastest� ¼ nArtwasteawg, nArtwastemin, nArtwastemax, nArtwasteVrp (35)

Let us demonstrate previous relations at business process, which deals with forming of glass articles (Ga) from glass melt (Gm), which is represented by three variables: (a) glass melt temperature (Gmtep), glass melt viscosity (Gmvis), and glass melt quantity (Gmquant) and generated glass articles (Gas) represented by three items and values: (a) number of good Gas (nArtgood), number of repaired Gas (nArtrep) and number of waste Gas. The relations among statistic values of selected variables might be defined via: (a) partial rules (see also formulas (36), (37), and (38), (b) complex rule (see also formula (31) and (c) set of complex rules (see also formulas (40), (41), and (42). However, all the above-mentioned rules might be time dependent as well, while they might create pairs (time interval (T(int)), Y (int) and create linguistic subsets, which could quantify a development trend (see

f½ � Gmtemp\_awg, GmVrp g¼f nArtgoodawg, nArtgoodmin, nArtgoodmax, nArtgoodVrp , (36)

7 Statistic evaluation = determination of Avg, Min, Max and extent of variation

½Article\_goodst� ¼ nArtgoodawg, nArtgoodmin, nArtgoodmax, nArtgoodVrp (33)

while formula (28) and (29) might be postulated8

*DOI: http://dx.doi.org/10.5772/intechopen.95350*

where

linguistic set.

postulated.

also formula (43)). Partial rules

8 Vrp – extend of variation

**203**

mat m2 ð Þ 22 t k ð Þ ð Þ … *:*mat m2 ð Þ ð Þ m11 t k ð Þ ð Þ , matm2 ð Þ� m12

½ �¼ Petx i, 1ab ð Þ ½ � Petx i, 1a ð Þ , Petx i, 1b ½ � ð Þ (29)

**nArtgood**¼ **nArtgood** ð Þt (30) **nArtrep** ¼ **nArtrep** ð Þt (31) **nArtwaste** ¼ **nArtwaste** ð Þt (32)

(27)

(28)

,

i = 1,2 … .n

jf = 1, 2 … .m1 - number of BPFs, the Pe business process, consists of.

Finally, we shall specify the {[Res1 (i, j3)]}, the content of which is closely related to number of good articles **nArtgood,** number of repaired articles **nArtrep,** and number of waste articles **nArtwaste,** while formulas (25) and (26) and (28) and (29) might be postulated.

$$\{\{\left[\text{Res1}\left(\mathbf{i}, \mathbf{j}\_3\right)\right]\}\} = \{\left[\text{Pop}\left(\mathbf{i}, \mathbf{j}\_3\right)\right], \left[\text{Particle\\_good}\right], \left[\text{Particle\\_repair}\right], \left[\text{Particle\\_waste}\right]\}\tag{19}$$

$$\mathbf{n}\_{\text{Artgood}} \in [\text{Article\\_good}],\tag{20}$$

$$\mathbf{n}\_{\text{Artrep}} \in [\text{Article\\_repair}],\tag{21}$$

$$\mathbf{n}\_{\text{Artwaste}, \mathbf{e}} \in [\text{Article\\_waste}]\}\tag{22}$$

[Pop (i, j3)] subset contains elements closely related to article type, article class, article name, article, measure unit.

When applying the PBPL Equation in a basic form (see also formula (16), formula (23) might be postulated

$$\{ [\text{Petx} \ (\mathbf{i}, \mathbf{1})], [\text{Petx} \ (\mathbf{i}, \mathbf{2})] \dots \dots [\text{Petx} \ (\mathbf{i}, \mathbf{m}\_1)] \} \otimes \Pi \left\{ [\text{BPF} \ (\mathbf{i}, \mathbf{j}\_\mathbf{f})] \right\} = \mathbf{i} = \mathbf{1}, 2 \dots \mathbf{n}; \mathbf{j}\_\mathbf{f} = \mathbf{1}, 2 \dots \mathbf{n}; \mathbf{m}\_\mathbf{f} = \mathbf{1}, 2 \dots \mathbf{n} \ \mathbf{m} = \mathbf{1}, \mathbf{2} \dots \mathbf{n} \ \mathbf{m} = \mathbf{1} \tag{23}$$

It should be noted that those linguistic set content is time depended and formula (24) might be postulated.

$$\begin{aligned} \{ [\text{Petx} \ (\text{i}, \text{1}, \text{t})], [\text{Petx} \ (\text{i}, \text{2}, \text{t})] \dots \dots [\text{Petx} \ (\text{i}, \text{m}\_1, \text{t})] \} \otimes \Pi \ \{ [\text{BPF} \ (\text{i}, \text{j}\_{\text{f}}, \text{t})] = \\ \text{i} &= 1, 2 \dots \text{n}; \\ \text{j}\_{\text{f}} &= 1, 2 \dots \text{m} \text{1} - \\ = \{ [\text{Pop} \ (\text{i}, \text{j}\_{\text{j}})], [\text{Artice\\_good} \ (\text{t})], [\text{Artice\\_repair} \ (\text{t})], [\text{Artice\\_waste} \ (\text{t})] \} \end{aligned} (24)$$

Formula (24) quantifies relation among BP input and output parameters and the actual content of the above-mentioned linguistic set will be discussed within Case study section.

#### *4.2.4 BPM knowledge support view consideration no. 4*

The knowledge related to BPM knowledge support view are derived based on appropriate item statistic values mentioned within previous section.

Let us consider the {[Petx (i, j)]}, which contains subsets [Petx (i, 1)], [Petx (i, 2)] … …  DOI: http://dx.doi.org/10.5772/intechopen.95350*

$$\begin{aligned} \left[ \text{Petx } (\text{i}, \text{m2a}) \right], &= \left[ \left( \text{mat } (\text{m2}) \text{11 } (\text{t} \text{ k}) \right), \text{mat } (\text{m2}) \text{12 } (\text{t} \text{k}) \right), (\text{mat } (\text{m2}) \text{ 21} (\text{t}), \\ &\quad \left[ \text{mat } (\text{m2}) \text{ 22} (\text{t} \text{k}) \right) \dots \text{mat } (\text{m2}) \left( \text{m1} \ (\text{t} \text{k}) \right), \text{mat } \text{m2} \right) (\text{m12}) \end{aligned} \tag{27}$$

Now, let us select [Petx (i, 1)] and undertake its content to statistic evaluation7 , while formula (28) and (29) might be postulated8

½ �¼ Petx i, 1b ð Þ ½ðmat 1ð Þ11 mat 1 ð ð Þ12Avg, mat 1 ð � ð Þ12MMin, mat 1 ð Þ ð Þ12MMax , mat 1 ð Þ ð Þ12Vrp (28)

$$[\text{Petx}\ (\text{i}, \textsf{1ab})] = [\textsf{Petx}\ (\text{i}, \textsf{1a})],\\[\textsf{Petx}\ (\text{i}, \textsf{1b})] \tag{29}$$

where

Pe i, j2, ´ ¼ Π BPF i, jf

, Article\_good ½ �, Article\_repair ½ �, Article\_waste ½ �

[Pop (i, j3)] subset contains elements closely related to article type, article class,

It should be noted that those linguistic set content is time depended and formula

Formula (24) quantifies relation among BP input and output parameters and the actual content of the above-mentioned linguistic set will be discussed within Case

The knowledge related to BPM knowledge support view are derived based on

… … [Petx (i, m1)], while any of those subsets contains time depended items and

½ � Petx i, 1a ð Þ , ¼ ½ðmat 1ð Þ11 t k ð Þ ð Þ ð Þ , mat 1ð Þ12 t k ð Þ ð Þ ,ðmat 1ð Þ 21 t k ð Þ ð Þ ,

½ � Petx i, 2a ð Þ , ¼ ½ðmat 2ð Þ11 t k ð Þ ð Þ , mat 2ð Þ12 t k ð Þ ð Þ ,ðmat 2ð Þ 21 t k ð Þ ð Þ ,

Let us consider the {[Petx (i, j)]}, which contains subsets [Petx (i, 1)], [Petx (i, 2)]

mat 1ð Þ 22 tð Þ … *:* mat 1ð Þðm11 t k ð Þ ð Þ , mat 1ð Þ ð Þ k ð Þ� m12 (25)

mat 2ð Þ 22 tð Þ … *:*mat 2ð Þ ð � m11 t k ð Þ ð Þ , mat 2ð Þ ð Þ m12 (26)

appropriate item statistic values mentioned within previous section.

f g ½ � Petx ið Þ *;* 1*;*t *;* ½ � Petx ið Þ *;* 2*;*t … … ½ � Petx ið Þ *;* m1*;*t ⊗ Π f½BPF ði, jf, t�g ¼

*;* ½ � Article\_good tð Þ *;* ½ � Article\_repair tð Þ *;* ½ � Article\_waste tð Þ

When applying the PBPL Equation in a basic form (see also formula (16),

f g ½ � Petx i, 1 ð Þ , Petx i, 2 ½ � ð Þ … … ½ � Petx i, m ð Þ1 ⊗ Π BPF i, jf

*4.2.4 BPM knowledge support view consideration no. 4*

values concerned to actual material input.

**nArtgood ∈** ½ � Article\_good , (20)

**nArtrep ∈** ½ � Article\_repair , (21)

**nArtwaste**, **∈** ½Article\_waste�g (22)

, Article\_good ½ �, Article\_repair ½ �, Article\_waste ½ �

¼ i ¼ 1, 2 … *:*n; jf

i ¼ 1, 2 … *:*n;

f ¼ 1, 2 … *:*m1�

j

jf = 1, 2 … .m1 - number of BPFs, the Pe business process, consists of. Finally, we shall specify the {[Res1 (i, j3)]}, the content of which is closely related to number of good articles **nArtgood,** number of repaired articles **nArtrep,** and number of waste articles **nArtwaste,** while formulas (25) and (26) and (28) and (29)

*Operations Management - Emerging Trend in the Digital Era*

i = 1,2 … .n

might be postulated.

¼ Pop i, j3

article name, article, measure unit.

formula (23) might be postulated

¼ 1, 2 … *:*m1� ¼ Pop i, j3

(24) might be postulated.

3

¼ Pop i*;* j

study section.

**202**

Res1 i, j3

(18)

(19)

(23)

(24)

m2a – index, which indicates a serial number of input record within Petx linguistic set.

m12 – index, which indicates a serial number of item and value input record. Formula (28) indicates statistic values of items assigned to selected input, while

formula (29) indicates an extension of [Petx (i, 1a)] linguistic set.

Now let us consider the {[Res1 (i, j3)]} and let us suppose that the **nArtgood, nArtrep nArtwaste** are time dependent, while formulas (30), (31), and (32) might be postulated.

$$\mathbf{n}\_{\text{Artgood}=} \mathbf{n}\_{\text{Artgood}}\,\left(\mathbf{t}\right)\tag{30}$$

$$\mathbf{n}\_{\mathbf{Artrep}} = \mathbf{n}\_{\mathbf{Artrep}} \begin{pmatrix} \mathbf{t} \end{pmatrix} \tag{31}$$

$$\mathbf{n}\_{\text{Artwaste}} = \mathbf{n}\_{\text{Artwaste}}\left(\mathbf{t}\right) \tag{32}$$

With respect to those issues, appropriate statistic values might be calculated.

$$\left[ \text{Article\\_goodst} \right] = \left[ \mathbf{n}\_{\text{Artgoodrwg}}, \mathbf{n}\_{\text{Artgoodmin}}, \mathbf{n}\_{\text{Artgoodmax}}, \mathbf{n}\_{\text{Artgood}\text{VPp}} \right] \tag{33}$$

$$\begin{bmatrix} \text{Particle\\_repaist} \end{bmatrix} = \begin{bmatrix} \mathbf{n}\_{\text{Artrep}} = & \mathbf{n}\_{\text{Artrep}\text{wg}}, \mathbf{n}\_{\text{Artrep}\text{min}}, \mathbf{n}\_{\text{Attrep}\text{max}}, \mathbf{n}\_{\text{Attrep}\text{Vrp}} \end{bmatrix} \tag{34}$$

$$\left[ \text{Articles\\_waste} \right] = \left[ \mathbf{n}\_{\text{Artwastezwg}}, \mathbf{n}\_{\text{Artwastezin}}, \mathbf{n}\_{\text{Artwastezwx}}, \mathbf{n}\_{\text{ArtwasteVrp}} \right] \tag{35}$$

Let us demonstrate previous relations at business process, which deals with forming of glass articles (Ga) from glass melt (Gm), which is represented by three variables: (a) glass melt temperature (Gmtep), glass melt viscosity (Gmvis), and glass melt quantity (Gmquant) and generated glass articles (Gas) represented by three items and values: (a) number of good Gas (nArtgood), number of repaired Gas (nArtrep) and number of waste Gas. The relations among statistic values of selected variables might be defined via: (a) partial rules (see also formulas (36), (37), and (38), (b) complex rule (see also formula (31) and (c) set of complex rules (see also formulas (40), (41), and (42). However, all the above-mentioned rules might be time dependent as well, while they might create pairs (time interval (T(int)), Y (int) and create linguistic subsets, which could quantify a development trend (see also formula (43)).

 On the other hand, any BPF might be quantified via multi-layer linguistic set, while at the first layer three significant

*Business Process Linguistic Modeling: Theory and Practice Part II: BPLM Business Process…*

• {[BPF\_TR (i, j1)]} – a content of which create rules, which regulate a progress

• {[BPF\_TT (i, j2)]} – a content of which create transformation functions, which

related to transformation of BPF inputs into pre-defined outputs

provide transformation of BPF inputs into pre-defined outputs

deals with BPF internal metrics with respect to formula (15)

Let us consider the {[Petx (i, j1)]}, which contains a finite number of elements denoted as pt.(i, 1), pt.(i, 2), … pt.(i, m1), while each of them is created by the element average and element extend of variations value (see also

tion of BPF inputs to predefined BPF outputs as well.

pt.(i, j1), = ((pt(i, j1)avg., (pt(i, j1)vrp)

pt.(i, jm1), = ((pt(i, jm1)avg., (pt(i, jm1)vrp)

with assignment of words to ratio value intervals (**Table 4**).

f g Rs ¼ 125n1811,1,5,1n4, 10n52,2,

*4.3.2 BPF inputs versus BPF outputs*

• {[BPM (i, j3)]} – a content of which create subsets closely related to BPF6external and internal metrics, while BPF external metrics linguistic

• [BPFEM (i, j1)]} deals with BPF external metrics and consists of [BPINP (i, j11)] subset the content of which is created by elements closely related to BPF inputs and [[BPOUTP (i, j12), the content of which is created by elements closely related to BPF outputs (see also formula (14) and the {[BPFIM (i, j2)]}

However, both the above-mentioned linguistic sets are very closed to {[BPF\_TT1 (i, j1)]} the content of which is created by elements closely related to transforma-

Let us consider a statistic file represented by **Table 1** and set of statistic indica-

270n1081,1, 60n49,9 ¼ f g 0, 069, 0, 784, 0, 191, 0, 249, 1202

Now, let us create a ratio set {Rs} and reference table (**Table 3**), which deals

pt*:*ð Þ i, j2 , ¼ ððpt i, j2 ð Þavg*:*, pt i, j2 ð Þ ð Þvrp (44)

*4.3.1 General overview*

set and

formula (44).

**4.4 Case study**

**205**

tors represented by **Table 2**.

Y m3 ð Þ ¼ f½ � Gmtemp\_awg ð Þ m3 *;* GmVrp ð Þ m3 *;* f½ � Gmtvis\_awg m3 ð Þ*;* GmVrp ð Þ m3 *;* ½Gmtvis\_awg ð Þ m3 *;* GmVrp �g ¼ f½nArtgoodawgð Þ m3 *;* nArtgoodmin*;* ð Þ m3 *;* nArtgoodmax*;* ð Þ m3 *;* nArtgoodVrpð Þ m3 *; ;*� ½ nArtrepawg*;* ð Þ m3 *;* nArtrepmin*;* nArtrepmax*;* ð Þ m3 *;* nArtrepVrpð Þ m3 *;* �*;* nArtwasteawgð Þ m3 *;* nArtwasteminð Þ m3 *;* nArtwastemaxð Þ2 *; ;* nArtwasteVrpð Þ m3 h ig

(42)

$$\{ [(\text{DevlTrend}] ]\} = \ [ (\text{T}(\mathbf{1}), \text{Y } (\mathbf{1}) ), [(\text{T}(2), \text{Y } (2)], \dots [(\text{T}(\mathbf{m3}), \text{Y } (\mathbf{m3}))] \} \tag{43}$$

In general, the knowledge stored with ES knowledge base are represented by semantic networks (SNWs), while partial rules might be compared **with partial SNW**s, complex rules might be compared with **ordinary SNWs** and development trends (DevlTrend) might be compared with **superior SNWs**. This approach will be discussed within Case study in more details and applied when designing and implemented an appropriate knowledge-based or expert system as well.

*Business Process Linguistic Modeling: Theory and Practice Part II: BPLM Business Process… DOI: http://dx.doi.org/10.5772/intechopen.95350*


**4. Flood as a destroyer**

In view of the context of the here and now benefits of floods, the negative impact of floods on education, despite being real, tend to be masked and yet have

**153**

in Zimbabwe.

acknowledged.

*Flooding and Its Impact on Education*

*DOI: http://dx.doi.org/10.5772/intechopen.94368*

a terrible impact on the same. A survey by the Asian Disaster Preparedness Center in 2002, in Cambodia speaks to this observation. The survey in question sought to identify the impacts of disasters on the education sector and the findings revealed that floods were one of the factors disrupting study program accomplishment and thus affecting the quality of current education, particularly in provinces which are prone to floods and where schools were constructed without proper flood resilience [13]. In the context of Zimbabwe, soon after gaining political independence in 1980, the introduced reforms in the education system that focused on the principle of 'Education for all' were adopted. Education for all principle embraced the practical principle of increasing the number of schools by building schools in marginalised areas and disadvantaged urban centres [14]. Incidentally some of the marginalised areas were in flood prone areas. As [14] further argues, the government involved local communities to help support schools through providing labour for moulding bricks and other resources. The emphasis was not so much on quality and cost effectiveness of the education system, but on accessibility to education. The Fast land reform programme in Zimbabwe did not help the situation either. People settled themselves under the disguise of black empowerment through access to land and they settled where ever they felt like. Some communities settled in flood prone areas. Owing to the population expansion in those places illegally occupied, the government had no option but to follow up with the construction of schools, commonly known as satellite schools. By allowing people to settle in such fragile spaces, in one way or the other, it helped to easy political tension that had started building in the country due to socio-economic hardships. However, like in the post-independence era quality of infrastructure in the context of resilience to shocks such as floods is not a priority. When floods eventually strike, because they impact communities in different degrees depending on the vulnerability of that community, the impact on education is least to be

The extent floods affect livelihoods and human life is well documented in literature. In fact, quantifying such loss has been the responders' priority. While that is the case, literature has it that one's political, social and economic status plays a significant role when it comes to exposure to risk of flooding. Poorest communities are the most vulnerable as they live in the most threatened locations [15] they lack the means to live in less vulnerable communities [16]. This construction of flooding implies that one's exposure to flooding is a social construction, thus in a way implying that if it is socially constructed, then flood fits well in the discussion of it as being man-made. Cann *et al.,* [17] are quick to remind us that floods affect the quality of drinking water thereby bringing with them water related infectious diseases such as cholera and hepatitis which will be compounded by damaged or overwhelmed sanitation system. Flood as destroyer has also been noted by other authors such as [18] who argue that it destroy agriculture, transport infrastructure, communication infrastructure, service buildings, and social facilities. Such loss compounds the deterioration of the social and economic lives of people as well as harming the national economy. While literature envisage an increase in flood threats due to various reasons and creations both natural and man-made [19], the extent to which it affects education systems globally has not received favourable attention. More often, after a floods we hear and read about the level of the impact on the socio-economic well-being of children if not mainly on economic related benefits of floods; As [13] have observed, the impacts on children's access and right to quality education have received little attention This has resulted in a lack of studies on the effects of floods on school children and infrastructure in most countries including


**Appendix C**

The sampled datasets of the vibration data updated on the server-side CMS were rendered for 3.0-blade (full blades), 2.5-blade and 2.0-blade wind turbine settings.

**Figure A1.** *Cont*.

**Figure A1.** *Cont*.

**Figure A1.** *Cont*.

**Figure A1.** Acceleration signals recorded for the full (normal) 3.0-blade turbine. (**a**) Data recorded along the X axis with different wind-speeds imposed. (**b**) Data recorded along the Y axis with different wind-speeds imposed. (**c**) Data recorded along the Z axis with different wind-speeds imposed.

**Figure A2.** *Cont*.

**Figure A2.** *Cont*.

**Figure A2.** Acceleration signals recorded for the 2.5-blade (partially broken) turbine. (**a**) Data recorded along the X axis with different wind-speeds imposed. (**b**) Data recorded along the Y axis with different wind-speeds imposed. (**c**) Data recorded along the Z axis with different wind-speeds imposed.

**Figure A3.** *Cont*.

**Figure A3.** *Cont*.

**Figure A3.** Acceleration signals recorded for the 2.0-blade (one blade missing) turbine. (**a**) Data recorded along the X axis with different wind-speeds imposed. (**b**) Data recorded along the Y axis with different wind-speeds imposed. (**c**) Data recorded along the Z axis with different windspeeds imposed.


*3.2. Design and Analysis of Finger End*

The stability of fruit grasping is one of the key techniques for fast and undamaged fruit picking. Additionally, the finger end is the only part in contact with the fruit. It is a crucial factor in achieving a stable grasp.


**4. Mitigation**

There are differences in Global Warming Potential (GWP) and lifetime of greenhouse gases in the atmosphere. One GWP has been assigned to CO2 and the warming potential of other gases are based and expressed relative to CO2 GWP [23]. For instance, 1 tonne of CH4 has a warming effect of about 25 and 72 tons of CO2 over 100- and 20 year periods respectively according to IPCC. Studies have shown that CH4 is more potent than CO2, so reducing CH4 emission will show more immediate and significant impact on mitigating changes in climate than reducing CO2 emissions [24] Another potent greenhouse gas is N2O for it remains in the atmosphere for 114 years [25, 26]) and 298 times as potent as CO2 over 100 years [27] (see **Table 1** below).

Increased Industrial agriculture is proposed to be a solution to the problems of climate change which is a contributor without its impact being addressed. In the

**155**

*Impact of Emerging Agricultural Contaminants on Global Warming*

climate change mitigation and partly for carbon trading [17].

negotiation for a new climate treaty that has been negotiated to follow the Kyoto protocol in 2012, agricultural practices have been proposed to be a means for

Livestock farming in Agriculture is one of the largest sources of water contaminant and this contamination maybe the easiest route of emerging agricultural contamination in getting to humans and the eco-system. Animal dung production helps in releasing massive amount of Methane into the environment hence posing challenging situations as intensive farming serves in meeting global food challenges. Also, Algae and Fungi bloom intensifies methane release into the environment, thus having adverse effects on Green-house gases. To mitigate emerging contaminants

1.Development of good environmental policies to mitigate unwarranted release of emerging contaminants such as standards for water policy, improved testing on pollution and emission, assessments on environmental impact of farms and

2.Enhancing the intake of digestible forage will mitigate GHG emissions from rumen fermentation and stored manure (For example, to reduce enteric methane emission replace corn silage with grass silage in diet, apply dietary lipids, use legume over grass as it contains more fiber in addition to replacing

3.Release of pollutants at the source of production should be reduced because

4.Reduction of the application of fertilizers and pesticides and introduction of

5.Restoration of degraded pastureland by utilization of traditional approaches or

6.Methanotrophs otherwise known as the methane-eating bacteria found in the ecosystem where methane is produced ensures the conversion of methane into substances such as sugars before being released into the atmosphere. In this way, the methanotrophs help in recycling methane all over the globe.

7.Biochemical method of mitigation of Greenhouse gases: This is the employment of feed supplements that have the potential of reducing methane emission. The bulk of complex molecules contained in ruminant feeds are broken down during fermentation by microbes releasing energy and other chemical compounds [7]. Plant Natural Products (PNP) are engaged to aid in the challenges observed in livestock production where there is wastage of nutrient caused by excess excretion and poor or inefficient digestibility of feeds, emission of CO2 and CH4 that results to 2–12% loss of feed energy [29]. These PNPs include Saponins, terpenoids, tannins, flavonoids, phenols, glycosides, alkaloids and essential oils These challenges brought the attention of Biochemists, Nutritionists and Microbiologists to look into the PNP application [30], yeasts [31] and enzymes as additives to feed. This incorporation as additives is meant to modify fermentation kinetics in ruminants and manipulate microbial ecosystems. The primary purpose of these modifications is to improve the utilization of animal feed and digestibility of fibrous feeds, decrease degradability of protein [32], inhibit the proliferation of pathogenic bacteria in the gastrointestinal tract [33] enhance

*DOI: http://dx.doi.org/10.5772/intechopen.94170*

the following can be employed:

irrigation systems.

inorganic fertilizer) [28].

techniques.

of its easy entrance to vulnerable environment.

natural pest-control methods should be encouraged.

**Table 1.**

*Global Warming Potential (GWP) and lifetime of greenhouse gases in the atmosphere.*

#### *Impact of Emerging Agricultural Contaminants on Global Warming DOI: http://dx.doi.org/10.5772/intechopen.94170*

*Emerging Contaminants*

N2O, CO2 and NH3 emissions.

duration [22].

**4. Mitigation**

[27] (see **Table 1** below).

According to Food and Agriculture Organization (FAO), Livestock production sector as the major emitter of all the greenhouse gases is responsible for about 18% on one fifth of human-induced greenhouse gas emissions [18]. For instance, in almost every step of egg, meat and milk production in agriculture, greenhouse gases that cause climate change are released into the atmosphere disturbing temperature, weather and health of ecosystem. Mitigating these problems will require changes in

Livestock Production as one of the Agricultural food-based industries has been described as leading or major contributor of the anthropogenic source of CH4 and CO2 greenhouse gases [19]. They contribute immensely to global warming, pollution and environmental degradation because of the large amount of greenhouse gases produced during the ruminal fermentation of feeds. For instance, anytime a cow burps or passes out gas, it puffs out a little methane which wafts into the atmosphere. Each of these puffs from the cow put together can result to a big effect on climate because methane as a potent greenhouse gas is about 25 times more powerful in trapping heat and increasing earth's global warming than Carbon dioxide on equal mass basis. The livestock sector therefore accounts for about 18% of CH4 and 9% of CO2 of all the greenhouse gases emissions [20] hence methane accounts for 50–60% of emitted gases during livestock production [21]. A lot of proposals have been focused on soil and plant production for the reduction of emission from agriculture leaving livestock production which accounts for major amounts of CH4,

Several gases cause chemical reactions that can result in producing other greenhouse gases among other effects and some trap heat energy better than others. Considering the lifetime of greenhouse gases, some persist in the atmosphere for different durations of time and some contribute to global warming due to their long

There are differences in Global Warming Potential (GWP) and lifetime of greenhouse gases in the atmosphere. One GWP has been assigned to CO2 and the warming potential of other gases are based and expressed relative to CO2 GWP [23]. For instance, 1 tonne of CH4 has a warming effect of about 25 and 72 tons of CO2 over 100- and 20 year periods respectively according to IPCC. Studies have shown that CH4 is more potent than CO2, so reducing CH4 emission will show more immediate and significant impact on mitigating changes in climate than reducing CO2 emissions [24] Another potent greenhouse gas is N2O for it remains in the atmosphere for 114 years [25, 26]) and 298 times as potent as CO2 over 100 years

Increased Industrial agriculture is proposed to be a solution to the problems of climate change which is a contributor without its impact being addressed. In the

**GHG Atmospheric lifetime GWP GWP (100 years)**

CO2 Centuries to Millenia 1 1 CH4 About 10 years 72 25 N2O 114 years 289 298

*Global Warming Potential (GWP) and lifetime of greenhouse gases in the atmosphere.*

agricultural practices and livestock consumption.

**154**

*Source: [27].*

**Table 1.**

negotiation for a new climate treaty that has been negotiated to follow the Kyoto protocol in 2012, agricultural practices have been proposed to be a means for climate change mitigation and partly for carbon trading [17].

Livestock farming in Agriculture is one of the largest sources of water contaminant and this contamination maybe the easiest route of emerging agricultural contamination in getting to humans and the eco-system. Animal dung production helps in releasing massive amount of Methane into the environment hence posing challenging situations as intensive farming serves in meeting global food challenges. Also, Algae and Fungi bloom intensifies methane release into the environment, thus having adverse effects on Green-house gases. To mitigate emerging contaminants the following can be employed:

performance of animals, reduce loss of dietary energy during fermentation in rumen and mitigate CH4 and CO2 productions. PNPs have been found to be natural and safer feed additives as they demonstrate vital role in mitigating methane and carbon dioxide productions without affecting fermentation in rumen during their production [6].


**9. Drugs inhibiting hemozoin formation and thereby inducing oxidative stress**

Besides the attacks of the immune systems of the respective host, where ROS are deployed to kill invading pathogens, the parasite faces another even bigger challenge: *Plasmodium* relies al‐ so on the digestion of human haemoglobin to obtain amino acids for its metabolism (Sherman, 1977). Haemoglobin is the major protein inside the erythrocyte and the parasite has evolved a unique pathway to utilise this molecule (Muller et al., 2011). Heme is the degradation product of haemoglobin, which has to be detoxified and stored as hemozoin within the food vacuole of the parasite – the place where the haemoglobin degradation occurs. Non-detoxified heme is extremely toxic (Papalexis et al., 2001) and leads not only to the generation of H2O2, ‧ OH and O2-. (Francis et al., 1997), but also to the highly reactive, non-radical molecule, singlet oxygen (1 O2) (Freinbicherler et al., 2011). Moreover, one 1 O2 molecule can be either synthesised by the reac‐ tion of ‧ OH and O2-. or two O2-. with two hydrogen ions (Khan and Kasha, 1994). In order to de‐ toxify these ROS, *Plasmodium* has developed – as outlined above - multiple antioxidant defence systems. However - excluding the membrane located lipophilic tocopherol (vitamin E) (Wang and Quinn, 1999) - none of the above mentioned defense systems are capable to detoxify 1 O2. The fact that vitamin B6 is linked to the defense against 1 O2 in plants and fungi (Tambasco-Stu‐ dart et al., 2005; Ehrenshaft et al., 1999), suggests that the vitamin B6 biosynthesis might also play a yet unrecognized role in combating 1 O2 in the malaria parasite *P. falciparum*. Very recent‐ ly this role of 1 O2 detoxification has been verified in the malaria parasite (Wrenger et al., 2005; Knöckel et al., 2012; Butzloff et al., 2012). Figure 1:

figure 2) are highly potent antimalarials that inhibit hemozoin formation at EC50-values in the low nano-molar range (Egan et al., 2000; Kotecka et al., 1997; O'Neill et al., 2003; Vennerstrom et al., 1992). Azole derivatives are also inhibitors of the hemozoin forma‐ tion and reveal efficacy against chloroquine sensitive as well as resistant plasmodial strains (Banerjee et al., 2009; Rodrigues et al., 2011). Another novel class, which has been identified to interact with heme and thereby prevent the hemozoin formation, are xan‐ thones (Docampo et al., 1990; Ignatushchenko et al., 1997; Xu Kelly et al., 2001). More‐ over, a variety of isonitrile derivatives gain their antimalarial activity from inhibition of the hemozoin synthesis (Kumar et al., 2007; Wright et al., 2001) resulting in EC50-values in the low nano-molar range (Badyopadhyay et al., 2001; Singh et al., 2002; Kumar et al., 2007). Benzylmenadione derivatives do not show any cytotoxicity against two human cell lines while they are effective against the chloroquine resistant *P. falciparum* strain Dd2 (Muller et al., 2011). The precise mode of action of benzylmenadione remains for elucidation, but it has been suggested that the molecule is initially oxidized to a naph‐ thoquinone derivative within the food vacuole of the parasite which leads subsequently

Oxidative Stress in Human Infectious Diseases – Present and Current Knowledge About Its Druggability

http://dx.doi.org/10.5772/53758

235

to the inhibition of the hemozoin formation (Davioud-Charvet et al., 2003).

Helminths are parasitic worms that encompass nematodes (roundworms), cestodes and trematodes (flatworms) and affect humans in all areas of the world, with more than onethird of humans harbouring these parasites that cause chronic, debilitating morbidity. Fur‐ thermore, co-endemicity and polyparasitism increase the burden of millions (Hotez et al., 2008). In the absence of vaccines, control relies on pharmacotherapy and pharmacoprophy‐ laxis to easy symptoms and reduce transmission. Helminthosis are treated with a limited number of anthelmintics by chemotherapy of symptomatic individuals or, more general, by control programmes that rely on mass drug administration (MDA) and require annual or bi‐ annual treatment of at-risk populations over prolonged period of time (Prichard et al., 2012). A major problem, however, is the development of resistance or tolerance by the parasites to these common antiparasitic drugs (Vercruysse et al., 2011). It is therefore essential to under‐ stand the underlying mechanisms of drug resistance and find new drugs to circumvent it.

Praziquantel has been used for over 20 years to treat a variety of human trematode infec‐ tions. Its precise mechanism of action has not been fully elucidated, however, there is exper‐ imental evidence that praziquantel acts by increasing the permeability of cell membranes towards calcium ions and/or by interfering with adenosine uptake (Jeziorski and Greenberg, 2006; Angelucci et al., 2007). Furthermore, it has been suggested that praziquantel reduces GSH concentrations, making the parasite more susceptible to the host immune response (Ribeiro et al., 1998). Interestingly, exposure to sub-lethal concentrations of praziquantel shows that schistosomes undergo a transcriptomic response similar to that observed during

**10. Druggability of oxidative stress systems in helminths**

oxidative stress (Aragon et al., 2009).


**Abstract**

MVD has evolved from an era where it was mandatory to treat all lesions, even very thin vessels. With the advent of more realistic anatomical scores such as the ERACI score and the gradient measurements with the fractional flow of reserve (FFR) and instantaneous wave-free ratio (iwFR), a more conservative era has begun, which benefits the patient in the long-term follow-up. The treatment of the LMCA remains a challenging lesion because of the amount of irrigation. It can be divided the treatment of the LMCA with a low or high ERACI score, in the first group is where the PCI has gained in confidence and dedication in addition to knowledge and bifurcation techniques. The second group with high score can only be performed in centers with high PCI experience, since their alternative will always be surgical as the first choice. The revascularization in MVD with STEMI, the priority is the culprit vessel and then evaluate the underlying lesions, an invasive or with a functional test in the short term. The patient with DM is a singular patient, and its treatment should always be evaluated by a multidisciplinary team. We believe that patients with low ERACI score have the possibility of being treated with PCI, but patients with high score are surgical.

**Keywords:** MVD, PCI, CABG, DM, MI, LMCA, MACCE, BMS, DES


**5. Acknowledgment**

The authors would like to thank DONET members, Takane Hori and Ryoko Nakata for giving beneficial comments. The authors also would like to thank Tohoku University researchers, Toru Matsuzawa, Ryota Hino and Akira Hasegawa for stimulating our study. J.-P. Ampuero helped us to improve our manuscript with thoughtful discussion. We appreciate publishing managers Igor Babic and Ivana Lorkovic for encouraging our publication, which was partly supported by Grant-in-Aid for Young Scientists (KAKENHI) 23710212.


**5.2 Convergence of the distributions of random sums of random vectors with finite covariance matrices to multivariate elliptically contoured Linnik distributions**

In 1953, Yu. V. Linnik [20] introduced the class of univariate symmetric probability distributions defined by the characteristic functions

$$f\_a^L(t) = \frac{1}{1+|t|^a}, \quad t \in \mathbb{R},$$

where *α* ∈ð � 0, 2 . Later, the distributions of this class were called *Linnik distributions* [21] or *α-Laplace distributions* [22]. Here the first term will be used since it has become conventional. With *α* ¼ 2, the Linnik distribution turns into the Laplace distribution corresponding to the density

$$f^{\Lambda}(\mathbf{x}) = \frac{1}{2}e^{-|\mathbf{x}|}, \qquad \mathbf{x} \in \mathbb{R}.$$

A random variable with the Linnik distribution with parameter *α* will be denoted *L*1,*α*.

The Linnik distributions possess many interesting analytic properties (see, e.g., [17, 18] and the references therein) but, perhaps, most often Linnik distributions are recalled as examples of geometric stable distributions often used as heavy-tailed models of some statistical regularities in financial data [23, 24].

The multivariate Linnik distribution was introduced by D. N. Anderson in [25] where it was proved that the function

$$f\_{a,\Sigma}^{(L)}(\mathbf{t}) = \frac{1}{\mathbf{1} + \left(\mathbf{t}^\top \Sigma \mathbf{t}\right)^{a/2}}, \quad \mathbf{t} \in \mathbb{R}^r, \quad a \in (0, 2), \tag{19}$$

is the characteristic function of an *r*-variate probability distribution, where Σ is a positive definite ð Þ *r* � *r* -matrix. In [25], the distribution corresponding to the

*From Asymptotic Normality to Heavy-Tailedness via Limit Theorems for Random Sums… DOI: http://dx.doi.org/10.5772/intechopen.89659*

characteristic function (19) was called *the r-variate Linnik distribution*. For the properties of the multivariate Linnik distributions, see [25, 26].

The *r*-variate Linnik distribution can also be defined in another way. For this purpose, recall that the distribution of a nonnegative random variable *Mδ* whose Laplace transform is

$$\psi\_{\delta}(\mathfrak{s}) \equiv \mathrm{E}e^{-s\mathcal{M}\_{\delta}} = \frac{\mathbf{1}}{\mathbf{1} + \mathfrak{s}^{\delta}}, \qquad \mathfrak{s} \ge \mathbf{0}, \tag{20}$$

where 0 <*δ*≤1, is called *the Mittag-Leffler distribution*. It is another example of heavy-tailed geometrically stable distributions; for more details see for example, [17, 18] and the references therein. The Mittag-Leffler distributions are of serious theoretical interest in the problems related to thinned (or rarefied) homogeneous flows of events such as renewal processes or anomalous diffusion or relaxation phenomena, see [27, 28] and the references therein. In [18], it was demonstrated that

$$L\_{1,a} \stackrel{d}{=} \mathbf{Y}\_1 \cdot \sqrt{2\mathbf{M}\_{a/2}},\tag{21}$$

where *Y*1 is a random variable with the standard univariate normal distribution independent of the random variable *Mα=*2 with the Mittag-Leffler distribution with parameter *α=*2.

Now let *Y* be a random vector such that Lð Þ¼ *Y* ΦΣ, where Σ is a positive definite ð Þ *r* � *r* -matrix, independent of the random variable *Mα=*2. By analogy with (21), introduce the random vector *Lr*,*α*,Σ as

$$L\_{r,a,\Sigma} = \sqrt{2\mathbf{M}\_{a/2}} \cdot Y.$$

Then, in accordance with what has been said in Section 2,

$$\mathcal{L}(L\_{r,a,\Sigma}) = E\Phi\_{2\mathcal{M}\_{a/2}\Sigma}.\tag{22}$$

The distribution (14) will be called *the* ð *centered*Þ *elliptically contoured multivariate Linnik distribution*.

Using Remark 1, we can easily make sure that the two definitions of the multivariate Linnik distribution coincide. Indeed, with the account of (20), according to Remark 1, the characteristic function of the random vector *Lr*,*α*,Σ defined by (22) has the form

$$\mathbb{E}\exp\left\{i\mathbf{t}^{\top}L\_{r,a,\Sigma}\right\}=\boldsymbol{\mathcal{V}}\_{a/2}\left(\mathbf{t}^{\top}\boldsymbol{\Sigma}\mathbf{t}\right)=\frac{\mathbf{1}}{\mathbf{1}+\left(\mathbf{t}^{\top}\boldsymbol{\Sigma}\mathbf{t}\right)^{a/2}}=\boldsymbol{f}\_{a,\Sigma}^{(L)}(\mathbf{t}),\ \mathbf{t}\in\mathbb{R}^{r},\ \mathbf{t}$$

that coincides with Anderson's definition (19).

Our definition (22) together with Theorem 2 opens the way to formulate a theorem stating that the multivariate Linnik distribution can not only be limiting for geometric random sums of independent identically distributed random vectors with infinite second moments [29], but it can also be limiting for random sums of independent random vectors with finite covariance matrices.

Theorem 5. *Let Nn* ! ∞ *in probability as n* ! ∞*. Assume that the random variables X*1, *X*2, … *satisfy condition* ð Þ7 *with an asymptotic covariance matrix* Σ*. Then*

random variables f g *Nn n*≥1 such that for each *n* ≥1 the random variable *Nn* is independent of the sequence f g *Sk k* ≥1.  In [25], the distribution corresponding to the

Theorem 4. *Let Nn* ! ∞ *in probability as n* ! ∞*. Assume that the random variables X*1, *X*2, … *satisfy condition* ð Þ7 *with an asymptotic covariance matrix* Σ*. Then*

with some infinitely increasing sequence of positive numbers f g *dn n*≥1 and some

) *ζα=*2,1

Proof. This theorem is a direct consequence of Theorem 2 with the account of

**5.2 Convergence of the distributions of random sums of random vectors with finite covariance matrices to multivariate elliptically contoured Linnik**

In 1953, Yu. V. Linnik [20] introduced the class of univariate symmetric proba-

where *α* ∈ð � 0, 2 . Later, the distributions of this class were called *Linnik distributions* [21] or *α-Laplace distributions* [22]. Here the first term will be used since it has become conventional. With *α* ¼ 2, the Linnik distribution turns into the Laplace

1 þ j j*t α* , *t* ∈ ,

, *x*∈ *:*

, *α*∈ ð Þ 0, 2 , (19)

1

1 2 *e* �∣*x*∣

A random variable with the Linnik distribution with parameter *α* will be

The Linnik distributions possess many interesting analytic properties (see, e.g., [17, 18] and the references therein) but, perhaps, most often Linnik distributions are recalled as examples of geometric stable distributions often used as heavy-tailed

The multivariate Linnik distribution was introduced by D. N. Anderson in [25]

is the characteristic function of an *r*-variate probability distribution, where Σ is a

*Nn dn*

) *Gα*,Σ ð Þ *n* ! ∞

nite matrix Σ.

*α*∈ ð � 0, 2 , if and only if

*Probability, Combinatorics and Control*

relations (17) and (18).

**distributions**

denoted *L*1,*α*.

**178**

as *n* ! ∞.

$$L\left(\frac{\mathbb{S}\_{N\_n}}{\sqrt{d\_n}}\right) \Rightarrow \mathcal{L}(L\_{r,a,\Sigma}) \qquad (n \to \infty)$$

with some infinitely increasing sequence of positive numbers f g *dn n*≥1 and some *α*∈ ð � 0, 2 , if and only if

$$\frac{N\_n}{d\_n} \Rightarrow 2M\_{a/2}$$

as *n* ! ∞.

Proof. This theorem is a direct consequence of Theorem 2 with the account of relation (22).


**Acknowledgements**

This chapter was supported by the Executive Unit for the Financing of Higher Education, Research, Development and Innovation (UEFISCDI) of the Ministry of National Education (project "PREdictive Machine Learning Algorithm for the Dynamic Evaluation of Pancreatic Cancer during Therapy Multimodal Therapy"— PREDYCT, code PN-III-P4-ID-PCE2020-0884 within PNCDI III).