**Preface to "Fuzzy Sets in Business Management, Finance, and Economics"**

Since the publication of Lotfi A. Zadeh's seminal paper "Fuzzy Sets" in 1965 in the journal Information and Control, there has been constant growth in theoretical developments and in the practical application of Fuzzy Set Theory and related mathematical tools. These tools have been applied widely, both by industry and academic research, to decision making and economics due to their versatility. On the one hand, they can efficiently represent and handle uncertain and vague information such as subjective judgements, non-precise observations on variables, or ill-defined relations between variables. On the other hand, they make implementing computations or identifying patterns in data much easier. To do so, Fuzzy Set Theory provides a vareity of mathematical techniques in fields such as Expert Systems, Soft Computing, Data Analysis, Mathematical Programming, and Multiple Criteria Decision Making. Business management, decision making, or actuarial modelling are some examples of practical applications in these fields. This Special Issue provided a platform for researchers from academia and industry to present novel work in the domain of applied developments for Fuzzy Sets and in methodologies related to business, financial, and economic analysis. We hope that these results will help to foster future research in the fields of economics and in the social sciences.


**5. Results**

For each of the 18 participants, we captured 15 parameters either measured directly or derived from ECG. For all these parameters, we also computed a moving average for an outlier-smoothed version of the same signal in order to get a better understanding of the signal's overall robustness and reliability. Additionally, we computed low/high-pass filtered versions of the GSR signals, as well as the complex demodulation amplitudes from the ECG signals. For each participant, we analysed 22 pairs of physiological parameters of the same type regarding similarity (e.g., heart rate from BioHarness sensor and heart rate from VarioPort sensor), and another 136 pairs of parameters of di fferent type regarding correlations (e.g., heart rate from BioHarness sensor and galvanic skin response from VarioPort sensor).

Since there are many di fferent parameters, we defined a naming convention that includes the physiological parameter of interest, the platform used to measure it, plus an indication of whether a time series is a moving averaged and/or a filtered version. For the naming of these parameters, we use the following notation:

For direct measurements:

#### <*parameter*> <*platform*> [*filt.*] [(*mv. avg*)]

where *parameter* can be GSR, HR, or IBI and *platform* can be BH, E4, or VP; *(mv. avg.)* indicates that this is the moving averaged version; *filt.* indicates that a first order high-pass (0.05 Hz) and first order low-pass (0.5 Hz) Butterworth filter has been applied to the original signal (this filter setting is used for further analysis to identify moments of stress [4,11]; however, this is not within the scope of this paper).

example: *GSR: VP (mv. avg.)* refers to the moving averaged version of galvanic skin response measured by VarioPort

For derived measurements:

> <derived parameter> from <original parameter> <platform> [(mv. avg.)]

where *derived parameter* can be HF, IBI, LF, VLF, *original parameter* can be ECG, and *platform* can be BH, or VP; *(mv. avg.)* indicates that this is the moving averaged version example: *IBI: from ECG BH* refers to the inter beat interval derived from the electrocardiogram measured by BioHarness

The following subsections are structured according to Figure 3. We use two representative time series, one HR and one GSR, as examples to guide the reader through the high number of physiological parameters investigated herein. These two examples are cross-referenced between several figures and thus provide views on the same data from di fferent perspectives, thereby fostering the consolidation of a more holistic picture.

#### *5.1. Visualisation: Exploratory Plots*

The aim of the exploratory plots is to obtain a basic understanding of the temporal behaviour and the relationship of equal-type physiological parameters. For this first insight, we investigate three complementary plots that provide di fferent views on the same data: a time series plot, a scatter plot, and a cross-correlation plot. These plots show two versions of the same parameter, namely a data-as-is version and moving averaged version. Note that for the cross-correlation plots the second parameter is used as the independent one. To illustrate the methodology and exemplary results, we only show representative sample plots, which highlight the characteristic patterns of about 80% of all plots. Overall, we produced more than 1000 plots based on unscaled and rescaled data.

Figures 4 and 5 each show a time plot (a), a scatter plot (b), and a cross-correlation plot (c,d). The physiological parameter of interest is HR, measured by HB and VP. The HR time plot (Figure 4a) shows two highly similar, almost identical curves. The blue curve has an o ffset, which is maximal in the low range and converges to zero in the high range. The corresponding error term seems

to include a reciprocal component: the higher the actual measurement, the lower the error. The HR scatter plot (Figure 4b) shows a high positive linear relationship with an R2 of 0.971 for raw data and 0.997 for the moving averaged data. This means that 97.1% and 99.7%, respectively, of the data's total variance can be explained by a linear model. This plot also confirms what is seen in the time plot, namely that in the low range the residuals are higher than in the high range. Note that the higher residuals in red in the upper right quarter of the plot refer to the time plot at ~750 s, where the blue curve drops below the red curve (indicated by a black arrow in Figure 4a,b). The HR cross-correlation plots show the highest cross-correlation for the as-is version (Figure 4c) at a lag of 1 s, and the highest cross-correlation for the moving averaged version (Figure 4d) at a lag of 2 s. In other words, the local trend of the BH is lagging 1 and 2 s, respectively, "behind" the local trend of the VP on average.

**Figure 4.** *Cont*.

**Figure 4.** Participant RP 5–14: time plot (**a**), scatter plot (**b**), and cross-correlation plot (**c**), and cross-correlation plot of moving averages (**d**) of heart rate HR [beats per minute] measured by Bioharness3 BH sensor and VarioPort VP.

In Figure 5, the physiological parameter of interest is GSR, measured by the E4 and the VP. Generally speaking, measuring GSR is, in comparison to HR, a delicate undertaking due to the measurement principle, which is solely based on the electrical conductivity of the skin. This conductivity is highly dependent on (1) the participant's skin characteristics and (2) the contact between the sensor electrodes and the skin, especially during physical activity. Thus, these two factors can have a significant impact on the reliability, and thus on the comparability, of the sensor measurements. Additionally, the mounting of the sensors' electrodes can differ as well. For instance, the VP electrodes need an isotonic electrolyte gel to ensure reliable measurements, while E4 does not require anything. The GSR time plot (Figure 5a) shows that the blue curve (VP) increases gradually. The red curve (E4) increases faster than the blue one and shows a local maximum after the 5-min warm-up phase (at around 300 s). This increase is followed by a decrease for another 5 min (until around 600 s). Aside from a little drop at around 900 s, the red curve increases until the end of the cool down phase. In general, the E4 seems to be

more responsive to sweating associated with physical effort than the VP, which may be due to its lack of stabilizing isotonic electrolyte gel. The GSR scatter plot (Figure 5b) shows a positive correlation with an R2 of 0.882 for raw data and 0.896 for the moving averaged data. This means that 88.2% and 89.6%, respectively, of the data's total variance can be explained by a linear model. The cross-correlation plots (Figure 5c) show the highest cross-correlation for the as-is version at lag of 2 s, and the highest cross-correlation for the moving averaged version at a lag of 1 s. In other words, the local trend of the E4 sensor is lagging 2 and 1 s, respectively, "behind" the local trend of the VP sensor on average.

**Figure 5.** *Cont*.

**Figure 5.** Participant RP 3–8: time plots (**a**), scatter plot (**b**), cross-correlation plot (**c**), and cross-correlation plot of moving averages (**d**) of galvanic skin response GSR measured by Empatica E4 and VarioPort.

#### *5.2. Quantitative Analysis*

The aim of the quantitative analysis is twofold: first, we assess the correlation and the similarity of equal-type parameters. Second, we assess potential associations in pairs of parameters of both equal-type and different types. In addition to global statistics, we also apply local measures to derive new information about the relationship between and among the different parameter pairs. This combination of global and local similarity and correlation measures on the individual level further enables a roll-up view on relationship patterns of physiological parameters among participants. Note that for similarity distance metrics, we rescaled measurements from min ... max of the original scale to 0 ... 1. For the correlation analyses we used the original values of the given parameter at the given range and the given unit in order to identify potential offsets.

#### 5.2.1. Linear Regression and Coefficient of Determination R2

The first statistic of interest is the coefficient of determination R2, which quantifies the percentage of the variance of the two given parameters that can be explained by a linear regression model. In addition to the R2 of individual pairs of parameters, as shown in the scatter-plots (refer to Section 5.1, Figures 4b and 5b), we now investigate all pairs among all participants and explore the corresponding R2 pattern. This pattern can be derived from the R2 matrix shown in Figure 6. Furthermore, for each group of parameters, e.g., all IBI related parameter, we calculate the total average per participant in order to get an impression of the impact of each participant's individual overall measured activity (GSR base level, skin contact of electrodes, etc.).

**Figure 6.** R2 matrix of pairs of parameter and participants; detail (**a**) complements Figure 4, detail (**b**) complements Figure 5; total average of individual pairs among participants is shown in the last column; total average of participants among individual parameter pairs is shown in the last row of each parameter group; colour: red indicates high correlation, blue indicates low correlation.

In the upper half of the R2 matrix, the pairs of equal-type parameters, measured by different sensors (or derived from another signal of the same sensor) show a high linear relationship across the majority of the participants. This relationship also indicates that these parameters are rather robust from a measuring point of view. However, the matrix also shows some cases with no relationship at all, see for instance IBI derived from ECG BH (moving averaged version), and IBI derived from ECG VP (moving averaged version) at row three for participant RP 8-20 and RP 1-2. This may indicate that one of the sensors did not have proper contact between the electrodes and the skin and thus failed to collect valid data.

The matrix shows that GSR in general, and IBI measured by Empatica E4, tend to have rather low or even no correlation, while some participants demonstrate the exact opposite (compare instance RP 4-11 and RP 2-5).

Note that the R2 matrix in Figure 6 is organized as follows: for each group of parameters, the top row shows the highest correlation among all participants, while the bottom row shows the lowest correlation. Further, the left column shows the participant with the highest correlations among all parameters, while the right column shows the participant with the lowest correlations among all parameters.

Figure 6 detail (a) refers to the HR example shown in Figure 4 and detail (b) refer to the GSR example shown in Figure 5.

In summary, the overall pattern shown in Figure 6 confirms that both the type of the parameter measured and the individual parameters, such as skin characteristics of the participant, significantly influence the reliability of the measurements and thus the quality of further analysis.


**1. Introduction**

Postural disorders and spinal deformities present major difficulties for affected people, not only from the medical point of view but also from the point of view of finding appropriate

© 2016 The Author(s). Licensee InTech. 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. © 2017 The Author(s). Licensee InTech. 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.

clothing. Without doubt, it can be stated that assuring garments with perfect fit and functionality taking into account the increased need for a modern design is not possible without an extensive use of modern computer-based technologies, above all three-dimensional (3D) body scanning, computer-aided design, and virtual prototyping. Moreover, additional methods for analyzing digitized geometry, such as CASP (Curvature, Acceleration, Symmetry, and Proportionality), are needed for assuring appropriate garment part designs and final fit of the garment. CASP methodology is a widely applicable approach in fields of use where a 3D virtual model is present. We have used it for virtual prototyping of garments for people with postural disorders and spinal deformities.

Nowadays, we can use virtual reality applications to produce digital prototypes of different garments and other textile forms, especially three-dimensional. The designers can alter their design creations with less time and cost. The aim of 3D virtual prototyping is to build a virtual model instead of developing a real product. Virtual garment prototyping is a technique which involves the application of computer-aided design systems used for the development of the garment pattern designs and the assessment of their fit to the 3D body model and virtual assessment of the appearance of the whole garment.

This chapter presents topics related to the multidisciplinary fields of computer graphics and analysis, 3D scanning, and 3D virtual modeling with the aim of supporting virtual prototyping of garments for people with postural disorders and spinal deformities. Mainly scoliosis and kyphosis are treated, because a significant share of the population is facing these problems, especially in the older population.

As a transformation tool between real world and virtual world, 3D scanning is used to capture and digitize real objects. 3D scans describe an object's shape. It makes sense to use precise 3D scanners for solid and rigid objects, where small details or deviations are important and can be measured, but for virtual prototyping, it is usually enough to have a rough shape of a person. Live persons are moving and changing shape literally with every breath and heart beat. Therefore, it is better to perform low-detail scans.

In this chapter, we present research relating to the applicability of CASP methodology to nonstandard body figures' garment pattern design with the aim of finding out whether CASP methodology is right for predicting the garment pattern design for persons with a curved spine, as well as for the construction of well-fitted garments.

After the theoretical background and study of the literature dealing with curves and shapes, CASP methodology is introduced and explained. Medical points of view regarding postural disorders and spinal deformities are detailed in order to highlight the need for adapted garment designs. Practical examples are discussed using CASP methodology, including three case studies dealing with curvature graphs, together with two examples related to the design and virtual prototyping of garments for people with postural disorders and spinal deformities. The chapter concludes with suggestions for further studies in this important and interesting research area.


**5.4. Amyopathic dermatomyositis**

Several neuromuscular diseases which may mimic PM/DM and should be considered in the differential diagnosis include drug or toxic myopathies (alcohol, colchicine, statins, etc.), endocrine myopathies (hyper-hypothyroidism), metabolic myopathies, mitochondrial myopathies, muscular dystrophies, infectious myositis, neuropathies, paraneoplastic syndromes, other connective tissue disorders, amyloidosis, and sarcoidosis [93]. Muscular dystrophies, where an increase of creatine kinase (CK), electrodiagnostic, and bioptic abnormalities similar to PM/DM may be present, can be distinguished from DM/PM by the positive family history, the relatively early insidious onset, and slow progression. Iatrogenic myopathy is secondary to corticosteroids use, where CK is normal and the histological examination shows atrophic changes of muscle fibers. Other diseases to consider in the differential diagnosis are endocrine or dysionemia-induced myopathies. Rheumatic polymyalgia (polymyalgia rheumatica) is characterized by normal CK and histological absence of inflammatory abnormalities. Infectious myositis especially viral and parasitic myositis are characterized by a diffuse muscular involvement and a subacute or chronic course. Bacterial myositis is localized and acute. Among other rare inflammatory myopathies, nodular focal myositis is considered as a variant of PM/DM and may present at onset (As localized, a differential diagnosis with muscular cancers and/or thrombophlebitis must be considered). Eosinophilic myositis, characterized by muscle eosinophil infiltrate, may be part of a hypereosinophilic syndrome (pneumonia, endocardial and myocardial fibrosis, and peripheral neuropathy, etc.) or be associated with eosinophilic fasciitis. Granulomatous myositis can be isolated or in the context of granulomatous syndromes, such as sarcoidosis or Crohn's disease; the main histological finding is the presence of granulomatous lesions which may contain epithelioid cells, histiocyte, and Langerhans giant cells. In the differential diagnoses of IBM, polyneuropathy and amyotrophic lateral sclerosis have also to be

Concerning extra-muscular involvement, respiratory disease is a major cause of morbidity and mortality in PM/DM [53, 95–100]. PM/DM-associated pulmonary disorders may manifest as ILD and as a consequence of respiratory muscle weakness leading to hypoventilation or aspiration pneumonia. ILD is the most common extra-muscular complication in PM/DM and have been recognized in 30–70% of the patients [100–102]. The reported prevalence varies depending on the modalities or tests for detection and patient selections. Since Tazelaar et al. reported a histopathological study of lung biopsy specimens in patients with PM/DM in terms of treatment responses and survivals, histopathology fairly serves relevant clinical decisions [53]. As for the prevalence of the different histopathologic patterns, NSIP is by far the most frequent finding, followed by DAD, UIP, and OP [54, 103–107]. Our study with HRCT scans of 14 cases of histologically proven NSIP associated with PM/DM showed that the predominant features were of reticular and/or ground-glass opacities with or without consolidation. Reticular and ground-glass opacities predominated in the lower zone of each lung, and consolidation predominated

In the context of subtypes of PM/DM, the following concepts of amyopathic dermatomyositis

and anti-synthetase syndrome warrant particular attentions.

considered [93, 94].

160 Contemporary Topics of Pneumonia

at the lung periphery [108].

Clinically amyopathic dermatomyositis (CADM), which is characterized by the cutaneous findings of DM with no muscle involvement or only minimal weakness, affects approximately 20% of patients with DM [109, 110]. Patients with CADM have a greater risk of developing ILD, especially prone to rapidly progressive lung disease corresponding to DAD [111, 112]. Anti-melanoma differentiation-associated gene 5 (MDA5) antibodies (also referred to as anti-CADM-140 antibodies) were identified in the serum from patients with CADM by firstly immunoprecipitation assays [113]. The presence of anti-MDA5 antibodies is strongly associated with DM, especially with CADM, and rapidly progressive ILD, which are thus associated with particularly poor clinical outcomes.

#### **5.5. Anti-synthetase syndrome (ASS)**

A subset of patients may manifest a clinical syndrome known as "anti-synthetase syndrome (ASS)," which is characterized by the presence of one of the anti-aminoacyl-t-RNA synthetase (ARS) antibodies such as anti-Jo-1, anti-PL-7, anti-PL-12, anti-EJ, anti-OJ, and anti-KS, together with stigmata of PM/DM including myositis, ILD, polyarthritis, fever, Raynaud's phenomenon, and mechanic's hand [114, 115]. Anti-Jo-1, the first anti-ARS antibody, is the best understood of the anti-synthetase antibodies, with a strong correlation with ILD in patients with PM/DM; the incidence of ILD approaches 90% [116, 117].

#### **5.6. Myositis-specific autoantibodies and myositis-associated autoantibodies**

Circulating autoantibodies directed against nuclear or cellular components are frequently detected in patients with PM or DM. These antibodies are categorized into two groups; one is specific to PM/DM, whereas the other is found in overlap syndrome with myositis. Targoff et al. designated these two categories of autoantibodies as "myositis-specific antibodies; MSAs" and "myositis-associated antibodies; MAAs," respectively [114]. Classical autoantibodies such as anti-aminoacyl transfer RNA synthetases (ARS) antibodies, anti-signal recognition particle (SRP) antibodies [118, 119], and Mi-2 antibodies are classified as MSAs, where especially anti-Mi-2 antibodies are DM specific [120]. Later, the new DM specific antibodies have been disclosed. These include the antibodies directed against melanoma differentiation– associated gene5 (MDA5) (anti-CADM-140 antibody, mentioned above) [113, 121, 122], transcriptional intermediary factor-1-gamma (anti-p155 antibody) [123, 124], NXP-2 (anti-NMP-2 antibody) [125, 126], and small ubiquitin-like modifier activating enzyme (anti-SAE antibody) [127]. Usually, MSAs are distinct, and their presence is mutually exclusive.

Because of their strong associations with a pattern of clinical features, such as myopathy, skin lesions, and ILD, these novel autoantibodies are useful biomarkers for classifying disease subgroups, predicting future organ involvement, and forecasting the prognosis of patients with PM/DM [114, 128–131]. The autoantibodies are detectable in PM/DM; both MSA and MAA are listed and summarized in **Table 4** [102]. The pathogenetic mechanisms of expression of such autoantibodies are still awaited to be illuminated.

**Autoantibodies**

**Other MSA**

Anti-SRP Anti-HMGR(200-100)

Anti-SAE

3-hydroxy-3-methylglu tarylcoenzyme A reductase

Small ubiquitin-like modifier

<1/5–10/1–9

DM

Unknown

activating enzymes

**Myositis associated autoantibodies**

Anti-RO/SSA

Anti-U1RNP

RNP complexes with small

12/13/0

cytoplasmic RNAs(hy-RNA)

70 KDa,A and C polypeptides of U1

5/6/6

7

DM, fever, RP, sclerodactyly

snRNP

Anti-PM/Scl(75 and

PM/Scl complex encompassing

6/9/4

38

Fever, RP, sclerodactyly

C1D,PM-SCl-100 and PM-SCl-75

proteins of the human exosome

80 and 70 KDa DNA binding dimeric

2/1/0

27 ADM: adult dermatomyositis; JDM: juvenile dermatomyositis; ILD: interstitial lung disease; SRP: signal recognition particle; ARS: aminoacyl-t-RNA synthetase; RP:

Raynaud's phenomenon; DM: dermatomyositis specific rash; RP-ILP: rapidly progressive ILD; JPM: juvenile poly myositis

Adapted from Lega et al. [120].

**Table 4.** Autoantibodies in polymyositis/dermatomyositis.

Fever, RP, sclerodactyly

Interstitial Pneumonia Associated with Connective Tissue Disease: A Comprehensive…

http://dx.doi.org/10.5772/intechopen.70864

163

protein

100 Kda)

Anti-Ku

Signal recognition particle

5/1/<3 10/<1/unknown

Unknown

15/0

Necrotising myopathy

Necrotising myopathy

 Unknown

Severe JPM

**Antibody target**

**Frequency in**

**Frequency of ILD**

**Clinical spectrum**

**In adulthood**

**In childhood**

**in adult /juvenile**

**myositis %**

**polymyositis/ADM/**

**JDM %**

**Autoantibodies**

**Myositis- specific autoantibodies (MSA**)

*Anti-t-RNA synthetase*

Anti-Jo1 (PL1)

Anti- PL7 Anti- PL12

Anti-KS Anti-OJ

Anti-EJ Anti-SC

Anti-JS Anti-YRS(Ha)

Anti-Zo

Tyrosyl-ARS Phenylalanyl-ARS

**Dermatomyositis Specific autoantibodies**

Anti-Mi2

Nucleosome remodeling deacetylase

1/9/4–10

4/0

Classical DM without

Mild or moderate JDM

extramuscular involvement

DM without extramuscular

Mild or moderate JDM

involvement, calcinosis

complex

Anti-NXP2(MJ,p140)

Anti-

MDA5(CADM-140)

Anti-TIF1γ(p1555/140)

Transcriptional intermediary factor 1γ

<1/10–30/14–29

<10/3

Melanoma differentiation-associated gene encoding RNA helicase

<1/14–46/7

Europe:60; Asia:90/

Europe:19; Asia:53

progressive ILD

Cancer associated DM in

78% of cases

Amyopathic DM, severe cutaneous ulcers, rapidly

Severe cutaneous ulcers,

RP-ILP, mediastinal

emphysema

Mild or moderate JDM

Nuclear matrix protein 2

10/0–3/12–25

 0/25

Histidyl-ARS Threonyl-ARS

Alanyl-ARS Asparaginyl-ARS

Isoleucyl-ARS

Glycyl-ARS

Lysyl-ARS Glutaminyl-ARS

**Antibody target**

**Frequency in**

**Frequency of ILD**

**Clinical spectrum**

**In adulthood**

**In childhood**

**in adult /juvenile**

**myositis %**

**polymyositis/ADM/**

**JDM %**

29/20/5

21/11/<3

5/2/<1 2/3/<1

<1

<1

<1

<1

<1

<1 <1

<1

84/63

66/63

Arthralgia, fever, RP,

Arthralgia, fever, RP,

162 Contemporary Topics of Pneumonia

mechanic's hand,

sclerodactyly

mechanic's hand, puffy

finger

ADM: adult dermatomyositis; JDM: juvenile dermatomyositis; ILD: interstitial lung disease; SRP: signal recognition particle; ARS: aminoacyl-t-RNA synthetase; RP: Raynaud's phenomenon; DM: dermatomyositis specific rash; RP-ILP: rapidly progressive ILD; JPM: juvenile poly myositis Adapted from Lega et al. [120].

**Table 4.** Autoantibodies in polymyositis/dermatomyositis.


*2.1. Direct Current Electrodeposition*

In Direct current (DC) electrodeposition, an electric current is continuously transferred through the system without any interruptions. DC electrodeposition is divided into two types depending on the orientation of the electrodes in electrolyte during the electrodeposition process. These are the conventional electrodeposition, and sediment codeposition (SCD) techniques. For conventional electrodeposition, the electrodes are placed vertically in the electrolyte, but for SCD they are placed horizontally. Adsorption of nanoparticles into the alloy matrix during electrodeposition is greatly influenced by forces acting on the suspended nanoparticles. The kinetics involved can be used to explain this difference. The two main forces at work during SCD electrodeposition are gravitational pull and the electrophoresis force, thereby giving more desirable properties compared to conventional deposition which solely relies on gravitational pull [30]. DC has several advantages over pulse electrodeposition and pulse reversal current (PRC) electrodeposition. These include simplicity, the availability of vast technical knowledge and affordability. Borkar T [31] reported that for all Ni and Ni nanocomposite coatings deposited, DC deposited coatings exhibited much stronger (less random) crystallographic textures compared to coatings deposited using PC and PRC deposition techniques. Furthermore, in DC electrodeposition, the Co content in the deposited Ni–Co coatings is dependent on the composition of the electrolyte, unlike in jet electrodeposition where Co electrodeposition is controlled by diffusion [4].

#### *2.2. Pulse Current Electrodeposition*

Pulse current electrodeposition (PC) has been used extensively over the years in Ni–Co electrodeposition [32]. The three most fundamental parameters that affect the properties of the coatings include in pulse current electrodeposition include: peak current (*Ipeak*), pulse imposition time (ON-time, *TON*) and switch off time (OFF-time, *TOFF*). These parameters relate mathematically to evaluate (1) pulse frequency, (2) duty cycle, and (3) average current density, as shown [32,33]:

$$f = \frac{1}{T\_{OFF} + T\_{ON}}\tag{1}$$

$$\gamma = \frac{T\_{ON}}{T\_{OFF} + T\_{ON}} \ast 100\tag{2}$$

$$I\_{\rm avg} \xrightarrow[T\_{OFF}]{T\_{ON}} \ast I\_{\rm peak} = I\_{\rm peak} \tag{3}$$

where γ is the duty cycle, *f* the frequency, *Ipeak* the peak current density, and *I*avg the average current density.

In pulse electrodeposition, peak current density has a significant effect on microhardness, crystallite size, surface morphology, microstructure, composition, and tensile strength of PC deposited Ni–Co alloys and their nanocomposites [34]. Crystallization and growth in turn determine the microstructure of the nanocomposite. The texture of the coatings is determined by both peak current density and organic surfactants [35]. The quantity of adatoms located at the surface is higher due to the applied higher current density as compared to DC electrodeposition. This results in smaller grain sizes [5]. Padmanabhan [36] reported that pulse electrodeposition is used as an effective method for the reduction of grain sizes to nanoscale [5].

Although it is a relatively low-cost synthesis technique with simple implementation, pulse electrodeposition is ideal for production of full density nanocrystalline materials [33]. Yang and Cheng [32] reported that the morphology of the deposited coatings changed from nodular to acicular, and a finer grain size was observed with increasing pulse frequency and decreasing duty cycle. It has also been reported that at low current densities, smoother surface morphologies are observed [37], but an increase in peak current density produces distinct colony-like morphologies characterized by clearer colony boundaries [34].

Pulse electrodeposition exhibits several advantages over DC electrodeposition, such as improved wear resistance and hardness, particle distribution, structure, morphological structure and the ability to control the grain sizes of the deposits [38]. PC electrodeposition has higher instantaneous current density compared to DC electrodeposition, thereby increasing its effectiveness in agitating the adsorption–desorption processes that occur at the Ni electrolyte interface. This makes it possible to control the electrodeposited Ni coating microstructure [39,40]. It has also been reported that PC deposits contain a higher nanoparticle content compared to coatings deposited by the DC deposition technique [31]. Yang and Cheng [32] concluded that the high microhardness of deposited Ni–Co–SiC coatings was primarily associated with increasing SiC content in the coatings with increasing pulse frequency and decreasing duty cycle. This significantly increased the microhardness as a function of the dispersion strengthening mechanism. Watts type baths used for pulse plating of Ni based coatings have been reported to produce the best coating results [2].

The PC deposition technique suffers from a drawback called the double layer capacitance effect. The double charging layer of the electrodes is subjected to charging and discharging occurrences. In a case where the ON- and OFF-times are much shorter than the charging and discharging times, the PC would revert to DC current. As such, care is taken to select a high frequency thus ensuring the effect of the double layer capacitance effect is negligible.