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Editorial Board A Refereed Monthly International Journal of Management
 Prof. B. P. Sharma (Editor in Chief) Prof. Mahima Birla (Group Editor) Dr. Khushbu Agarwal (Editor) Ms. Asha Galundia (Circulation Manager) Editorial Team Dr. Devendra Shrimali Dr. Dharmesh Motwani www.swisscasinotest.com

 1
 l
 m
 u
 l                          m                       u

Figure 1:  Triangular fuzzy numbers

Methodology of fuzzy AHP

Laarhoren and Padrycz - two researchers from Netherlands - proposed a method for fuzzy AHP in 1983 which was based on the Logarithmic Least Squares technique. That method did not turn popular due to high computational volume and complicated phases of implementation. In 1996, another method called Extent Analysis Method (EA) was introduced by “Chang”, a Chinese researcher. That approach uses triangular fussy numbers. Concepts and definitions in Fuzzy AHP based on EA method would bebriefly described here (Momeni, 2013).

Take two numbers of M1=(I1, m1, u1) and M2=(I2, m­2, u2) which are shown on the graph in Figure 2.

 1
 0
 I1
 m1
 I2
 u1
 m2
 u2

Figure 2: triangular numbers M1 and M2

Mathematical operators are defined for them as:

M1+M2 = (I­2+I­2, m1 + m2, u1 + u2)

M1×M2 = (I­2×I­2, m1 × m2, u1 × u2)

M1-1=  , M2-1 =

Note that the product of two TFNs or the reciprocal of a TFN are not TFN anymore. These relations only state an approximation of real product of two TFNs or the reciprocal of a TFN. In EA method, a value of Sk is defined for each row of the mutual comparison matrix that itself is a triangular number. This value is calculated as:

Sk =

in which, k indicates the row number, while i and j are the choice number and index number, respectively.

The calculation of Sk values in EA method is followed by calculating their degree of relative greatness over each other. Generally, if M1 and M2 are two TFNs, the degree of greatness for M1 over M2 is shown as V(M1 >M2) which is defined as:

Also,

Hgt (M1 M2) =

The degree of greatness for a TFN over K other TFNs would be given by the following relation:

V(M1 M2,…,Mk) = Min[V(M1 M2),…, V(M1 MK)]

The weight of indices inside the pairwise comparison matrix would be calculated in EA method as the following:

W' (xi) = Min {V(Si SK)},              K=1,2,….,n,    K i

Therefore, the vector of weights for the indices would be:

W'= [W' (c­1), W' (c2),…., W'(cn)]T

which is identical to non-normalized Fuzzy AHP coefficients vector.

Linguistic phrases are used in order to compare the measures. Table 1 is the tool which is used to transform pairwise comparisons into Triangular Fuzzy Numbers (Wang et al., 2009).

Table 1: Transforming linguistic phrases into fuzzy numbers

 degree of importance Linguistic Phrase Fuzzy Numbers 1 equal (1,1,1) 2 very low (1,2,4) 3 relatively low (1,3,5) 4 low (2,4,6) 5 high (3,5,7) 6 relatively high (4,6,8) 7 very high (5,7,9) 8 very very high (6,8,9) 9 extremely high (7,9,9)

Calculating consistency rate for fuzzy pairwise comparison matrices

It is necessary to check the problem for inconsistency before trying to solve the problem, since an inconsistent matrix might result in errors in output. Therefore the rate of consistency should be calculated for each matrix. This task is tackled by the present study using the method proposed in Gogus and Boucher (1998).

Gogus and Boucher proposed that two matrices (middle number and fuzzy number limit) should be derived from each fuzzy matrix, and then the Consistency Rate (CR) of the matrix can be calculated using Saaty’s method. The consistency rate for fuzzy pairwise comparison matrices would be determined as the following.

Step 1: The fuzzy triangular matrix is divided into two matrices. The first matrix is consisted of middle numbers of triangular judgments  while the second matrix is consisted of upper and lower geometrical limits of triangular numbers   .

Step 2: vector of weights for each matrix is calculated using Saaty’s method as:

Step 3: The largest eigen value is calculated for each matrix as the following:

Step 4: The Consistency Index (CI) is calculated using the following equations.

Step 5: In order to calculate the Consistency Rate (CR), we need to divide the CI index by the value of Random Index (RI). The matrix is considered consistent and applicable if the resulted value is less than 0.1. Thus we need to calculate CR for those two matrices according to the following equations and compare them to the 0.1 threshold.

The fuzzy matrix is consistent if both calculated values are lower than the 0.1 threshold. If both values are higher than 0.1, the decision maker would be asked to reconsider the priorities. Finally, if only one of two values (CRm or CRg) is higher than 0.1, then the decision maker is to reconsider the values of middle numbers (limits) of fuzzy judgments (Ramezani et al., 2013).

4.  Data analysis

After reviewing the literature and examining the studies in the field of intellectual capital and the IC components, we selected the relevant IC components which were used by Calabrese et al. (2013) for ICT services industry as adequate components to be considered while examining the Telecommunication Company of Khuzestan province. IC components covered two dimensions of human capital (including competency, morale, and intellectual agility measures), and structural capital (including measures of relationships, organization, renovation and development). Table 2 shows the components, measures and indices related to IC along with their symbols.

Table 2:  components of Intellectual Capital

 symbol dimension symbol Measure symbol Index IC components B1 human capital C4 intellectual agility D1 effect of efficiency of procedures and processes C5 morale D2 innovation in process and product C6 competency D3 customer satisfaction B2 structural capital C1 renovation and development D4 investment in R&D C2 relationships D5 work environment C3 organization D6 personnel’s incentives D7 education

Therefore, the AHP decision tree was created following the identification of relevant IC components. Figure 3 shows that decision tree.

 Prioritization of IC components
 Human capital
 Structural capital
 competency
 morale
 Intellectual agility
 Relationships
 Organization
 Renovation & Development
 Education
 Personnel’s incentives
 Work environment
 R&D investments
 Customer satisfaction
 Innovation in process and product
 Effect of efficiency of procedures and processes

Figure 3: The components of IC – AHP decision tree

To make the pairwise comparisons possible, a questionnaire was designed and distributed to 10 senior managers of Khuzestan Telecommunication Company which were deemed to have the required authority to respond. The managers were asked to compare IC components in pairs using the scale provided in Table 1. As mentioned before, the weights of IC components and their priorities were determined using Fuzzy AHP method along with the approach that was proposed by Chang (1996). First, the pairwise comparisons were made by the managers and were in the form of linguistic phrases had to be transformed into fuzzy numbers. The scale provided by Wang et al. (2009) (Table 2) was implemented to do this task. Note that all the calculations regarding data analysis has been done using MS EXCEL software implementing the capability of the program to work with macros. For example, pairwise comparisons by one of the managers regarding human capitals are presented in Table 3. As we can see, the obtained CR value is lower than 0.1 which suggests that matrix is consistent.

Table 3:  Pairwise comparisons for human capital criteria

 CR=0،022 C4 C5 C6 C4 Linguistic 1 0,167 4 Fuzzy 1 1 1 0,25 0,167 0,125 6 4 2 C5 Linguistic 6 1 1 Fuzzy 8 6 4 1 1 1 1 1 1 C6 Linguistic 0,25 1 1 Fuzzy 0,5 0,25 0,167 1 1 1 1 1 1

Furthermore, following transformation of all pairwise comparisons provided by the managers into fuzzy numbers and making sure the judgments are consistent; the arithmetic mean of the judgments was calculated in order to sum up all of responds provided by managers. The weights for measures of human capital were calculated through Fuzzy AHP process. Table 4 shows the results.

Table 4: Weights for measures of human capital

 Human Capital Symbol C4 C5 C6 Measure Intellectual Agility Morale Competency Weight 0,229 0,502 0,269 Priority 3 1 2

As could be observed, managers believe that morale or emotional state of personnel is more important as a measure of human capitals than the other two measures. Similarly, the relevant weights were calculated for measure indices associated with structural capital. The results are shown in Table 5 below.

Table 5: Weights for measures of structural capital

 Structural Capital Symbol C1 C2 C3 Measure Renovation & Development Relationships Organization Weight 0,300 0,338 0,362 Priority 3 2 1

In case of structural capital, the importance priorities are “organization”, “relationships” and “Renovation & Development” respectively as suggested by managers through the judgments they had made.

Table 6: Weights for measures of human capital

 Intellectual Capital (IC) Symbol B1 B2 Measure Human Capital Structural Capital Weight 0,819 0,181 Priority 1 2

As the Table 6 shows, among two dimensions of IC, much more importance is associated to the human capital in comparison to structural capital.

Table 7: Weights of indices for structural capitals

 Structural Capital Symbol D1 D2 D3 D4 D5 D6 D7 Measure Effect of efficiency of procedures and processes Innovation in process and product Customer satisfaction R&D investments Work environment Personnel’s incentives Education Weight 0,262 0,206 0,069 0,171 0,156 0,050 0,086 Priority 1 2 6 3 4 7 5

Table 8: Weights of indices for Human capitals

 Human Capital Symbol D1 D2 D3 D4 D5 D6 D7 Measure Effect of efficiency of procedures and processes Innovation in process and product Customer satisfaction R&D investments Work environment Personnel’s incentives Education Weight 0,207 0,197 0,0794 0,175 0,157 0,0791 0,105 Priority 1 2 6 3 4 7 5

The weights for indices regarding the structural capital are calculated as the products of weights associated with structural capital and general weights of indices (calculated using Chang’s method). A similar procedure was followed when calculating the weights for human capitals. Information in Tables 7 and 8 suggest that “effect of efficiency of procedures and processes”, and “Innovation in process and product” are the most important measures in regard to both human capital and structural capital aspects. Furthermore, the sequences of measures for both human and structural capitals are similar.

Table 9:  Final priorities of indices

 Intellectual Capital (IC) Symbol D1 D2 D3 D4 D5 D6 D7 Measure Effect of efficiency of procedures and processes Innovation in process and product Customer satisfaction R&D investments Work environment Personnel’s incentives Education Weight 0,251 0,204 0،071 0,172 0,156 0,056 0,090 Priority 1 2 6 3 4 7 5

The final priorities of indices of IC are shown in Table 9. According to this data, the most important indices are “effects of efficiency of procedures and processes” and “innovation in process and product” respectively, followed by “customer satisfaction”, “R&D investment” and “work environment” in the next priorities.

5.   Conclusion

The present study was designated in order to determine the priorities of 7 constituent measures, namely “effect of efficiency in procedures and processes”, “innovation in process and product”, “customer satisfaction”, “investment in R&D”, “work environment”, “personnel incentives” and “education” in different aspects of intellectual capital using the Fuzzy AHP approach. First, main indices associated with each aspect of human capital were compared to each other as pairs. According to the managers’ judgments, the index of personnel’s morale was at the highest level of importance, based on the degree of importance (DI) of 0.502 assign to it, when compared to two other indices of competency with DI equal to 0.269, and intellectual agility with DI equal to 0.229, respectively. Moreover, regarding to indices pertaining to structural capital, the index of “organization” received the DI of 0.362 which places it at a higher importance level when compared to “relationships” with DI of 0.338 and “renovation and development” with DI equal to 0.30, respectively. Also a comparison was carried out between two different dimensions of IC which are “human capital” and “structural capital”. The results suggested that human capital is deemed to be more important with DI of 0.819 in relation with structural to which a DI of 0.181 was assign through the judgments by managers. Then, a set of pairwise comparisons were performed between 7 components of “effect of efficiency in procedures and processes”, “innovation in process and product”, “customer satisfaction”, “investment in R&D”, “work environment”, “personnel incentives” and “education” in regard to general component of intellectual capital in IC. Results obtained from those comparisons suggested that “effect of efficiency of procedures and processes” was considered more important (DI equal to 0.251) than other components in managers’ point of view. Following that, “innovation in process and product”, “R&D investments”, “work environment”, “education”, “customer satisfaction”, and “personnel’s incentives” are respectively at the second to seventh ranks of importance. Those results are different to those from Calabrese et al., (2013) to some extent. Those differences might be caused by the type of strategies which the companies follow as well as diverse viewpoints of managers. Overall ranking performed by the managers of Telecommunication Company through the present study suggests that human capital and the aspect of human resources are highly important to achieve the organizational goals since the human resources would allow other resources to be effective. Among the indices pertaining to human capital, devoting more attention to personnel’s morale in comparison to two other indices, namely “intellectual agility” and “competency”, might result in highest levels of efficiency within the organization. This observation needs to be considered when arranging the practical priorities of managers.

In light of the priorities which are determined according to the judgments of managers in Telecommunication Company, human capital is considered to be more important than the structural capital. That suggests that managers need to pay special attention to human capital and its associated indices when designing work plans and strategies of the organization. That is because human capital as an intangible asset propels the progress of the organization and differentiates it from other firms in the arena of competition. This type of assets could be transformed as a competitive advantage which does not erode and leads to success for the organization while making it to survive in long terms. What resulted from the managers’ own judgments is that paying more attention to personnel’s morale and incentives in light of human capital should be strongly considered while more relatively more attention is needed to be given to other indices as well.

Among seven components under examination in this study, a higher level of importance was assigned to “effect of efficiency of procedures and processes”. Therefore company managers should arrange the procedures and processes in the way that provide the organization with required level of effectiveness and efficiency. This important goal could be achieved through standardization of process and procedures. Another component which needs to receive a special attention from the Telecommunication Company is to innovate in process and products. That company can gain higher social acceptance rates through innovations in its process and products. In other words, innovation can be incited by progresses in technology and improving and/or reinforcing resources and capabilities of the organization, which in turn leads to differentiation from the competitors.

Companies need to continuously develop their designs and extend theirproducts and services. Ceaseless changes in technology, presence of competitors and varying priorities of customers have rendered the developments in designs, products and services inevitable. Considering the investment in Research and Development (R&D) and maintaining a R&D department could lead to differentiate the company from competitors. R&D is a factor which is absolutely necessary for every company and greatly contributes to survival of the businesses.

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