Prof. Ta Chung Chu
Student: Nguyen Khoa Tu Uyen_M977Z215
Abstract:
This is one part of the paper “A Fuzzy MCDM approach for evaluating banking performance based on Balanced Scorecard”
(Hung-Yi Wu,
Gwo-Hshiung Tzeng, Yi-Hsuan Chen, 2009) which introduces Fuzzy analytic hierarchy process (FAHP) and its process.
Keywords:
Fuzzy Analytic Hierarchy Process (FAHP)
I.
Introduction
The Analytic Hierarchy Process (AHP) was devised by Saaty
(1980,1994). It is a useful approach to solve complex decision problems. It prioritizes the relative importance of a list of criteria (critical factors and sub-factors) through pair-wise comparisons amongst the factors by relevant experts using a nine-point scale. Buckley (1985) incorporated the fuzzy theory into the AHP, called the Fuzzy Analytic Hierarchy Process (FAHP).
II.
The procedure of FAHP for determining the evaluation weights
Step 1: Construct fuzzy pair-wise comparison matrix
Through expert questionnaires, each expert is asked to assign linguistic terms by TFN ( As shown in Table 1 and Figure 1 ) to the pair-wise comparisons among all criteria in the dimensions of a hierarchy system. The result of the comparisons is constructed as fuzzy pair-wise comparison matrix as shown in equation (1).

Figure 1.
Membership functions of the linguistics variables for criteria comparisons
Equation (1)
Step 2: Examine the consistency of the fuzzy pair-wise comparison matrix.
According to the research of Buckley (1985), it proves that if is a positive reciprocal matrix then is a fuzzy positive reciprocal matrix. That is, if the result of the comparisons of is consistent, then it can imply that the result of the comparisons of is also consistent. Therefore, this research employs this method to validate the questionnaire.
Step 3: Compute the fuzzy geometric mean for each criterion.

The geometric technique is used to calculate the geometric mean of the fuzzy comparison values of criterion i to each criterion, as shown in equation (2) , where is a fuzzy value of the pair-wise comparison of criterion i to criterion n (Buckley, 1985)
Equation (2)
Step 4: Compute the fuzzy weights by normalization
The fuzzy weight of the criterion can be derived as equation (3) , where is denoted as = by a TFN and , and represent the lower, middle and upper values of the fuzzy weight of the criterion.
Equation (3)