Conclusions and future research
In this research we compared performance of nine FAHP methods among which five FAHP methods are the most popular ones in the literature. Compatibility Index Value (CIV) is used as a performance metrics to evaluate all nine FAHP methods. Three experimental conditions are considered as part of the analysis, namely, size of the matrix (n), fuzzification level (α) and inconsistency (C.R). For the fuzzification parameter four levels are assumed as 0.25, 0.50, 0.75 and 1.00. The fuzzification parameter is not inherent to the problem that the decision maker is facing but more a decision variable as part of the process. That is to say, the decision analysts can set the fuzzification level and conduct FAHP accordingly. On the other hand the inconsistency parameter refers to the inconsistency of the decision maker and is not a decision variable but depends on the fuzzy comparison matrices elicited from the experts. For the analysis three levels are considered for the inconsistency which is low, medium and high based on the consistency ratio (C.R) values as explained before. Finally, four different matrix sizes are considered which are 3, 7, 11 and 15. Note that one can consider 3 as the representative of small sized problems, 7 and 11 are for medium sized problems and 15 for larger cases. As a result of this set up total of 48 (= 4 ∗ 3 ∗ 4) different experimental conditions are constructed. For each condition 13 replications are created randomly. Hence the total dataset is composed of six hundred and twenty four matrices with varying parameters for size of the matrix, fuzzification levels and inconsistency.
