Multiple Criteria Group Decision Making with Triangular Interval Type-2 Fuzzy Sets

In this paper, the triangular interval type-2 fuzzy set extension of the Analytic Hierarchy Process is introduced. The priority vectors are elicited from the pairwise comparison matrix with triangular interval type-2 fuzzy sets which represent the linguistic relative importance judged by experts. First, the triangular interval type-2 fuzzy set logarithmic regression function is defined with respect to the pairwise comparison matrix of the criteria. Then, the sets of linear systems corresponding to the end points of the upper and lower membership functions are formulated by minimizing the logarithmic regression function. The non-normalized weights are solved. It is shown in this paper that the sets of linear systems are all dependent. Accordingly, the final normalized weights can be obtained. A quadratic programming model for finding the optimum normalized weights is constructed in the sense of minimizing the fuzziness of the interval type-2 fuzzy weights. Analogously, if the pairwise comparisons are for the alternatives, then the final normalized triangular interval type-2 fuzzy rates are also obtained. The aggregation process of the triangular interval type-2 fuzzy sets is proposed to obtain the overall rate of each alternative. The interval type-2 fuzzy set ranking method is proposed and used to find the final preference of the alternatives. A numerical example about selecting the best professor candidate is examined.