Fuzzy Genetic Prioritization in Multi-Criteria Decision Problems

A new method is presented to derive a priority vector W = (w1 , w2 , .... w n )T defining the ranking of competing alternatives and factors or criteria from fuzzy pairwise judgments. The pairwise comparisons are accepted as linguistic evaluations or assessments expressing relative importance of pairs ( i , j ) .These evaluations are quantified in the form of trapezoidal fuzzy numbers expressed as quadruples (a i j, bi j, c i j, d i j) in order to model the vagueness and imprecision in linguistic evaluations. The problem of finding components of priority vector W, given n (n-1) / 2 quadruples (a i j, bi j, c i j, d i j) is formulated in an optimization model with a newly introduced objective function. The problem is solved by means of a genetic algorithm. The complications and inappropriateness in finding inconsistencies of fuzzy pairwise comparisons, as presented in existing literatures, are treated and resolved in the present work by introducing ratios of inconsistency index to index of inconsistency of random fuzzy comparisons. The proposed method is illustrated by numerical examples and compared with some of the existing methods in literatures.