Decision Analysis Using Set of Fuzzy Priority Weight Vectors Estimated from a Fuzzy Pairwise Comparison Matrix

The fuzzy numbers have been introduced to the analytic hierarchy process (AHP) to reflect the vagueness of the decision maker's judgments. In fuzzy AHP, fuzzy priority weights are estimated from a fuzzy pairwise comparison matrix (PCM). However, when considering the deviation between a component of a given fuzzy PCM and the ratios of estimated fuzzy priority weights, we obtain multiple solutions having the same deviations in estimation problems of fuzzy priority weights from the fuzzy PCM. In this paper, we propose a fuzzy AHP approach to decision analysis using all optimal normalized fuzzy priority weight vectors to the estimation problem from a fuzzy PCM. First, we study the normalized fuzzy priority weight vector estimation problem under a given fuzzy PCM. After the review of the conventional approach to this estimation problem, we show the non-uniqueness of the normalized fuzzy weight vector associated with a consistent fuzzy PCM. Subsequently, we propose a simple method for obtaining all solutions having the same deviations from the given fuzzy PCM as the estimated normalized fuzzy weight vector to the problem. A decision analysis is proposed using all of these normalized fuzzy priority weight vectors. In numerical examples, we demonstrate a detailed decision analysis from many points of view using all potential orders of alternatives. Therefore, the decision maker may select the final solution from several recommended orders of alternatives in various ideas according to her/his consent.