Decision analysis using set of fuzzy priority weight vectors estimated from a fuzzy pairwise comparison matrix

Abstract 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 (FAHP), a normalized fuzzy priority weight vector is estimated from a fuzzy pairwise comparison matrix (FPCM). Because the FPCM components are supposed to show the ratios of fuzzy priority weights, the deviations between them are considered natural criteria. Thus, if a normalized fuzzy priority weight vector has the same deviations as a solution to the estimation problem, it can be considered another solution. We may find such solutions, and the estimation problem can have many solutions. In this paper, we propose an FAHP approach to decision analysis using a set of solutions to the estimation problem under an FPCM. First, we study the estimation problem of the normalized fuzzy priority weight vector under a given FPCM and review a conventional approach. Minimizing the deviations between the FPCM components and the ratios of fuzzy priority weights becomes more complex than the conventional approach. We adopt a solution of the conventional approach. We extend it to a set of solutions because we can find other normalized fuzzy priority weight vectors having the same deviations as the solution. A decision analysis is proposed using all of these normalized fuzzy priority weight vectors. In numerical examples, we demonstrate a detailed decision analysis from multiple perspectives, considering 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.