A new comprehensive decision making method under bimodal information

Abstract

This paper introduces comprehensive and theoretically-driven approach to decision making under bimodal uncertainty in form of Z-numbers. The proposed decision making approach relies on synergy of consistency-driven preferences construction method, eigenvector determination method of Z-number valued matrixes proposed by author and his colleagues and modified WSM model. Consistency-driven preferences construction method is used to obtain a consistent Z-valued pair-wise comparison matrix (PCM) given inconsistent one. Indeed, initial Z-number-valued degrees of pairwise comparison of criteria importance provided by a decision maker are often inconsistent. Next, an eigenvector of the consistent Z-valued PCM is computed to derive criteria importance weights. To arrive at normalized Z-values of criteria, a normalization technique is proposed. Overall evaluations of alternatives are computed as a weighted sum of normalized criteria values. Finally, overall values are compared by using ranking of Z-numbers. The suggested decision method is rank reversal free. Correctness and feasibility of suggested method is illustrated by example.