Group fuzzy comprehensive evaluation method under ignorance

Abstract

This paper aims at solving such a group fuzzy comprehensive evaluation (FCE) problem that the global or local ignorance may exist in judgments made by experts and the importance degrees of experts are different. The basic probability assignment (BPA) function is used to extract the expert's judgment information and the super fuzzy relationship matrices consisting of the individual type and the general type are constructed by Shafer's discounting and Dempster's rule. Then each type of super fuzzy relationship matrix is combined with factor weight set via a specified fuzzy operator and the comprehensive evaluation result that is a belief distribution on the power set of grade levels is obtained. A multi-objective programming model is established to compute the optimal belief distribution on each grade level and an algorithm is summarized to derive the final grade level that the evaluated alternative belongs to. Moreover, the numerical comparisons between the proposed method and relevant existing methods are given to clarify the advantages of the proposed method. Finally, an illustrative example is provided to demonstrate the applicability of the proposed method and algorithm. It is worth noting that the proposed method can be easily converted into a core algorithm, which is benefit for developing fuzzy expert system from the perspective of ignorance, and thus it has an important impact and significance on expert and intelligent systems.