A NOVEL MULTIPLE CRITERIA DECISION-MAKING METHOD USING A LIKELIHOOD-BASED COMPROMISE APPROACH UNDER COMPLEX UNCERTAINTY

Jih-Chang Wang, Ting-Yu Chen

Abstract: The purpose of this paper is to develop a new multiple criteria decision analysis method that uses a likelihood-based compromise approachwithin the environment of interval type-2 fuzzy sets. The theory of interval type-2 fuzzy sets, interval type-2 trapezoidal fuzzy numbers especially, is useful and valuable for modeling impressions and quantifying the ambiguous nature of subjective judgments. This paper presents some novel concepts of likelihood indices, weighted likelihood indices, likelihood-based compromise indices, and likelihood-based compromise values. Using a likelihood-based compromise approach, this paper develops a simple and effective method that can address the multiple criteria decision-making problems and avoid the computational complexity attached to interval type-2 trapezoidal fuzzy numbers. This paper introduces the concept of approximate positive-ideal and negative-ideal solutions to facilitate anchored judgments about the evaluative ratings of alternatives. Based on the likelihood of a binary relation, this paper establishes the likelihood index and the weighted likelihood index relative to the approximate ideals. A novel likelihood-based compromise index of the characteristics for each alternative is proposed to determine the corresponding likelihood-based compromise value using a signed distance-based method. This paper develops an algorithmic procedure using the proposed likelihood-based compromise approach for the purpose of acquiring the priority orders of the alternatives. Finally, the feasibility and applicability of the proposed method are illustrated with a practical application.

Keywords: Multiple criteria decision analysis, Interval type-2 fuzzy set, Likelihood index, Approximate ideal, Likelihood-based compromise index.

DOI: https://doi.org/10.15623/ijret.2017.0606009