An interval type-2 fuzzy PROMETHEE method using a likelihood-based outranking comparison approach

Based on the preference ranking organization method for enrichment evaluations (PROMETHEE), the purpose of this paper is to develop a new multiple criteria decision-making method that uses the approach of likelihood-based outranking comparisons within the environment of interval type-2 fuzzy sets. Uncertain and imprecise assessment of information often occurs in multiple criteria decision analysis (MCDA). The theory of interval type-2 fuzzy sets is useful and convenient for modeling impressions and quantifying the ambiguous nature of subjective judgments. Using the approach of likelihood-based outranking comparisons, this paper presents an interval type-2 fuzzy PROMETHEE method designed to address MCDA problems based on interval type-2 trapezoidal fuzzy (IT2TrF) numbers. This paper introduces the concepts of lower and upper likelihoods for acquiring the likelihood of an IT2TrF binary relationship and defines a likelihood-based outranking index to develop certain likelihood-based preference functions that correspond to several generalized criteria. The concept of comprehensive preference measures is proposed to determine IT2TrF exiting, entering, and net flows in the valued outranking relationships. In addition, this work establishes the concepts of a comprehensive outranking index, a comprehensive outranked index, and a comprehensive dominance index to induce partial and total preorders for the purpose of acquiring partial ranking and complete ranking, respectively, of the alternative actions. The feasibility and applicability of the proposed method are illustrated with two practical applications to the problem of landfill site selection and a car evaluation problem. Finally, a comparison with other relevant methods is conducted to validate the effectiveness of the proposed method.