Likelihoods of interval type-2 trapezoidal fuzzy preference relations and their application to multiple criteria decision analysis

Interval type-2 fuzzy sets are useful and valuable for depicting uncertainty and managing imprecision in decision information. In particular, interval type-2 trapezoidal fuzzy numbers, as a special case of interval type-2 fuzzy sets, can efficiently express qualitative evaluations or assessments. In this work, the concept of the likelihoods of interval type-2 trapezoidal fuzzy preference relations based on lower and upper likelihoods is investigated, and the relevant properties are discussed. This paper focuses on the use of likelihoods in addressing multiple criteria decision analysis problems in which the evaluative ratings of the alternatives and the importance weights of the criteria are expressed as interval type-2 trapezoidal fuzzy numbers. A new likelihood-based decision-making method is developed using the useful concepts of likelihood-based performance indices, likelihood-based comprehensive evaluation values, and signed distance-based evaluation values. A simplified version of the proposed method is also provided to adapt the decision-making context in which the importance weights of the criteria take the form of ordinary numbers. The practical effectiveness of the proposed method is validated with four applications, and several comparative analyses are conducted to verify the advantages of the proposed method over other multiple criteria decision-making methods.