A likelihood-based assignment method for multiple criteria decision analysis with interval type-2 fuzzy information

The purpose of this paper was to develop a likelihood-based assignment method based on interval type-2 fuzzy sets and apply it to decision-making problems involving multiple criteria evaluation and the ranking/selection of alternatives. The linear assignment method is a well-known outranking method in the field of multiple criteria decision analysis. The theory of interval type-2 fuzzy sets is useful for addressing the uncertainty and imprecision associated with a subjective environment. In this paper, the key feature of the proposed method is the incorporation of the extended concept of likelihoods of fuzzy preference relations between interval type-2 trapezoidal fuzzy numbers into the main structure of the linear assignment methodology. An effective ranking procedure using the optimal membership degree determination method is proposed to determine criterion-wise preference rankings of the alternatives. The proposed method establishes the novel concepts of an (adjusted) rank frequency matrix and an (adjusted) rank contribution matrix to combine the relative performances of the alternatives in terms of each criterion. Based on a signed distance comparison approach, this paper constructs a likelihood-based assignment model to obtain an aggregate ranking of the alternatives that is in the closest agreement with the criterion-wise preferences of the alternatives. The feasibility and applicability of the proposed method are illustrated with two practical multiple criteria decision-making applications concerning the selection of landfill sites and the selection of treatment options. Finally, a comparative analysis with other relevant methods is conducted to validate the effectiveness and advantages of the current methods in decision aiding.