A fuzzy multi-criteria decision-making model by associating technique for order preference by similarity to ideal solution with relative preference relation

Generally, classical multi-criteria decision-making (MCDM) methods were extended to encompass uncertainty and vagueness of messages under fuzzy environment for solving decision-making problems, especially for technique for order preference by similarity to ideal solution (TOPSIS). In the fuzzy extension of TOPSIS, fuzzy numbers comparison and aggregation based on fuzzy preference relation are important issues to compute distance values between alternatives and ideal (or anti-ideal) solution or rank feasible alternatives, because lots of messages are reserved by fuzzy preference relation. However, fuzzy preference relation on pair-wise comparison is commonly too complex to calculate. To avoid the drawback, we use a relative preference relation improved from fuzzy preference relation in the fuzzy extension of TOPSIS for computing distance values between alternatives and ideal (or anti-ideal) solution, or obtaining relative closeness coefficients of alternatives. Thus the relative preference relation on fuzzy numbers will be associated with TOPSIS under fuzzy environment to develop a fuzzy multi-criteria decision-making (FMCDM) model. Through the association above, FMCDM problems can be easily solved by the model. Further, we compare the proposed model with other methods to demonstrate the model’s feasibility and rationality.