A Study On Multi-criteria Decision-making Method In Type-2Fuzzy Environment

Abstract:Multi-criteria decision-making problems are widely existed in the practical life. Moreover, type-2fuzzy set as an extension of type-1fuzzy set can capture more uncertainty than type-1fuzzy set. Based on summarizing and analyzing research achievements of predecessors, this article discussed the multi-criteria decision-making problems in which the criteria evaluating values take in the forms of type-2fuzzy set and provide several corresponding decision-making methods. The main works shows as follows:(1) After analyzing the shortcomings of the existed computational model for type-1fuzzy number, a new computational model is proposed for type-1fuzzy number, and then the proposed computational model is extended for interval type-2fuzzy number (IT2FN). Based on the proposed operational rules of IT2FN, several aggregating operator of IT2FN are defined, including data-dependent operators and criteria-related operators, and some desirable properties of them is also discussed. To measure the difference among IT2FNs, some distance measure functions for IT2FN are defined based on the distance axiomatization formula and then a weight determination method based on the interval type-2fuzzy distance functions are provide for group decision-making problem. Finally, two corresponding group decision-making method based on IT2FN are provided, and illustrative examples are provide to show the feasibility and validation of the proposed methods.(2) Balancing the computational simplicity and the capacity of capturing uncertainty, a new well-regulated type-2fuzzy set, i.e. Three-parameter type-2fuzzy number (TT2FN) are defined. The operational rule and ranking value function for TT2FN are also discussed. Several aggregating operators for TT2FNs are provided and a corresponding multi-criteria decision-making method based on TT2FN is proposed. An illustrative example is provided that applying the proposed method for the fuzzy linguistic decision-making problem. The illustrative example shows that the TT2FN can capture more uncertainty than IT2FN and decision-makers can choose different weighting function and optimistic parameter when calculating the ranking value of TT2FN and then get different ranking results. A comparative study with existed method is also conducted to show the character of the proposed method and its validation.(3) Based on the classical outranking theory, a new outranking MCDM method in the type-2fuzzy environment is proposed. First, the outranking relation for type-1fuzzy set is proposed. Then, based on the wavy representation theory of type-2fuzzy set, the proposed outranking relation is extend to IT2FN and TT2FN. Based on the defined outranking relation for type-2fuzzy number, a new outranking MCDM method that similar with Promethee method is proposed. In the proposed method, a group of type-1fuzzy numbers is randomly generated for each type-2fuzzy number. The illustrative example show that when different number of the type-1fuzzy number are generated for each type-2number, the ranking results of the proposed decision-making method show different stability, which provide the decision-makers an excellent analysis tool for decision-making.