TOPSIS with fuzzy belief structure for group belief multiple criteria decision making

TOPSIS is one of the major techniques in dealing with multiple criteria decision making (MCDM) problems, and Belief Structure (BS) model and Fuzzy BS model have been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with Fuzzy BS model is proposed to solve Group Belief MCDM problems. Firstly, the Group Belief MCDM problem is structured as a fuzzy belief decision matrix in which the judgments of each decision maker are described as Fuzzy BS models, and then the Evidential Reasoning approach is used for aggregating the multiple decision makers’ judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. In order to measure the separation from the ideal belief solutions, the concept and algorithm of Belief Distance Measure are introduced to compare the difference between Fuzzy BS models. Using the Belief Distance Measure, the relative closeness and ranking index can be calculated for ranking the alternatives. A numerical example is finally given to illustrate the proposed method.

Research highlights
► TOPSIS with fuzzy belief structure model is proposed to solve group belief MCDM problems.
► Fuzzy belief decision matrix is used to formulate the decision making problem, and the Evidential Reasoning approach is used to aggregate multiple decision makers’ judgments.
► In order to compare the difference between fuzzy belief structure models, a novel belief distance measure is defined and its basic properties are proved.
► Using the belief distance measure, the relative closeness and ranking index can be calculated for ranking the alternatives.