An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis

This paper proposes an approach to interval-valued intuitionistic stochastic multi-criteria decision-making (MCDM) problems using set pair analysis. This approach is applicable to MCDM problems in which the criterion weights are incomplete or the weights are certain, and evaluation values of alternatives take the form of interval-valued intuitionistic stochastic variables. To begin with, we briefly introduce the concepts of interval-valued intuitionistic fuzzy set, interval-valued intuitionistic stochastic variable, and set pair analysis. Then, we define a new similarity measure between interval-valued intuitionistic fuzzy numbers, after which we establish a mathematical programming model based on the technique for order preference by similarity to an ideal solution method and the maximizing deviation method in order to determine criterion weights. We then use connection degree to represent interval-valued intuitionistic fuzzy information and transform the interval-valued intuitionistic stochastic decision-making matrixes into corresponding connection degree matrixes. Finally, we rank the alternatives according to the value of set pair potential after calculating the connection degree of each alternative. After defining the method, we apply it to a practical decision-making problem and provide a comparison analysis with existing methods to illustrate the feasibility and validity of the proposed approach.