A decision variable-based combinatorial optimization approach for interval-valued intuitionistic fuzzy MAGDM

Abstract

Abstract Some interval-valued intuitionistic fuzzy information MAGDM problems with combinatorial optimization characteristics have so many feasible alternatives that they can hardly be enumerated and evaluated. Moreover, due to the lack of quantitative functions, they are difficult to be solved with traditional combinatorial optimization methods. Therefore, by combining the MAGDM with combinatorial optimization, we propose a decision variable-based combinatorial optimization approach for the purpose of solving the interval-valued intuitionistic fuzzy MAGDM problems in this paper. Firstly, the utility evaluation matrix of decision maker is defined and the interval-valued intuitionistic fuzzy weighted average operator is used to aggregate utility evaluation matrices with decision makers’ preference information. Then, the 0–1 integer decision variable is introduced and a combinatorial optimization model is established for the interval-valued intuitionistic fuzzy MAGDM problem. For the purpose of comparison, a multi-attribute decision-making method based on the weighted relative distance is adopted to rank different alternatives. Besides, an artificial bee colony algorithm improved by integer encoding, ranking selection and elite guidance is used to solve the combinatorial optimization model. Finally, two applications of the approach are proposed: research group dispatch and group weapon-group target assignment. Through the comparison of the algorithms, the feasibility of the proposed approach was verified.