Multiobjective security game with fuzzy payoffs

Document Type : Original Manuscript


1 Researcher in Army command and staff university

2 Department of Mathematics, University of Birjand, Birjand, Iran

3 Department of Industrial Engineering, Birjand University of Technology, Birjand, Iran.


A multiobjective security game problem with fuzzy payoffs is studied in this paper. The problem is formulated as a bilevel programming problem with fuzzy coefficients. Using the idea of nearest interval approximation of fuzzy numbers, the problem is transformed into a bilevel programming problem with interval coefficients. The Karush-Kuhn-Tucker conditions is applied then to reduce the problem to an interval multiobjective single-level problem. It is shown that the solutions of this problem are obtained by solving a single-objective programming problem. Validity and applicability of the method are illustrated by a practical example. 


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