A defender-attacker game with intuitionistic fuzzy payoffs

In this paper, a defender-attacker game is considered. This game, also called a security game, is a game containing two players: a defender and an attacker. It is assumed that the payoffs of game are imprecise, and they are expressed as the intuitionistic fuzzy numbers. The problem is formulated as a bi-level programming with intuitionistic fuzzy coefficients. The nearest interval approximation of the intuitionistic fuzzy numbers is used to convert the problem into a bi-level programming problem with interval coefficients. Then, Karush-Kuhn-Tucker conditions for interval-valued problems are applied to the problem. These conditions transforms the problem to a single-level programming. Finally, a method is proposed to obtain the game solution. Validity and applicability of the method are illustrated by a practical example.

Keywords:

Security game , Bi-level programming , Intuitionistic fuzzy , Defender-attacker game.