Fuzzy boolean programming problems with fuzzy costs: A general study

This paper deals with boolean linear programming problems involving coefficients in the objective function as fuzzy numbers. In the study of these problems different approaches can be proposed to use ranking fuzzy numbers methods and fuzzy preference relations obtaining auxiliary classical boolean programming problems, and to use the representation theorem obtaining a convex set with extreme points defined by the lower or upper bound of the α-level sets of the fuzzy coefficients, and consequently an auxiliary interval boolean programming problem. In this paper the authors develop and link the different approaches.