Duality of optimization problems with generalized fuzzy relation equation and inequality constraints

A generalization of fuzzy relation equations and inequalities is introduced. An explicit method for solving optimization problems, the feasible set of which is described by a system of generalized fuzzy relation equations and inequalities, is considered. The objective function of the problems is equal to the maximum of continuous increasing functions of one variable. A duality concept for such problems is proposed. The problems are considered in a finitely dimensional space.