Optimization of the reducible objective functions with monotone factors subject to FRI constraints defined with continuous t-norms

Abstract

In this paper, we investigate a special kind of optimization with fuzzy relational inequalities constraints where a continuous t-norm is considered as the fuzzy composition and the objective function can be expressed as in which and are increasing and decreasing functions, respectively, and is a commutative and monotone binary operator. Some basic properties have been extended a necessary and sufficient condition is presented to realize the feasibility of the problem. Also, an algorithm is given to optimize the objective function on the region of the FRI constraints. Finally, five examples are appended with two continuous t-norms, Lukasiewicz and Yager, and different objective functions, for illustrating.