Optimization of linear problems subjected to the intersection of two fuzzy relational inequalities defined by Dubois-Prade family of t-norms

Abstract

In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated In doing so, the feasible region is formed by the intersection of two inequality fuzzy systems and Dubois-Prade family of t-norms which are considered as fuzzy composition. The most well-known continuous t-norms are Archimedean such as Frank, Yager, Hamacher, Sugeno-Weber and Schweizer-Sklar family. An interesting family of t-norms that is not Archimedean has been introduced by Dubois and Prade. In this paper, the resolution of the feasible region of the problem is initialy investigated when it is defined with max-Duboise-Prade composition. A necessary and sufficient condition along with three other necessary conditions are derived for determining the feasibility. of the problem. Moreover, two procedures have also been presented with the aim of simplifying the current linear problems. A method is proposed to generate random feasible max-Dubois-Prade fuzzy relational inequalities and an algorithm is accordingly presented to solve the problem. Finally, an example is described to illustrate this algorithm.