Solving Bipolar Max-Tp Equation Constrained Multi-Objective Optimization Problems

Abstract

This work considers the multi-objective optimization problem constrained by a system of bipolar fuzzy relational equations with max-product composition. An integer optimization based technique for order of preference by similarity to the ideal solution is proposed for solving such a problem. Some critical features associated with the feasible domain and optimal solutions of the bipolar max-T p equation constrained optimization problem are studied. An illustrative example verifying the idea of this paper is included. This is the first attempt to study the bipolar max-T equation constrained multi-objective optimization problems from an integer programming viewpoint.

Bipolar equations on complete distributive symmetric residuated lattices: The case of a join-irreducible right-hand side

“…Various studies have been devoted to the resolution of bipolar max- * equations on the real unit interval, in particular when * is one of the three basic t-norms: the minimum operation [24,25], the algebraic product [9,11,22] and the Łukasiewicz t-norm [26,32,33]. In all cases, the involutive negation considered is the standard negation ¬ S defined by…”

Multiple objective optimization for systems with addition–min fuzzy relational inequalities

“…Moreover, a variety of multiple objective optimization problem based on fuzzy relational equations are still developed by researchers. Hu et al (2016) considered the multiple objective optimization problem constrained by a system of bipolar fuzzy relational equations with max-product composition, then an integer optimization based technique for order of preference by similarity to the ideal solution (TOPSIS) was proposed for solving such a problem.…”

Abductive reasoning in normal residuated logic programming via bipolar max-product fuzzy relation equations

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