Solving nonlinear optimization problems with bipolar fuzzy relational equation constraints

Abstract This paper considers the problem of minimizing a nonlinear objective function subject to a system of bipolar fuzzy relational equations with max- T L $T_{L}$ composition, where T L $T_{L}$ is the Łukasiewicz triangular norm. It shows that the feasible domain, i.e., the solution set of a system of bipolar fuzzy relational equations, can be reformulated as a system of 0-1 mixed integer inequalities. Consequently, such a type of optimization problems can be handled within the framework of 0-1 mixed integer optimization requiring no particular solving techniques