Solving nonlinear optimization problems with bipolar fuzzy relational equation constraints

• Main Authors: Jian Zhou, Ying Yu, Yuhan Liu, Yuanyuan Zhang
• Format: Article
• Language: English
• Published: SpringerOpen 2016-04-01
• Series: Journal of Inequalities and Applications
• Subjects: fuzzy relational equations; nonlinear optimization; mixed integer optimization
• Online Access: http://link.springer.com/article/10.1186/s13660-016-1056-6

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.