TY - JOUR ID - 7978 TI - Solving a non-convex non-linear optimization problem constrained by fuzzy relational equations and Sugeno-Weber family of t-norms JO - Journal of Algorithms and Computation JA - JAC LA - en SN - 2476-2776 AU - Ghodousian, Amin AU - Ahmadi, A. AU - Dehghani, A. AD - Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran Y1 - 2017 PY - 2017 VL - 49 IS - 2 SP - 63 EP - 101 KW - Fuzzy relational equations KW - nonlinear optimization KW - genetic algorithm DO - 10.22059/jac.2017.7978 N2 - Sugeno-Weber family of t-norms and t-conorms is one of the most applied one in various fuzzy modelling problems. This family of t-norms and t-conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t-conorms were suggested as addition rules by Sugeno for so-called  $\lambda$–fuzzy measures. In this paper, we study a nonlinear optimization problem where the feasible region is formed as a system of fuzzy relational equations (FRE) defined by the Sugeno-Weber t-norm. We firstly investigate the resolution of the feasible region when it is defined with max-Sugeno-Weber composition and present some necessary and sufficient conditions for determining the feasibility of the problem. Also, two procedures are presented for simplifying the problem. Since the feasible solutions set of FREs UR - https://jac.ut.ac.ir/article_7978.html L1 - https://jac.ut.ac.ir/article_7978_699476726464c0890fc1bd731369b4c2.pdf ER -