Generalized fuzzy relational inequalities as constraints for non-linear optimization problems

Ghodousian, Amin; Chopannavaz, Mohammad Sedigh; Pedrycz, Witold

doi:10.22111/ijfs.2026.54847.9719

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	Generalized fuzzy relational inequalities as constraints for non-linear optimization problems
Iranian Journal of Fuzzy Systems
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 مهر 1405 اصل مقاله (637.62 K)
نوع مقاله: Original Manuscript
شناسه دیجیتال (DOI): 10.22111/ijfs.2026.54847.9719
نویسندگان
Amin Ghodousian^* ¹؛ Mohammad Sedigh Chopannavaz²؛ Witold Pedrycz³
¹Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran.
²Department of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran.
³Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada
چکیده
The study of non-linear programming under fuzzy relational inequalities (FRI) defined by max-min and max-product t- norms has been conducted in a wide variety of fields, both theoretically and practically. The paper presents a novel system of fuzzy relational inequalities (max-FRIs) and investigates a new general class of optimization models. This optimization model has a non-linear objective function defined by a combination of an arbitrary continuous s-norm and an arbitrary continuous t-norm. Additionally, the problem constraints are based on a combination of two arbitrary continuous t-norms formed by a system of max-FRIs. We begin by examining a few important special cases of the model and their applications. A complete characterization of the feasible region is then presented, as well as two necessary and sufficient conditions for determining the problem's feasibility. Subsequently, a general method is presented for determining the exact optimal solution. Using five rules, the algorithm is accelerated to find the best solution with less computational effort. To address some practical special cases of the main problem, a polynomial-time method is presented. To aid comprehension, we provide a numerical example, where the objective function is given by a combination of the Lukasiewicz t-norm and Dubois-Prade t-norm, and the constraints are defined by a combination of the product and Yager t-norms.
کلیدواژه‌ها
Fuzzy relation inequality؛ non-linear optimization؛ continuous t-norms؛ continuous s-norms؛ latticized linear programming

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Generalized fuzzy relational inequalities as constraints for non-linear optimization problems