Optimization problems constrained by generalized fuzzy relational inequalities

Document Type : Original Manuscript

Authors

1 Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran.

2 Department of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran.

3 Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada

Abstract

The study of non-linear programming under fuzzy relational inequalities (FRI) defined by max-min and max-product t-norms have been studied 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.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 6
November and December 2026
Pages 1-16

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