A non-linear generalization of optimization problems subjected to continuous max-t-norm fuzzy relational inequalities

• Published in: Soft computing (Berlin, Germany) Vol. 28; no. 5; pp. 4025 - 4036
• Main Authors: Ghodousian, Amin, Rad, Babak Sepehri, Ghodousian, Oveys
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2024; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Computational Intelligence; Control; Engineering; Feasibility; Fuzzy sets; Inequalities; Linear functions; Linear programming; Mathematical Logic and Foundations; Mechatronics; Optimization; Peer to peer computing; Polynomials; Robotics; Fuzzy relational inequalities; Latticized linear programming; Continuous t-norms; Continuous s-norms; Non-linear optimization
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-023-09376-2

Recently, the latticized linear programming problems subjected to max–min and max-product fuzzy relational inequalities (FRI) have been studied extensively and have been utilized in many interesting applications. In this paper, we introduce a new generalization of the latticized optimization problems whose objective is a non-linear function defined by an arbitrary continuous s-norm (t-conorm), and whose constraints are formed as an FRI defined by an arbitrary continuous t-norm. Firstly, the feasible region of the problem is completely characterized and two necessary and sufficient conditions are proposed to determine the feasibility of the problem. Also, a general method is proposed for finding the exact optimal solutions of the non-linear model. Then, to accelerate the general method, five simplification techniques are provided that reduce the work of computing an optimal solution. Additionally, a polynomial-time method is presented for solving general latticized linear optimization problems subjected to the continuous FRI. Moreover, an application of the proposed non-linear model is described where the objective function and the FRI are defined by the well-known Lukasiewicz s-norm and product t-norm, respectively. Finally, a numerical example is provided to illustrate the proposed algorithm.