LP problems constrained with D-FRIs

Document Type : Research Paper

Authors

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

2 University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation

Abstract

In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Dombi family of t-norms is considered as fuzzy composition. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. The resolution of the feasible region of the problem is firstly investigated when it is defined with max-Dombi composition. Based on some theoretical results, a necessary and sufficient condition and three other necessary conditions are derived for determining the feasibility. Moreover, in order to simplify the problem, some procedures are presented. It is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. A method is proposed to generate random feasible max-Dombi fuzzy relational inequalities and an algorithm is presented to solve the problem. Finally, an example is described to illustrate these algorithms.

Keywords

Journal of Algorithms and Computation
Volume 50, issue 2 - Serial Number 2
December 2018
Pages 59-79

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