An algorithm to Solve the Linear Programming Problem Constrained with the Harmonic–Fuzzy Relational Equalities

Document Type : Research Paper

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 Assistant Professor in Structural Engineering, Department of Engineering, Takestan Branch, Islamic Azad University, Takestan, Iran.

10.22059/jac.2022.90817

Abstract

In this paper, a linear programming problem is investigated in which the feasible region is formed as the intersection of fuzzy relational equalities and the harmonic mean operator is considered as fuzzy composition. Theoretical properties of the feasible region are derived. It is proved that the feasible solution set is comprised of one maximum solution and a finite number of minimal solutions. Furthermore, some necessary and sufficient conditions are additionally presented to determine the feasibility of the problem. Moreover, an algorithm is presented to find the optimal solutions of the problem and finally, an example is described to illustrate the algorithm.

Keywords

Journal of Algorithms and Computation
Volume 54, Issue 2
December 2022
Pages 123-135

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