University of TehranJournal of Algorithms and Computation2476-277654220221201An algorithm to Solve the Linear Programming Problem Constrained with the Harmonicâ€“Fuzzy Relational Equalities1231359081710.22059/jac.2022.90817ENAminGhodousianFaculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran.0000-0002-9224-8470BabakSepehri RadDepartment of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran.OveysQodousianAssistant Professor in Structural Engineering, Department of Engineering, Takestan Branch, Islamic Azad
University, Takestan, Iran.Journal Article20230128In 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.https://jac.ut.ac.ir/article_90817_d77b09758784394d35f48b5dffd0213f.pdf