Journal of Algorithms and Computation
Open Access

On the resolution of LP-FRE defined by the convex combination operator

Document Type : Research Paper

Authors

Amin Ghodousian 1
parsa hadadian 2

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

https://doi.org/10.22059/jac.2022.88806
Abstract
In this paper, a linear programming problem is investigated in which the feasible region is formed as a special type of fuzzy relational equalities (FRE). In this type of FRE, fuzzy composition is considered as the convex combination operator. It is proved that the feasible region of the problem can be written by one maximum solution and a finite number of minimal solutions. Some theoretical properties of the feasible region are derived and some necessary and sufficient conditions are also presented to determine the feasibility of the problem. Based on some structural properties of the problem, an algorithm is presented to find the optimal solutions and finally, an example is described to illustrate the algorithm.

Keywords

Fuzzy relational equalities
mean operators
fuzzy compositions
linear programming
Journal of Algorithms and Computation
Volume 54, Issue 1
June 2022
Pages 175-186

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