Journal of Algorithms and Computation
Open Access

A comparison between the resolution and linear optimization of FREs defined by product t-norm and geometric mean operator

Document Type : Research Paper

Authors

Amin Ghodousian 1
Sara Falahatkar 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.2022.87918
Abstract
In this paper, a type of fuzzy system is firstly investigated whereby the feasible region is defined by the fuzzy relational equalities and the geometric mean as fuzzy composition. Some related basic and theoretical properties of such fuzzy relational equations are derived and the feasible region is completely determined. Also, it is proved that the feasible solutions set can be stated by one maximum solution and a finite number of minimal solutions. Moreover, a comparison is made between this region and fuzzy relational equations defined by the product t-norm. Finally, an example is described to illustrate the differences of these two FRE systems.

Keywords

Fuzzy relational equalities
fuzzy compositions
t-norm
geometric mean operator and linear optimization
Journal of Algorithms and Computation
Volume 54, Issue 1
June 2022
Pages 11-22

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