Linear optimization problem subjected to fuzzy relational equations and fuzzy constraints

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Ghodousian A.; Yousef F.S.

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Journal Paper

Paper Information

Journal: Iranian Journal of Fuzzy Systems Year:2023 | Volume:20 | Issue:2 Page(s): 1-20

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Information Journal Paper

Title

Linear optimization problem subjected to fuzzy relational equations and fuzzy constraints

Author(s)

Ghodousian A. | Yousef F.S. | Issue Writer Certificate

Keywords

Fuzzy relational equations fuzzy constraints continuous t-norms linear optimization PSO algorithm

Abstract

In this paper, we introduce a new optimization problem with respect to a generalized form of fuzzy relational equations (FRE) in which fuzzy equality replaces ordinary equality in the constraints (FRE-FC). Fuzzy constraints enable us to attain optimal points (called super-optima in this paper) that are better solutions than those resulted from the resolution of the similar problems with ordinary equality constraints. Some structural properties of the FRE-FC problems are studied and a new formulation is presented in which the fuzzy constraints (equations) are precisely modeled. Subsequently, a new PSO-based algorithm is proposed to solve the FRE-FC problems defined by arbitrary continuous t-norms. The proposed algorithm is tested with different test problems generated by ten well-known continuous t-norms used in the literature. Moreover, the generated solutions for these problems, are also compared with some well-known meta-heuristic methods which have been applied to many practical optimization problems. It is shown that the optimal intensity of electromagnetic radiation problem can be formed as a special case of FRE-FC problems in which fuzzy composition is defied by max-product composition.

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