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## Linear optimization problem subjected to fuzzy relational equations and fuzzy constraints | ||

Iranian Journal of Fuzzy Systems | ||

مقاله 2، دوره 20، شماره 2، خرداد و تیر 2023، صفحه 1-20 اصل مقاله (1.42 M)
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شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7552 | ||

نویسندگان | ||

A. Ghodousian^{*} ؛ F. S. Yousefi
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^{}School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran | ||

چکیده | ||

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. | ||

کلیدواژهها | ||

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

مراجع | ||

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