Optimizing linear functions over novel fuzzy relation equations: Structure, feasibility, and global solutions

Document Type : Research Paper

Authors

1 School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran.

2 Department of Mathematics, Faculty of Mathematics and Computer Science, University of M¨ unster, M¨ unster, Germany.

3 Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

4 Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Bratislava, Slovakia.

5 Palack´ y University Olomouc, Faculty of Science, Dept. Algebra and Geometry, 17. listopadu 12, 771 46 Olomouc, Czech Republic

Abstract

We investigate the linear objective function optimization problem constrained by a new system of fuzzy relation
equations, utilizing the minimum t-norm for fuzzy compositions. Our findings reveal that the feasible region is
characterized as a finite union of closed convex cells. We provide necessary and sufficient conditions to determine
the problem’s feasibility. To streamline optimization, seven novel rules are proposed, on which an algorithm is based
to achieve a global optimum. Notably, a specific instance of our problem is shown to be equivalent to the well-known
minimal vertex cover problem. The efficacy of our algorithm is demonstrated through a concrete example.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 22, Issue 3
May and June 2025
Pages 151-179

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