Optimizing linear functions over novel fuzzy relation equations: Structure, feasibility, and global solutions
نویسندگان
1 Department of Mathematics, Faculty of Mathematics and Computer Science, University of M¨ unster, M¨ unster, Germany.
2 Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
3 Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Bratislava, Slovakia.
4 School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran.
doi
10.22111/ijfs.2025.9295چکیده
We investigate the linear objective function optimization problem constrained by a new system of fuzzy relationequations, utilizing the minimum t-norm for fuzzy compositions. Our findings reveal that the feasible region ischaracterized as a finite union of closed convex cells. We provide necessary and sufficient conditions to determinethe problem’s feasibility. To streamline optimization, seven novel rules are proposed, on which an algorithm is basedto achieve a global optimum. Notably, a specific instance of our problem is shown to be equivalent to the well-knownminimal vertex cover problem. The efficacy of our algorithm is demonstrated through a concrete example.
