2023/09/21 by Amin Ghodousian, Ghodousian, Amin, Mahdi Mollakazemiha +1
Computer Science · Engineering · #FOS: Mathematics #Fuzzy Logic and Control Systems #Infrastructure Maintenance and Monitoring #Optimization and Control (math.OC) #Vehicle Routing Optimization Methods
paper · pdf · doi:10.48550/arxiv.2309.12185
openalex publication_date 2023/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers the linear objective function optimization with respect to a novel system of fuzzy relation equations, where the fuzzy compositions are defined by the minimum t-norm. It is proved that the feasible solution set is formed as a union of the finite number of closed convex cells. Some necessary and sufficient conditions are presented to conceptualize the feasibility of the problem. Moreover, seven rules are introduced with the aim of simplifying the original problem, and then an algorithm is accordingly presented to find a global optimum. It is shown that the original problem in a special case is reduced to the well-known minimum vertex cover problem. Finally, an example is described to illustrate the proposed algorithm.