Minimizing a linear objective function under a max-overlap function fuzzy relational equation constraint

• Published in: Fuzzy sets and systems Vol. 447; pp. 1 - 21
• Main Author: Fang, Bo Wen
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.10.2022
• Subjects: Fuzzy optimization; Fuzzy relational equation; Max-overlap function composition; Max-overlap function composition; Fuzzy relational equation; Fuzzy optimization
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2021.12.005

Max-t-norm compositions are commonly utilized to optimize a linear objective function subject to fuzzy relational equations, especially, max-min and max-product compositions. However, the associativity is not forcefully needed in many cases. In this paper, the max-overlap function composition is considered for the same optimization model. Then some properties of the solution set are obtained. According to these properties, the characterization of the optimal solution for the optimization model is proposed. Furthermore, a simple value matrix with rules is proposed to reduce problem size. Thus, a solution procedure is presented for determining optimal solutions without translating such an optimization problem into two sub-problems. A numerical example is provided to illustrate the procedure.