标题：General decomposition of fuzzy relations: Semi-tensor product approach
作者：Fan H.; Feng J.-E.; Meng M.; Wang B.
作者机构：[Fan, H] School of Mathematics, Shandong University, Jinan, 250100, China, School of Mathematics Sciences, Dezhou University, Dezhou, 253023, China;[ 更多
通讯作者地址：[Feng, J.-E] School of Mathematics, Shandong UniversityChina;
来源：Fuzzy Sets and Systems
关键词：Fuzzy relational equation; General decomposition problem; Semi-tensor product; Vector expression
摘要：This paper focuses on the general decomposition problem of fuzzy relations, which can be regarded as an extension of the common one, modeled by fuzzy relational equation (FRE) X∘X=R. The considered decomposition problem is described by an FRE X∘Y=R. For the purpose of deriving all solutions to the decomposition problem, the structure of solutions to the corresponding FRE is investigated first, and a necessary and sufficient condition for the existence of solutions is obtained. Then, based on semi-tensor product (STP) of matrices, an algebraic approach is proposed. Furthermore, all solutions to the general decomposition problem can be computed via the proposed method. In order to demonstrate the effectiveness of the presented approach, two numerical examples are given. © 2019 Elsevier B.V.