General decomposition of fuzzy relations : semi-tensor product approach

• Main Authors: Fan, Hongbiao, Feng, Jun-e, Meng, Min, Wang, Biao
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2021
• Subjects: Engineering::Electrical and electronic engineering; General Decomposition Problem; Fuzzy Relational Equation
• Online Access: https://hdl.handle.net/10356/151512
• Institution: Nanyang Technological University

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.