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Title: General decomposition of fuzzy relations : semi-tensor product approach
Authors: Fan, Hongbiao
Feng, Jun-e
Meng, Min
Wang, Biao
Keywords: Engineering::Electrical and electronic engineering
Issue Date: 2020
Source: Fan, H., Feng, J., Meng, M. & Wang, B. (2020). General decomposition of fuzzy relations : semi-tensor product approach. Fuzzy Sets and Systems, 384, 75-90.
Journal: Fuzzy Sets and Systems
Abstract: 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.
ISSN: 0165-0114
DOI: 10.1016/j.fss.2018.12.012
Rights: © 2019 Elsevier B.V. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:EEE Journal Articles

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