General decomposition of fuzzy relations : semi-tensor product approach
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 d...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/151512 |
| _version_ | 1824455507066224640 |
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| author | Fan, Hongbiao Feng, Jun-e Meng, Min Wang, Biao |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Fan, Hongbiao Feng, Jun-e Meng, Min Wang, Biao |
| author_sort | Fan, Hongbiao |
| collection | NTU |
| description | 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. |
| first_indexed | 2025-02-19T03:39:18Z |
| format | Journal Article |
| id | ntu-10356/151512 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:39:18Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1515122021-06-29T06:03:13Z General decomposition of fuzzy relations : semi-tensor product approach Fan, Hongbiao Feng, Jun-e Meng, Min Wang, Biao School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering General Decomposition Problem Fuzzy Relational Equation 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. This work was partially supported by NNSF of China (61773371,61877036). 2021-06-29T06:03:13Z 2021-06-29T06:03:13Z 2020 Journal Article 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. https://dx.doi.org/10.1016/j.fss.2018.12.012 0165-0114 0000-0001-6892-6035 0000-0002-2192-6481 https://hdl.handle.net/10356/151512 10.1016/j.fss.2018.12.012 2-s2.0-85059345956 384 75 90 en Fuzzy Sets and Systems © 2019 Elsevier B.V. All rights reserved. |
| spellingShingle | Engineering::Electrical and electronic engineering General Decomposition Problem Fuzzy Relational Equation Fan, Hongbiao Feng, Jun-e Meng, Min Wang, Biao General decomposition of fuzzy relations : semi-tensor product approach |
| title | General decomposition of fuzzy relations : semi-tensor product approach |
| title_full | General decomposition of fuzzy relations : semi-tensor product approach |
| title_fullStr | General decomposition of fuzzy relations : semi-tensor product approach |
| title_full_unstemmed | General decomposition of fuzzy relations : semi-tensor product approach |
| title_short | General decomposition of fuzzy relations : semi-tensor product approach |
| title_sort | general decomposition of fuzzy relations semi tensor product approach |
| topic | Engineering::Electrical and electronic engineering General Decomposition Problem Fuzzy Relational Equation |
| url | https://hdl.handle.net/10356/151512 |
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