Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology

Fuzzy relational equations and the covering problem

Authors
Qing-quan Xiong, Qian-yu Shu
Corresponding Author
Qing-quan Xiong
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.14How to use a DOI?
Keywords
Fuzzy relational equation, Maximal solutions, Covering problem, Irredundant covering
Abstract

The work considers the problem of solving a system of fuzzy relational equations with inf-implication composition and introduces the concepts of a characteristic matrix and attainable components. It is first shown that solving the system is closely related with the covering problem. Further, it is proved that maximal solutions of the system correspond to irredundant coverings of the characteristic matrix. At last, the necessary and sufficient conditions that the system has a unique(maximal) solution are given.

Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
Series
Advances in Intelligent Systems Research
Publication Date
June 2015
ISBN
978-94-62520-77-6
ISSN
1951-6851
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.14How to use a DOI?
Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Qing-quan Xiong
AU  - Qian-yu Shu
PY  - 2015/06
DA  - 2015/06
TI  - Fuzzy relational equations and the covering problem
BT  - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 77
EP  - 84
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.14
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.14
ID  - Xiong2015/06
ER  -