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

On (OP)-polynomial implications

Authors
Sebastia Massanet, Juan Vicente Riera, Daniel Ruiz-Aguilera
Corresponding Author
Sebastia Massanet
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.171How to use a DOI?
Keywords
Fuzzy implication, (OP)-polynomial implication, R-implication, exchange principle.
Abstract

The disposal of many families of fuzzy implications is crucial to handle the great number of applications these operators have. In this work, the class of fuzzy (OP)-polynomial implications is introduced as those fuzzy implications satisfying the ordering property (OP) whose expression in the region where x > y is given by a polynomial of two variables. Since not all polynomials are adequate to generate a fuzzy implication, some properties related to the values of the coefficients of the polynomial to accomplish this fact have been studied. The (OP)-polynomial implications with degree less than 2 are fully characterized. Among the implications obtained in these results, there are some well-known implications such as the ukasiewicz implication, among many others. Finally, several construction methods of these implications from other well-known families of fuzzy implications 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-15.2015.171How 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  - Sebastia Massanet
AU  - Juan Vicente Riera
AU  - Daniel Ruiz-Aguilera
PY  - 2015/06
DA  - 2015/06
TI  - On (OP)-polynomial implications
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  - 1208
EP  - 1215
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.171
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.171
ID  - Massanet2015/06
ER  -