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

Residual implications derived from uninorms satisfying Modus Ponens

Authors
Margarita Mas, Miquel Monserrat, Daniel Ruiz-Aguilera, Joan Torrens
Corresponding Author
Margarita Mas
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.35How to use a DOI?
Keywords
Fuzzy implication function, residual implication, Modus Ponens, uninorm.
Abstract

Modus Ponens is a key property for fuzzy implication functions that are going to be used in fuzzy inference processes. In this paper it is investigated when fuzzy implication functions derived from uninorms via residuation, usually called RUimplications, satisfy the modus ponens with respect to a continuous t-norm T, or equivalently, when they are T-conditionals. For RU-implications it is proved that T-conditionality only depends on the underlying t-norm TU of the uninorm U used to derive the residual implication and this fact leads to a lot of new solutions of the Modus Ponens property. Along the paper the particular cases when the uninorm lies in any of the most usual classes of uninorms are considered.

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-15.2015.35How 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  - Margarita Mas
AU  - Miquel Monserrat
AU  - Daniel Ruiz-Aguilera
AU  - Joan Torrens
PY  - 2015/06
DA  - 2015/06
TI  - Residual implications derived from uninorms satisfying Modus Ponens
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  - 233
EP  - 240
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.35
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.35
ID  - Mas2015/06
ER  -