International Journal of Computational Intelligence Systems

Volume 13, Issue 1, 2020, Pages 201 - 211

On the Use of Conjunctors With a Neutral Element in the Modus Ponens Inequality

Authors
Ana Pradera1, *, Sebastia Massanet2, 3, Daniel Ruiz2, 3, Joan Torrens2, 3
1 Departamento de Ciencias de la Computación, Arquitectura de Computadores, Lenguajes y Sistemas Informáticos y Estadística e Investigación Operativa, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
2 Soft Computing, Image Processing and Aggregation (SCOPIA) Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, 07122 Palma, Spain
3 Balearic Islands Health Research Institute (IdISBa), 07010 Palma, Spain
*Corresponding author. Email: ana.pradera@urjc.es
Corresponding Author
Ana Pradera
Received 14 May 2019, Accepted 4 February 2020, Available Online 14 February 2020.
DOI
https://doi.org/10.2991/ijcis.d.200205.002How to use a DOI?
Keywords
Modus ponens, Fuzzy implication function, Conjunctor, Neutral element, Semi-copula, T-norm, Uninorm
Abstract

The inference rule of Modus Ponens has been extensively investigated in the framework of approximate reasoning, especially for the case of t-norms. Recently, more general kinds of conjunctors have also been considered, like semi-copulas, copulas, and conjunctive uninorms. A common feature of all these kinds of conjunctors is the fact that they have a neutral element e]0,1]. This paper is devoted to the study of Modus Ponens for conjunctors with a neutral element with no additional conditions. Many properties are proved to be necessary for a fuzzy implication function I to satisfy the Modus Ponens with respect to a conjunctor with neutral element e]0,1]. Although the most usual families of fuzzy implication functions do not satisfy all these properties, other possibilities for I are presented showing many new examples and generalizing some already known results on this topic. Moreover, all fuzzy implication functions satisfying the Modus Ponens with respect to the least (and with respect to the greatest) conjunctor with neutral element e]0,1[ are characterized. The particular case of e=1, that provides semi-copulas, is studied separately, retrieving many known results that can be easily derived from the current study.

Copyright
© 2020 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
13 - 1
Pages
201 - 211
Publication Date
2020/02
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
https://doi.org/10.2991/ijcis.d.200205.002How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Ana Pradera
AU  - Sebastia Massanet
AU  - Daniel Ruiz
AU  - Joan Torrens
PY  - 2020
DA  - 2020/02
TI  - On the Use of Conjunctors With a Neutral Element in the Modus Ponens Inequality
JO  - International Journal of Computational Intelligence Systems
SP  - 201
EP  - 211
VL  - 13
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.200205.002
DO  - https://doi.org/10.2991/ijcis.d.200205.002
ID  - Pradera2020
ER  -