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

Ana Pradera; Sebastia Massanet; Daniel Ruiz; Joan Torrens

doi:10.2991/ijcis.d.200205.002

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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}

¹Departamento 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

²Soft Computing, Image Processing and Aggregation (SCOPIA) Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, 07122 Palma, Spain

³Balearic 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: 10.2991/ijcis.d.200205.002 How 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.
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: 2020/02/14
ISSN (Online): 1875-6883
ISSN (Print): 1875-6891
DOI: 10.2991/ijcis.d.200205.002 How to use a DOI?
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

ris enw bib

TY  - JOUR
AU  - Ana Pradera
AU  - Sebastia Massanet
AU  - Daniel Ruiz
AU  - Joan Torrens
PY  - 2020
DA  - 2020/02/14
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  - 10.2991/ijcis.d.200205.002
ID  - Pradera2020
ER  -

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