On the Use of Conjunctors With a Neutral Element in the Modus Ponens Inequality
- https://doi.org/10.2991/ijcis.d.200205.002How to use a DOI?
- Modus ponens, Fuzzy implication function, Conjunctor, Neutral element, Semi-copula, T-norm, Uninorm
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 . 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 to satisfy the Modus Ponens with respect to a conjunctor with neutral element . Although the most usual families of fuzzy implication functions do not satisfy all these properties, other possibilities for 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 are characterized. The particular case of , that provides semi-copulas, is studied separately, retrieving many known results that can be easily derived from the current study.
- © 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 -