On the T -conditionality of T -power based implications

Zuming Peng

Kybernetika (2022)

  • Volume: 58, Issue: 1, page 43-63
  • ISSN: 0023-5954

Abstract

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It is well known that, in forward inference in fuzzy logic, the generalized modus ponens is guaranteed by a functional inequality called the law of T -conditionality. In this paper, the T -conditionality for T -power based implications is deeply studied and the concise necessary and sufficient conditions for a power based implication I T being T -conditional are obtained. Moreover, the sufficient conditions under which a power based implication I T is T * -conditional are discussed, this discussions give an ideas to construct a t-norm T * such that the power based implication I T is T * -conditional.

How to cite

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Peng, Zuming. "On the $T$-conditionality of $T$-power based implications." Kybernetika 58.1 (2022): 43-63. <http://eudml.org/doc/298132>.

@article{Peng2022,
abstract = {It is well known that, in forward inference in fuzzy logic, the generalized modus ponens is guaranteed by a functional inequality called the law of $T$-conditionality. In this paper, the $T$-conditionality for $T$-power based implications is deeply studied and the concise necessary and sufficient conditions for a power based implication $I^\{T\}$ being $T$-conditional are obtained. Moreover, the sufficient conditions under which a power based implication $I^\{T\}$ is $T^\{\ast \}$-conditional are discussed, this discussions give an ideas to construct a t-norm $T^\{\ast \}$ such that the power based implication $I^\{T\}$ is $T^\{\ast \}$-conditional.},
author = {Peng, Zuming},
journal = {Kybernetika},
keywords = {$T$-power based implications; $T$-conditionality; t-norms; generalized modus ponens},
language = {eng},
number = {1},
pages = {43-63},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the $T$-conditionality of $T$-power based implications},
url = {http://eudml.org/doc/298132},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Peng, Zuming
TI - On the $T$-conditionality of $T$-power based implications
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 1
SP - 43
EP - 63
AB - It is well known that, in forward inference in fuzzy logic, the generalized modus ponens is guaranteed by a functional inequality called the law of $T$-conditionality. In this paper, the $T$-conditionality for $T$-power based implications is deeply studied and the concise necessary and sufficient conditions for a power based implication $I^{T}$ being $T$-conditional are obtained. Moreover, the sufficient conditions under which a power based implication $I^{T}$ is $T^{\ast }$-conditional are discussed, this discussions give an ideas to construct a t-norm $T^{\ast }$ such that the power based implication $I^{T}$ is $T^{\ast }$-conditional.
LA - eng
KW - $T$-power based implications; $T$-conditionality; t-norms; generalized modus ponens
UR - http://eudml.org/doc/298132
ER -

References

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