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Kybernetika 58 no. 1, 43-63, 2022

On the T-conditionality of T-power based implications

Zuming PengDOI: 10.14736/kyb-2022-1-0043

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 IT being T-conditional are obtained. Moreover, the sufficient conditions under which a power based implication IT is T∗-conditional are discussed, this discussions give an ideas to construct a t-norm T∗ such that the power based implication IT is T∗-conditional.

Keywords:

t-norms, T-power based implications, T-conditionality, generalized modus ponens

Classification:

03E72, 03B52

paper.pdf

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