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Keywords:
$T$-power based implications; $T$-conditionality; t-norms; generalized modus ponens
$T$-power based implications; $T$-conditionality; t-norms; generalized modus ponens
Summary:
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.
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