Characterizations of fuzzy implications satisfying the Boolean-like law $y\leq I(x,y)$

Anderson CruzBenjamín BedregalRegivan Santiago

Properties valid on the classical theory (Boolean laws) have been extended to fuzzy set theory and so-called Boolean-like laws. The fact that they are not always valid in any standard fuzzy set theory induced a wide investigation. In this paper we show the sufficient and necessary conditions that the Boolean-like law $yleq I(x,y)$ holds in fuzzy logic. We focus the investigation on the following classes of fuzzy implications: (S,N)-, R-, QL-, D-, (N,T)- and $h$-implications.

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