Fuzzy Implication Classes Satisfying a Boolean-Like Law

@inproceedings{Cruz2013FuzzyIC,
  title={Fuzzy Implication Classes Satisfying a Boolean-Like Law},
  author={Anderson Paiva Cruz and Benjam{\'i}n R. C. Bedregal and Regivan H. N. Santiago},
  booktitle={AGOP},
  year={2013}
}
Properties that are always true in the classical theory (Boolean laws) have been extended to fuzzy theory and so-called Boolean-like laws. The fact that they do not remain valid in any standard fuzzy set theory has induced a broad investigation. In this paper we show the sufficient and necessary conditions that a fundamental Boolean-like law—y ≤ I(x,y)—holds in fuzzy logics. We focus the investigation on the following classes of fuzzy implications: (S,N)-, R-, QL-, D-, (N,T)-, f-, g- and h… 

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