NDLI: On the Generalized Cross-Law of Importation in Fuzzy Logic

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On the Generalized Cross-Law of Importation in Fuzzy Logic

Content Provider	MDPI
Author	Zhao, Yifan Li, Kai
Copyright Year	2020
Description	Recently, Baczyński et al. introduced two pexider-type generalisations of the law of importation in fuzzy logic, i.e., $I(C(x,α),y)=I(x,J(α,y)$ (GLI) and $I(C(x,α),y)=J(x,I(α,y)$ (CLI), where C is a fuzzy conjunction and I, J are fuzzy implications. However, (CLI) has not been adequately investigated so far. In this paper, we firstly show that (CLI) can be derived from the α-migrativity of an R-implication obtained from an α-migrative t-norm. Secondly, the relationships between the satisfaction of the law of importation (LI) by the pairs (C, I) or (C, J) and the satisfaction of (CLI) by the triple (C, I, J) are studied. Moreover, some necessary conditions of (CLI) are given. Finally, we study (CLI) under three different perspectives.
Starting Page	1681
e-ISSN	22277390
DOI	10.3390/math8101681
Journal	Mathematics
Issue Number	10
Volume Number	8
Language	English
Publisher	MDPI
Publisher Date	2020-10-01
Access Restriction	Open
Subject Keyword	Mathematics Artificial Intelligence Fuzzy Logic Connectives Fuzzy Implication Law of Importation Α-migrativity T-norm
Content Type	Text
Resource Type	Article

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