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On the Generalized Cross-Law of Importation in Fuzzy Logic

Author

Listed:
  • Yifan Zhao

    (School of Cyber Security and Computer, Hebei University, Baoding 071002, China)

  • Kai Li

    (School of Cyber Security and Computer, Hebei University, Baoding 071002, China)

Abstract

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.

Suggested Citation

  • Yifan Zhao & Kai Li, 2020. "On the Generalized Cross-Law of Importation in Fuzzy Logic," Mathematics, MDPI, vol. 8(10), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1681-:d:422577
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