JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (5): 99-111.doi: 10.6040/j.issn.1671-9352.0.2018.381

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(O,N)-implication and its characterizations

LIU Xiao, ZHOU Hong-jun*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xian, 710119, Shaanxi, China
  • Published:2019-05-09

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Abstract: Fuzzy implications paly an important role in both theoretic and applied communities of fuzzy set theory. The well-known fuzzy implications are usually constructed in appropriate ways from t-norms, t-conorms and fuzzy negations, and according to construction methods, they can be roughly classified into five classes, namely (S,N)-implications, R-implications, QL-implications, Yagers implications and ordinal sum implications. We introduce a new class of implications, called (O,N)-implications, generated from overlap functions O and fuzzy negations N inspired by the classical tautology p→q≡(p∧q). We discuss the properties of (O,N)-implications and give some characterizations of them. Finally, grouping functions and overlap functions generated by (O,N)-implications and fuzzy negations are investigated.

Key words: fuzzy implication, (O,N)-implication, overlap function, fuzzy negation

CLC Number: 

  • O142
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