JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (11): 71-81.doi: 10.6040/j.issn.1671-9352.0.2017.164

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(T,N)-implication and its basic properties

YU Jun-hong, ZHOU Hong-jun*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Received:2017-04-17 Online:2017-11-20 Published:2017-11-17

Abstract: Fuzzy implications play a fundamental role in fuzzy logic and approximate reasoning. According to construction methods, there are mainly four classes of fuzzy implications, namely,(S,N)-implications, R-implications, QL-implications and Yagers generated implications. We introduce a new class of implications, called(T,N)-implications, generated from t-norms T and fuzzy negations N inspired by the classical tautology p→q≡(p∧q). We discuss the properties of(T,N)-implications and study some classical logic tautologies(e.g., law of importation and distributivity over t-norms or t-conorms)for (T,N)-implications. And the relationships of (T,N)-implications to f-implications, g-implications,(S,N)-implications and R-implications are investigated.

Key words: triangular norm, triangular conorm, (T,N)-implication, R-implication, g-implication, fuzzy implication, f-implication, (S,N)-implication, distributivity equation, fuzzy negation

CLC Number: 

  • O142
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