(T,N)-implication and its basic properties
- YU Jun-hong, ZHOU Hong-jun
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(11):
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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 Yagers 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.