Study of the generalized hypothetical syllogism for some well known families of fuzzy implications with respect to strict t-norm

Document Type : Research Paper

Authors

1 College of Mathematics and Computer Sciences, Yangtze Normal University, 408100, Chongqing, PR China

2 College of Mathematics and Statistics, Yangtze Normal University, 408100, Chongqing, PR China

Abstract

The generalized hypothetical syllogism (GHS) is an important property of fuzzy implications for its applications in approximate reasoning. Due to the complexity of the (GHS) and the variety of fuzzy implications, in this work, we study the (GHS) property with respect to a strict t-norm T for fuzzy implications which come from some well known families of fuzzy implications, viz., (S, N)-, QL-, g-, (U, N)-, (T, N)-implications. First, some results on the (GHS) for fuzzy implications are presented. Second, the (GHS) property of (S, N)-, QL-, g-, (U, N)-, and (T, N)-implications is studied. Finally, the (GHS) property for the fuzzy implications generated from old ones using the method of sup-T composition is also studied.

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Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 21, Issue 2
March and April 2024
Pages 181-200

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