Study of the generalized hypothetical syllogism for some well known families of fuzzy implications with respect to strict t-norm
نویسندگان
1 College of Mathematics and Statistics, Yangtze Normal University, 408100, Chongqing, PR China
2 College of Mathematics and Computer Sciences, Yangtze Normal University, 408100, Chongqing, PR China
doi
10.22111/ijfs.2024.46361.8164چکیده
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.
