Fuzzy implications satisfying the generalized hypothetical syllogism based on the Bandler-Kohout subproduct with semicopulas

Document Type : Research Paper


1 School of Information and Engineering, Zhejiang Ocean University, Zhoushan, 316000, China

2 Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan, 316022, China


Generalized hypothetical syllogism (GHS) plays a very important role in fuzzy inference.
Therefore, it is valuable to investigate the GHS based on the Bandler-Kohout  subproduct (BK-GHS) in order to measure the availability of fuzzy inference.  This paper aims to study the (BK-GHS) property   of some well-known fuzzy implications including (S, N)-, QL-, $f$-, $g$-, probabilistic and probabilistic S-implications in detail. We use the method of automorphism transformation to investigate (S, N)- and QL-implications and make better use of some essential properties about  $f$-, $g$-, probabilistic and probabilistic S-implications to make them satisfy (BK-GHS) with semicopulas. With these results, (BK-GHS) can be more effectively applied in practice.


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