Y. Zhang - School of Information and Engineering, Zhejiang Ocean University, Zhoushan, ۳۱۶۰۰۰, China
D. C. Li - School of Information and Engineering, Zhejiang Ocean University, Zhoushan, ۳۱۶۰۰۰, 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.

Fuzzy implication, generalized hypothetical syllogism, Semicopula, Bandler-Kohout subproduct