Fuzzy inference with fuzzy implications satisfying generalized hypothetical syllogism

Fuzzy inference has been applied widely in many fields, such as artificial intelligence, decision-making, classification, and so on. Generalized hypothetical syllogism (GHS), as a generalization of hypothetical syllogism (HS) in classical logic, can measure the validity of compositional rule of inference (CRI) method. To promote the capability of CRI method, this paper mainly studies the GHS property of well-known fuzzy implications with a t-norm and constructs a CRI method based on the GHS property. First, some t-norms are found for some R-implications, (S, N)-implications and QL-implications, such that they satisfy the GHS property, respectively. And then, it is revealed that continuous (S, N)-implications generated by strict t-conorms, f-implications with \(f(0)=\infty \) $f(0)=\infty$ , and g-implications with \(g(1)=\infty \) $g(1)=\infty$ do not satisfy the GHS property with any t-norm. Finally, we propose a CRI method using the fuzzy implications which satisfy the GHS property. Two examples are also provided to illustrate our proposed method.