A fuzzy control system which is a typical system utilizing fuzzy model is mainly using the Max-Min CRI (Compositional Rule of Inference) method by Zadeh and Mamdani for fuzzy inference. But the Max-Min CRI method suffers from drawbacks including: error-prone weighting strategy, inefficient compositional rule of inference, and subjective formulation of membership functions. Because of these prob...

The compositional rule of inference with several relations, which is the mainly used inference rule in approximate reasoning, is considered in this paper. Stability results are given and exact computational formulae are provided.

This paper provides a short introduction to the compositional rule of inference (Zadeh 1973), which is the mainly used inference rule in approximate reasoning. Stability results are given and exact computational formulas are provided.

This paper deals with Zadeh’s compositional rule of inference [12] under triangular norms: IF X is P AND X and Y have relation R, THEN Y is Q, where P and Q are fuzzy sets of the real line IR, R is a fuzzy relation on IR and the conclusion Q is defined via sup-T composition of P and R: μQ(y) = sup x∈IR T (μP (x), μR(x, y)), y ∈ IR. It is shown that (i) when the triangular norm T and the members...

The compositional rule of inference (CRI) introduced by Zadeh is widely used in approximate reasoning schemes using fuzzy sets. In this work we show that the Bandler-Kohout subproduct does possess all the important properties such as equivalent and reasonable conditions for their solvability, their interpolative properties and the preservation of the indistinguishability that may be inherent in...

The database of a rule-based systemmay contain imprecisionswhich appear in the description of the rules given by the expert. Because such an inference can not be made by the methods which use classical two valued logic or many valued logic, Zadeh in (Zadeh, 1975) and Mamdani in (Mamdani, 1977) suggested an inference rule called "compositional rule of inference". Using this inference rule, sever...

This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp antecedents; in case of fuzzy booleans this set contains only two rules. It is shown that Zadeh's ext...

Rule-driven processing is a proven way of achieving high-speed in fuzzy processing. Up to now, ruledriven architectures where designed to work with minimum or product as T-norm. Nevertheless, a Lukasiewicz T-norm is typically used with the compositional rule of inference in expert systems applications that are based on a fuzzy inference engine. This paper presents a rule-driven processing archi...

Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed by Zadeh [1] in our ...