We consider a multiple-rule, generalized modus ponens inference scheme, with an interpretation based on compositional rule of inference (CRI) and a residuated implication. We show that such a system is equivalent, as far as CRI is concerned, to a system that satis5es the “basic requirement for fuzzy reasoning”, proposed by Turksen and Tian (Fuzzy Sets and Systems 58 (1993) 3–40). We establish a...

We present a tool-supported framework for proving that the composition of the behaviors of the separate parts of a complex system ensures a desired global property of the overall system. A compositional inference rule is formally introduced and encoded in the logic of the PVS theorem prover. Methodological considerations on the usage of the inference rule are presented, and the framework is the...

This paper partially considers the annoying problem of reaching outputs contradictory with the inputs in an inference process. This problem is studied in cases in which there is more than one rule conducted by means of the Compositional Rule of Fuzzy Inference and more than one universe of discourse. We suggest to do some restrictions on the inputs to reach safe inferences when using Mandani-La...

The main condition of the differently implicational inferencealgorithm is reconsidered from a contrary direction, which motivatesa new fuzzy inference strategy, called the double fuzzyimplications-based restriction inference algorithm. New restrictioninference principle is proposed, which improves the principle of thefull implication restriction inference algorithm. Furthermore,focusing on the ...

. By using special group of fuzzy operators like distance based operators or uninorms a novel reasoning method appears, which is based on residual operators of uninorms. The 3-dimensional representation of the compositional rule of inference will be given.

This paper is devoted to the derivation of exact calculation formulas for the compositional rule of inference under Archimedean t-norms, when both the observation and the relation parts are given by Hellendoorn’s φ-function [6].

This paper proposes a novel approach to similarity-based approximate reasoning in an interval-valued fuzzy environment. In a rule-based system, an ‘if ... then ...’ rule can be translated into an intervalvalued fuzzy relation by suitable implication operations. The similarity grade between a case and the antecedent of a rule is computed and used to modify the relation. A consequent is derived f...

A concept called the decomposition of multivariable control rules is presented. Fuzzy control is the application of the compositional rule of inference and it is shown how the inference of the rule base with complex rules can be reduced to the inference of a number of rule bases with simple rules. A fuzzy logic based controller is applied to a simple magnetic suspension system. The controller h...

In the approximate fuzzy reasoning the covering over of fuzzy rule base input and rule premise of a rule determines the importance of that fuzzy rule and the rule output as well. An axiom system has been created, describing the relationship between the fuzzy rule base system, rule input and rule output. By using distance-based operators a novel reasoning method appears by the compositional rule...