Approximate Reasoning in Fuzzy Resolution

Banibrata Mondal, Swapan Raha

Department of Mathematics, Visva-Bharati University, Santiniketan, West Bengal, India.

DOI: 10.4236/ijis.2013.32010                

Abstract

Resolution is an useful tool for mechanical theorem proving in modelling the refutation proof procedure, which is mostly used in constructing a “proof” of a “theorem”. An attempt is made to utilize approximate reasoning methodology in fuzzy resolution. Approximate reasoning is a methodology which can deduce a specific information from general knowledge and specific observation. It is dependent on the form of general knowledge and the corresponding deductive mechanism. In ordinary approximate reasoning, we derive from A→B and by some mechanism. In inverse approximate reasoning, we conclude from A→B and using an altogether different mechanism. An important observation is that similarity is inherent in fuzzy set theory. In approximate reasoning methodology-similarity relation is used in fuzzification while, similarity measure is used in fuzzy inference mechanism. This research proposes that similarity based approximate reasoning-modelling generalised modus ponens/generalised modus tollens—can be used to derive a resolution—like inference pattern in fuzzy logic. The proposal is well-illustrated with artificial examples.

Keywords

Approximate Reasoning; Similarity Index; Similarity Based Reasoning; Resolution Principle

Conflicts of Interest

The authors declare no conflicts of interest.

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