Similarity in Approximate Reasoning

This paper presents an approach to similarity based approximate reasoning that elucidates the connection between similarity and existing approaches to inference in approximate reasoning methodology. A set of axioms is proposed to compute a reasonable measure of similarity between two fuzzy sets. Such a measure of similarity is then used at different stages to derive a conclusion in approximate reasoning methodology. In the process, Zadeh’s compositional rule of inference and existing similarity based reasoning are integrated to produce the proposed mechanism of inference. As an illustration of its effectiveness the proposed mechanism is used to develop a multi-rule based fuzzy system. Based on the specificity measure of fuzzy sets, a new defuzzification scheme for similarity based fuzzy systems is proposed. Simulation results are presented for the well-known d.c. shunt motor. Copyright c © 2006 Yang’s Scientific Research Institute, LLC. All rights reserved.