Fuzzy Inference Based on Similarity Measure

Abstract

According to the understanding in mathematics essence of approximate reasoning, we study the fuzzy inference course based on similarity measure, propose a new approximate reasoning algorithm (SMTT fuzzy inference algorithm) based on similarity measure and transformation by “peak drift” of fuzzy sets, and introduce the general formal expression of this fuzzy inference algorithm. This algorithm avoids the “relational composition” process which is often in doubt in CRI algorithm, but replaces it with transformation by “peak drift” based on similarity measure to generate the inference conclusion. Moreover, we study the relationship between this fuzzy inference algorithm and interpolating algorithm, and prove that this fuzzy inference algorithm is equivalent with the true value deferral method-fuzzy inference interpolating algorithm in a special circumstance. This algorithm not only has the characters of convenient calculation and good nature, but also solves the questions existing in the true value deferral method-fuzzy inference interpolating algorithm satisfactorily, thereby, the rationality of the true value deferral method -fuzzy inference interpolating algorithm is added to explain.KeywordsFuzzy inferencesimilarity measureCRI algorithmtrue value deferral methodSMTT fuzzy inference algorithm