| Fuzzy similarity measures,similarity measures for short,are a kind of similarity measures between fuzzy sets.As an important concept of fuzzy set theory,fuzzy similarity measures reflects difference degree between fuzzy sets or fuzzy vectors.Moreover,similarity measures play an important role in many applied fields such as pattern recognition,approximate reasoning,decision analysis,and so on.In view of the importance of similarity measures in both theoretical and application research,it is necessary to construct some new similarity measures.At the same time,it is very meaningful to discuss properties of similarity measures,and to consider possible applications of similarity measures in fuzzy reasoning.The main contents of this thesis are to study properties and construction methods of similarity measures,and apply similarity measures to fuzzy reasoning.Since the concept of restricted equivalence function is proposed,related results of properties and construction methods of restricted equivalence functions do not appear in the literatures.Thus this thesis discusses main properties and construction methods of restricted equivalence functions.Then basic properties of the similarity measures constructed by restricted equivalence functions are investigated.Based on the theory of restricted dissimilarity functions,this thesis discusses properties of the restricted dissimilarity functions and proposes a new method of constructing distances between fuzzy sets.And the relationship between two distances,some new methods of constructing fuzzy entropy are proposed in this thesis.As an important application,based on the similarity inference method and several important implication operators,FMP rules and FMT rules are discussed in detail,and the corresponding similarity inference algorithm are constructed.Then these similarity inference algorithms are extended to more general situation,and some results are obtained.Finally,the reduction problem of similarity inference algorithms discussed. |
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