A fuzzy similarity inference method for fuzzy reasoning

Authors:
De-Gang Wang;Yan-Ping Meng;Hong-Xing Li
Affiliations:
School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, PR China;School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, PR China;School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

In this paper, Fuzzy Similarity Inference (FSI) is investigated. First, the axiomatic definition of the fuzzy similarity measure is introduced. It is a generalization of the similarity measure. Some formulas are given to compute the fuzzy similarity of two fuzzy sets. Second, a novel fuzzy reasoning, called fuzzy similarity inference, is proposed. Computational formulas for both fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) are obtained. Based on the theory of partial valuations, FSI method is put under the framework of logic semantically. Furthermore, the generalized problem of FSI is investigated. Computational formulas for @a-FSI FMP and @a-FSI FMT are obtained. At last, reversibility properties of FSI are proved.