FUZZY SIMILARITY AND MEASURE OF SIMILARITY WITH LUKASIEWICZ IMPLICATOR
ISMAT BEG, SAMINA ASHRAF
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Source: Crossref
Published: Jul 1, 2008
DOI: 10.1142/s1793005708000994
Open original source ↗Source abstract
Given a universe of discourse X. A fuzzy similarity mapping S T,Inc : F(X) × F(X) → F(X) is defined, where F(X) denotes the set of all fuzzy subsets of X. Mapping S T,Inc maps two fuzzy sets A and B to a fuzzy set S T,Inc (A,B) in X called their fuzzy set of similarity. A measure of similarity between A and B is then obtained by applying the composite of fuzzy measure and fuzzy similarity mapping on the pair (A,B). Several properties of fuzzy set of similarity and the measure of fuzzy similarity are obtained within the framework of Lukasiewicz fuzzy implicator and its respective t-norm and t-conorm. Many examples of measure of similarity are also constructed.
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