FUZZY SIMILARITY AND MEASURE OF SIMILARITY WITH LUKASIEWICZ IMPLICATOR

Ismat Beg and Samina Ashraf
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Samina Ashraf: Department of Mathematics and Centre for Advanced Studies in Mathematics, Lahore University of Management Sciences, 54792- Lahore, Pakistan

New Mathematics and Natural Computation (NMNC), 2008, vol. 04, issue 02, 191-206

Abstract: Given a universe of discourseX. A fuzzy similarity mappingST,Inc: F(X) × F(X) → F(X)is defined, whereF(X)denotes the set of all fuzzy subsets ofX. MappingST,Incmaps two fuzzy setsAandBto a fuzzy setST,Inc(A,B)inXcalled their fuzzy set of similarity. A measure of similarity betweenAandBis 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 respectivet-norm andt-conorm. Many examples of measure of similarity are also constructed.

Keywords: Fuzzy set of similarity; measure of fuzzy similarity (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S1793005708000994

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