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Fuzzy Similarity And Measure Of Similarity With Lukasiewicz Implicator

  • ISMAT BEG

    ()

    (Department of Mathematics and Centre for Advanced Studies in Mathematics, Lahore University of Management Sciences, 54792- Lahore, Pakistan)

  • SAMINA ASHRAF

    (Department of Mathematics and Centre for Advanced Studies in Mathematics, Lahore University of Management Sciences, 54792- Lahore, Pakistan)

Given a universe of discourse X. A fuzzy similarity mapping ST,Inc : F(X) × F(X) → F(X) is defined, where F(X) denotes the set of all fuzzy subsets of X. Mapping ST,Inc maps two fuzzy sets A and B to a fuzzy set ST,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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Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

Volume (Year): 04 (2008)
Issue (Month): 02 ()
Pages: 191-206

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Handle: RePEc:wsi:nmncxx:v:04:y:2008:i:02:p:191-206
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