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Fuzzy Similarity And Measure Of Similarity With Lukasiewicz Implicator

Author

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  • 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)

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.

Suggested Citation

  • Ismat Beg & Samina Ashraf, 2008. "Fuzzy Similarity And Measure Of Similarity With Lukasiewicz Implicator," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 191-206.
    • Handle: RePEc:wsi:nmncxx:v:04:y:2008:i:02:n:s1793005708000994
    DOI: 10.1142/S1793005708000994
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    Cited by:

    1. Beg, Ismat & Syed, Ayesha, 2016. "An interactive fuzzy judgment aggregation model for consensus with partially undecided judges," MPRA Paper 96096, University Library of Munich, Germany, revised 14 Apr 2017.

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