This paper presents a new type of fuzzy sets, called "Hierarchical Fuzzy Sets," that apply when the considered domain of values is not "flat," but contains values that are more specific than others according to the "kind of" relation. We study the properties of such fuzzy sets, that can be defined in a short way on a part of the hierarchy, or exhaustively (by their "closure") on the whole hierarchy. We show that hierarchical fuzzy sets form equivalence classes in regard to their closures and that each class has a particular representative called "minimal fuzzy set." We propose a use of this minimal fuzzy set for query enlargement purposes and, thus, present a methodology for hierarchical fuzzy set generalization. We finally present an experimental evaluation of the theoretical results described in the paper, in a practical application.


    Access

    Download


    Export, share and cite



    Title :

    Fuzzy sets defined on a hierarchical domain


    Contributors:

    Publication date :

    2006-01-01


    Remarks:

    IEEE Transactions on Knowledge and Data Engineering 10 (18), 1397-1410. (2006)



    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English



    Classification :

    DDC:    629




    Study on Optimization of Fuzzy Sets of Fuzzy Control System Based on Hierarchical Genetic Algorithms

    Guo, X.-j. / Zhou, Y. / Gong, D.-w. | British Library Online Contents | 2003


    Dominant Sets and Hierarchical Clustering

    Pavan, M. / Pelillo, M. / IEEE | British Library Conference Proceedings | 2003


    Dominant sets and hierarchical clustering

    Pavan, / Pelillo, | IEEE | 2003


    Poverty reduction: Fuzzy sets vs. crisp sets compared

    Olsen, Wendy / Nomura, Hisako | BASE | 2009

    Free access

    Shadows of fuzzy sets

    Zadeh, L. A. | NTRS | 1965