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    Professor / yyao@cs.uregina.ca

    University of Regina

    COMBINATION OF ROUGH AND FUZZY SETS BASED ON ?-LEVEL SETS

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    A fuzzy set can be represented by a family of crisp sets using its ?-level sets, whereas a rough set can be represented by three crisp sets. Based on such representations, this paper examines some fundamental issues involved in the combination of rough-set and fuzzy-set models. The rough-fuzzy-set and fuzzy-rough-set models are analyzed, with emphasis on their structures in terms of crisp sets. A rough fuzzy set is a pair of fuzzy sets resulting from the approximation of a fuzzy set in a crisp approximation space, and a fuzzy rough set is a pair of fuzzy sets resulting from the approximation of a crisp set in a fuzzy approximation space. The approximation of a fuzzy set in a fuzzy approximation space leads to a more general framework. The results may be interpreted in three different ways.

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    New Full text for this article was not available? Send a request to the author(s).
    Title : COMBINATION OF ROUGH AND FUZZY SETS BASED ON ?-LEVEL SETS
    Abstract : A fuzzy set can be represented by a family of crisp sets using its ?-level sets, whereas a rough set can be represented by three crisp sets. Based on such representations, this paper examines some fundamental issues involved in the combination of rough-set and fuzzy-set models. The rough-fuzzy-set and fuzzy-rough-set models are analyzed, with emphasis on their structures in terms of crisp sets. A rough fuzzy set is a pair of fuzzy sets resulting from the approximation of a fuzzy set in a crisp approximation space, and a fuzzy rough set is a pair of fuzzy sets resulting from the approximation of a crisp set in a fuzzy approximation space. The approximation of a fuzzy set in a fuzzy approximation space leads to a more general framework. The results may be interpreted in three different ways.
    Subject : unspecified
    Area : Computer Science
    Language : English
    Affiliations : 
    Url : http://www2.cs.uregina.ca/~yyao/rough_set_paper/combination.pdf
    Doi : 10.1.1.137.7132

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