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Fuzzy tolerance quotient spaces and fuzzy subsets

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Abstract

The structure and characteristic of fuzzy subsets are discussed by using the concepts of granulation and hierarchy in quotient space theory. First, the equivalence relation based quotient space theory is extended to the fuzzy tolerance relation. Second, the isomorphism and its discriminant of fuzzy tolerance relations are discussed. Finally, by using the fuzzy tolerance relation to define the fuzzy subset, its properties are addressed. The main results are given below: (1) several equivalent statements of fuzzy tolerance relations; (2) the definition of isomorphism of fuzzy tolerance relations; (3) the isomorphic discriminant of fuzzy tolerance relations; (4) the definition and properties of fuzzy subsets based on the fuzzy tolerance relations; and (5) the necessary and sufficient condition of the isomorphism of fuzzy subsets. These results will help us further comprehend the concepts of fuzzy tolerance relations and fuzzy subsets.

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Authors and Affiliations

  1. Computer Science & Technology College, Anhui University, Anhui, 230039, China

    Ling Zhang

  2. State Key Laboratory of Intelligent Technology and Systems, Beijing, 100084, China

    Bo Zhang

  3. Tsinghua National Laboratory of Information Science & Technology, Beijing, 100084, China

    Bo Zhang

  4. Information Science & Technology College, Computer Science & Technology Department, Tsinghua University, Beijing, 100084, China

    Bo Zhang

Authors
  1. Ling Zhang
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  2. Bo Zhang
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Correspondence to Bo Zhang.

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Zhang, L., Zhang, B. Fuzzy tolerance quotient spaces and fuzzy subsets. Sci. China Inf. Sci. 53, 704–714 (2010). https://doi.org/10.1007/s11432-010-0076-y

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  • DOI: https://doi.org/10.1007/s11432-010-0076-y

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