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On Characterization of Rough Type-2 Fuzzy Sets

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  • Tao Zhao
  • Zhenbo Wei

Abstract

Rough sets theory and fuzzy sets theory are important mathematical tools to deal with uncertainties. Rough fuzzy sets and fuzzy rough sets as generalizations of rough sets have been introduced. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle high uncertainties. In this paper, the rough type-2 fuzzy set model is proposed by combining the rough set theory with the type-2 fuzzy set theory. The rough type-2 fuzzy approximation operators induced from the Pawlak approximation space are defined. The rough approximations of a type-2 fuzzy set in the generalized Pawlak approximation space are also introduced. Some basic properties of the rough type-2 fuzzy approximation operators and the generalized rough type-2 fuzzy approximation operators are discussed. The connections between special crisp binary relations and generalized rough type-2 fuzzy approximation operators are further examined. The axiomatic characterization of generalized rough type-2 fuzzy approximation operators is also presented. Finally, the attribute reduction of type-2 fuzzy information systems is investigated.

Suggested Citation

  • Tao Zhao & Zhenbo Wei, 2016. "On Characterization of Rough Type-2 Fuzzy Sets," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-13, February.
    • Handle: RePEc:hin:jnlmpe:4819353
    DOI: 10.1155/2016/4819353
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    Cited by:

    1. Vladik Kreinovich & Olga Kosheleva & Patricia Melin & Oscar Castillo, 2022. "Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty," Mathematics, MDPI, vol. 10(13), pages 1-15, July.
    2. You, Xingxing & Shi, Mingyang & Guo, Bin & Zhu, Yuqi & Lai, Wuxing & Dian, Songyi & Liu, Kai, 2022. "Event-triggered adaptive fuzzy tracking control for a class of fractional-order uncertain nonlinear systems with external disturbance," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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