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On Multi-Fuzzy Rough Sets, Relations, and Topology

Author

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  • Gayathri Varma

    (Department of Mathematics, National Institute of Technology, Kerala, India)

  • Sunil Jacob John

    (Department of Mathematics, National Institute of Technology, Kerala, India)

Abstract

This article describes how rough set theory has an innate topological structure characterized by the partitions. The approximation operators in rough set theory can be viewed as the topological operators namely interior and closure operators. Thus, topology plays a role in the theory of rough sets. This article makes an effort towards considering closed sets a primitive concept in defining multi-fuzzy topological spaces. It discusses the characterization of multi-fuzzy topology using closed multi-fuzzy sets. A set of axioms is proposed that characterizes the closure and interior of multi-fuzzy sets. It is proved that the set of all lower approximation of multi-fuzzy sets under a reflexive and transitive multi-fuzzy relation forms a multi-fuzzy topology.

Suggested Citation

  • Gayathri Varma & Sunil Jacob John, 2019. "On Multi-Fuzzy Rough Sets, Relations, and Topology," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 8(1), pages 101-119, January.
    • Handle: RePEc:igg:jfsa00:v:8:y:2019:i:1:p:101-119
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