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Fuzzy rough sets in Šostak sense

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Abstract

In this paper, we defined the fuzzy operator Φλ in a fuzzy ideal approximation space (X, R, \({\cal I}\)) associated with a fuzzy rough set λ in Šostak sense. Associated with Φλ, there are fuzzy ideal interior and closure operators int λΦ and cl λΦ , respectively. r-fuzzy separation axioms, r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces. There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces. Lastly, using a fuzzy grill, we will get the same results given during the context.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

    Ismail Ibedou

  2. Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt

    S. E. Abbas

Authors
  1. Ismail Ibedou
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  2. S. E. Abbas
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Correspondence to Ismail Ibedou or S. E. Abbas.

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Ibedou, I., Abbas, S.E. Fuzzy rough sets in Šostak sense. Appl. Math. J. Chin. Univ. 37, 563–582 (2022). https://doi.org/10.1007/s11766-022-4100-y

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  • DOI: https://doi.org/10.1007/s11766-022-4100-y

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