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Axiomatic characterizations of (,)-fuzzy rough approximation operators via overlap and grouping functions on a complete lattice.

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Title: Axiomatic characterizations of (,)-fuzzy rough approximation operators via overlap and grouping functions on a complete lattice.
Authors: Sun, Yan1 (AUTHOR), Pang, Bin1 (AUTHOR) pangbin1205@163.com, Mi, Ju-Sheng2 (AUTHOR)
Source: International Journal of General Systems. Aug2023, Vol. 52 Issue 6, p664-693. 30p.
Subjects: Rough sets, Approximate reasoning, Fuzzy sets, Axioms
Abstract: Recently, Jiang, H. B., and B. Q. Hu. [2022. "On (O,G)-Fuzzy Rough Sets Based on Overlap and Grouping Functions Over Complete Lattices." International Journal of Approximate Reasoning 144: 18–50. doi:10.1016/j.ijar.2022.01.012] constructed a (G , O) -fuzzy rough set model with the logical connectives–a grouping function G and an overlap function O on a complete lattice, which provided a new constructive approach to fuzzy rough set theory. The axiomatic approach is as important as the constructive approach in rough set theory. In this paper, we continue to study axiomatic characterizations of (G , O) -fuzzy rough set. Traditionally, the associativity of the logical connectives plays a vital role in the axiomatic research of existing fuzzy rough set models. However, a grouping function G and an overlap function O lack the associativity. So we explore a novel axiomatic approach to O -upper and G -lower fuzzy rough approximation operators without associativity. Further, we provide single axioms to characterize O -upper and G -lower fuzzy rough approximation operators instead of sets of axioms. Finally, we use single axioms to characterize fuzzy rough approximation operators generated by various kinds of fuzzy relations including serial, reflexive, symmetric, G -transitive, O -transitive fuzzy relations as well as their compositions. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of General Systems is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Axiomatic characterizations of (,)-fuzzy rough approximation operators via overlap and grouping functions on a complete lattice.
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+General+Systems%22">International Journal of General Systems</searchLink>. Aug2023, Vol. 52 Issue 6, p664-693. 30p.
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  Data: <searchLink fieldCode="DE" term="%22Rough+sets%22">Rough sets</searchLink><br /><searchLink fieldCode="DE" term="%22Approximate+reasoning%22">Approximate reasoning</searchLink><br /><searchLink fieldCode="DE" term="%22Fuzzy+sets%22">Fuzzy sets</searchLink><br /><searchLink fieldCode="DE" term="%22Axioms%22">Axioms</searchLink>
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  Data: Recently, Jiang, H. B., and B. Q. Hu. [2022. "On (O,G)-Fuzzy Rough Sets Based on Overlap and Grouping Functions Over Complete Lattices." International Journal of Approximate Reasoning 144: 18–50. doi:10.1016/j.ijar.2022.01.012] constructed a (G , O) -fuzzy rough set model with the logical connectives–a grouping function G and an overlap function O on a complete lattice, which provided a new constructive approach to fuzzy rough set theory. The axiomatic approach is as important as the constructive approach in rough set theory. In this paper, we continue to study axiomatic characterizations of (G , O) -fuzzy rough set. Traditionally, the associativity of the logical connectives plays a vital role in the axiomatic research of existing fuzzy rough set models. However, a grouping function G and an overlap function O lack the associativity. So we explore a novel axiomatic approach to O -upper and G -lower fuzzy rough approximation operators without associativity. Further, we provide single axioms to characterize O -upper and G -lower fuzzy rough approximation operators instead of sets of axioms. Finally, we use single axioms to characterize fuzzy rough approximation operators generated by various kinds of fuzzy relations including serial, reflexive, symmetric, G -transitive, O -transitive fuzzy relations as well as their compositions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of General Systems is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/03081079.2023.2201901
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      – Code: eng
        Text: English
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        PageCount: 30
        StartPage: 664
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      – SubjectFull: Rough sets
        Type: general
      – SubjectFull: Approximate reasoning
        Type: general
      – SubjectFull: Fuzzy sets
        Type: general
      – SubjectFull: Axioms
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      – TitleFull: Axiomatic characterizations of (,)-fuzzy rough approximation operators via overlap and grouping functions on a complete lattice.
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            – D: 01
              M: 08
              Text: Aug2023
              Type: published
              Y: 2023
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