L-fuzzy upper approximation operators associated with L-generalized fuzzy remote neighborhood systems of L-fuzzy points

Shoubin Sun; Lingqiang Li; Kai Hu; A. A. Ramadan; Shoubin Sun; Lingqiang Li; Kai Hu; A. A. Ramadan

doi:10.3934/math.2020360

AIMS Mathematics

2020, Volume 5, Issue 6: 5639-5653. doi: 10.3934/math.2020360

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Research article

L-fuzzy upper approximation operators associated with L-generalized fuzzy remote neighborhood systems of L-fuzzy points

1.
School of Computer Science and Technology, Liaocheng University, Liaocheng 252059, P. R. China
2.
Department of Mathematics, Liaocheng University, Liaocheng 252059, P. R. China
3.
Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

Received: 10 May 2020 Accepted: 22 June 2020 Published: 01 July 2020
MSC : 03E72, 03E75

It is well known that the approximation operators are always primitive concepts in kinds of general rough set theories. In this paper, considering L to be a completely distributive lattice, we introduce a notion of L-fuzzy upper approximation operator based on L-generalized fuzzy remote neighborhood systems of L-fuzzy points. It is shown that the new approximation operator is a fuzzification of the upper approximation operator in the rough set theory based on general remote neighborhood systems of classical points. Then the basic properties, axiomatic characterizations and the reduction theory on the L-fuzzy upper approximation operator are presented. Furthermore, the L-fuzzy upper approximation operators corresponding to the serial, reflexive, unary and transitive Lgeneralized fuzzy remote neighborhood systems, are discussed and characterized respectively.
- fuzzy mathematics,
- fuzzy rough sets,
- fuzzy points,
- fuzzy upper approximation operator,
- fuzzy remote neighborhood system
Citation: Shoubin Sun, Lingqiang Li, Kai Hu, A. A. Ramadan. L-fuzzy upper approximation operators associated with L-generalized fuzzy remote neighborhood systems of L-fuzzy points[J]. AIMS Mathematics, 2020, 5(6): 5639-5653. doi: 10.3934/math.2020360

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Abstract

It is well known that the approximation operators are always primitive concepts in kinds of general rough set theories. In this paper, considering L to be a completely distributive lattice, we introduce a notion of L-fuzzy upper approximation operator based on L-generalized fuzzy remote neighborhood systems of L-fuzzy points. It is shown that the new approximation operator is a fuzzification of the upper approximation operator in the rough set theory based on general remote neighborhood systems of classical points. Then the basic properties, axiomatic characterizations and the reduction theory on the L-fuzzy upper approximation operator are presented. Furthermore, the L-fuzzy upper approximation operators corresponding to the serial, reflexive, unary and transitive Lgeneralized fuzzy remote neighborhood systems, are discussed and characterized respectively.

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