A New Single-Valued Neutrosophic Rough Sets and Related Topology

Qiu Jin, Kai Hu, Chunxin Bo, Lingqiang Li and Yongqiang Fu

Journal of Mathematics, 2021, vol. 2021, 1-14

Abstract: (Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationships to neutrosophic topology are discussed. The main results include the following: (1) For a single-valued neutrosophic approximation space U,R, a pair of approximation operators called the upper and lower ordinary single-valued neutrosophic approximation operators are defined and their properties are discussed. Then the further properties of the proposed approximation operators corresponding to reflexive (transitive) single-valued neutrosophic approximation space are explored. (2) It is verified that the single-valued neutrosophic approximation spaces and the ordinary single-valued neutrosophic topological spaces can be interrelated to each other through our defined lower approximation operator. Particularly, there is a one-to-one correspondence between reflexive, transitive single-valued neutrosophic approximation spaces and quasidiscrete ordinary single-valued neutrosophic topological spaces.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5522021

DOI: 10.1155/2021/5522021

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