A New Single-Valued Neutrosophic Rough Sets and Related Topology

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.

Single-Valued Neutrosophic Ideal Approximation Spaces

“…He defined the neutrosophic sets to be characterized by three membership functions independently: truth, indeterminacy and falsity. For this reason, the neutrosophic set theory becomes an attractive field for scientists and researchers who like to develop their concerns and match up their works in this scope, such as Wang et al [16] who formed the single-valued neutrosophic sets, Yang et al, and Qiu at al., [17,18] who proposed the single-valued neutrosophic relations and single-Valued neutrosophic rough sets, and also Saber et al [19][20][21][22][23][24][25][26][27][28][29][30] The incentive of this paper is to present a new better single-valued neutrosophic lower and single-valued neutrosophic upper sets through which we get a more consistent single-valued neutrosophic boundary region set off a single-valued neutrosophic set α n . From these single-valued neutrosophic lower and single-valued neutrosophic upper sets, we introduced concepts of new single-valued neutrosophic interior and single-valued neutrosophic closure operators related to a specific single-valued neutrosophic set α n ∈ ζ F .…”

Neutrosophic κ-Structures in Ordered Semigroups

“…In [3], Rosenfeld introduced the concepts of fuzziness in groups and obtained several results. Recently, many researchers pursue their research in this area and these concepts have been applied to different algebraic structures such as semigroups, ordered semigroups, rings (see [4][5][6][7][8][9][10]).…”

The Energy of rough neutrosophic matrix and its application to MCDM problem for selecting the best building construction site

“…The objective of the study is to establish a causal relationship between the illness and the patient's symptoms and to examine the patient's state using a rough neutrosophic set. The notions of the neutrosophic soft set with rough set theory (Das et al, 2021), neutrosophic single-valued rough sets, and including topology (Jin et al, 2021;Almathkour et al,, 2022) will be further developed. The rough set is important in every field of the neutrosophic environment as result.…”