A New Type of Single Valued Neutrosophic Covering Rough Set Model

Abstract

Recently, various types of single valued neutrosophic (SVN) rough set models were presented based on the same inclusion relation. However, there is another SVN inclusion relation in SVN sets. In this paper, we propose a new type of SVN covering rough set model based on the new inclusion relation. Furthermore, the graph and matrix representations of the new SVN covering approximation operators are presented. Firstly, the notion of SVN β 2 -covering approximation space is proposed, which is decided by the new inclusion relation. Then, a type of SVN covering rough set model under the SVN β 2 -covering approximation space is presented. Moreover, there is a corresponding SVN relation rough set model based on a SVN relation induced by the SVN β 2 -covering, and two conditions under which the SVN β 2 -covering can induce a symmetric SVN relation are presented. Thirdly, the graph and matrix representations of the new SVN covering rough set model are investigated. Finally, we propose a novel method for decision making (DM) problems in paper defect diagnosis under the new SVN covering rough set model.

On Different Types of Single-Valued Neutrosophic Covering Rough Set with Application in Decision-Making

“…By the above discussion and extend the other work (see [46,47]) in SVNβ-CRS. We will generalize these methods in [46,47] by boosting the lower approximation and minimizing the upper approximation, which is a big challenge to every author. Consequently, the motivation of this paper is to improve this area is obtained by introducing the notion of 1-SVN complementary β-neighborhood (resp., 2-SVN complementary β-neighborhood) to build novel classes of 1-SVNβ-CRS (resp., 2-SVNβ-CRS).…”

“…e notions of neutrosophic soft rough sets and its generalizations are presented in [48][49][50][51][52][53]. By the above discussion and extend the other work (see [46,47]) in SVNβ-CRS. We will generalize these methods in [46,47] by boosting the lower approximation and minimizing the upper approximation, which is a big challenge to every author.…”

“…e major purpose of our presented work is eligible to raise the lower approximation and reduce the upper approximation of the previous study by Wang and Zhang's methods [46,47], as visible in Examples 2 and 4. To clarify the comparisons between Wang and Zhang's methods [46,47] and our methods, the sorting outcomes of these decision-making models are listed in Table 10 for 1-SVNβCAS and Table 11 for 2-SVNβCAS.…”

“…In 2018, Wang et al [39] established the notion of SVN β-covering approximation space, and then, Wang and Zhang [46,47] used this notion to create two types of the covering method as in the following definition.…”

“…By using SVN relation, Yang et al [45] introduced the SVN rough set model, and based on the notion of Type-1 SVN β-neighborhoods, Wang and Zhange [46] proposed two models of Type-1 SVNβ-covering rough sets (briefly, SVNβ-CRS). Furthermore, they presented a new kind of SVNβ-CRS called Type-2 SVNβ-CRS utilizing Type-2 SVN β-neighborhoods in [47].…”