A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application

Guo, Zhi-Lian; Liu, Yanling; Yang, Hai-Long

doi:10.3390/sym9070119

Cited by 11 publications

(6 citation statements)

References 39 publications

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“…This paper investigates a new type of SVN covering rough set model, which can be seen as a new bridge linking SVN sets and covering-based rough sets. Comparing the existing literatures [36,37,48,49], the main contributions of this paper are concluded as follows.…”

Section: Discussionmentioning

confidence: 99%

“…By introducing some definitions and properties in SVN β 2 -covering approximation spaces, we present the type-2 SVN covering rough set model based on the type-2 inclusion relation. The existing literatures [36,37,48,49] used the type-1 inclusion relation to study the combination of SVN sets and rough sets. Hence, this paper presents a new and interesting viewpoint to study the combination of SVN sets and rough sets.…”

Section: Discussionmentioning

confidence: 99%

“…Further study will be deserved by the following research topics. On the one hand, the type-2 inclusion relation or graph theory can be considered into other SVN rough set models [34,36,48,49] in future research. On the other hand, neutrosophic sets and related algebraic structures [50][51][52][53][54][55] will be connected with the research content of this paper in further research.…”

Section: Discussionmentioning

confidence: 99%

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A New Type of Single Valued Neutrosophic Covering Rough Set Model

Wang

Zhang

2019

Symmetry

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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A New Type of Single Valued Neutrosophic Covering Rough Set Model

Wang

Zhang

2019

Symmetry

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“…Each of these theories have their own restrictions and limitation. Many applications of these theories in data mining, pattern recognition, knowledge discovery and machine learning can be seen in [10][11][12][13][14][15][16][17]. While dealing with such theories, a question arises how to handle multi-attributes?…”

Section: Introductionmentioning

confidence: 99%

Soft covering based rough graphs and corresponding decision making

et al. 2019

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Soft set theory and rough set theory are two new tools to discuss uncertainty. Graph theory is a nice way to depict certain information. Particularly soft graphs serve the purpose beautifully. In order to discuss uncertainty in soft graphs, some new types of graphs called soft covering based rough graphs are introduced. Several basic properties of these newly defined graphs are explored. Applications of soft covering based rough graphs in decision making can be very fruitful. In this regard an algorithm has been proposed.

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“…The rough sets theory defined by Pawlak is based on partition or an equivalence relation. Many applications of rough set theory, probability theory, and rough set theory can be seen in the followings [4,5,[8][9][10][11][12][13], these include applications in data mining, machine learning, pattern recognition and knowledge discovery. The blending of rough sets with fuzzy sets and referring them to graphs with concepts of fuzzy sets or rough sets can be seen in [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Another Approach to Roughness of Soft Graphs with Applications in Decision Making

et al. 2018

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Fuzzy sets, rough sets and soft sets are different tools for modeling problems involving uncertainty. Graph theory is another powerful tool for representing the information by means of diagrams, matrices or relations. A possible amalgamation of three different concepts rough sets, soft sets and graphs, known as soft rough graphs, is proposed by Noor et al. They introduced the notion of vertex, edge induced soft rough graphs and soft rough trees depending upon the parameterized subsets of vertex set and edge set. In this article, a new framework for studying the roughness of soft graphs in more general way is introduced. This new model is known as the modified soft rough graphs or MSR-graphs. The concept of the roughness membership function of vertex sets, edge sets and of a graph is also introduced. Further, it has been shown that MSR-graphs are more robust than soft rough graphs. Some results, which are not handled by soft rough graphs, can be handled by modified soft rough graphs. The notion of uncertainty measurement associated with MSR-graphs is introduced. All applications related to decision makings are only restricted to the information of individuals only, not their interactions, using this technique we are able to involve the interactions (edges) of individuals with each other that enhanced the accuracy in decisions.

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A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application

Cited by 11 publications

References 39 publications

A New Type of Single Valued Neutrosophic Covering Rough Set Model

A New Type of Single Valued Neutrosophic Covering Rough Set Model

Soft covering based rough graphs and corresponding decision making

Another Approach to Roughness of Soft Graphs with Applications in Decision Making

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