A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

Al-Quran, Ashraf; Hassan, Nasruddin; Marei, Emad

doi:10.3390/sym11030384

Cited by 14 publications

(10 citation statements)

References 31 publications

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“…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%

“…Smarandache [31] and Wang et al [32] presented single valued neutrosophic (SVN) sets, which can be regarded as an extension of intuitionistic fuzzy sets [33]. Both neutrosophic sets and rough sets can deal with partial and uncertainty information [34]. Therefore, it is necessary to combine them.…”

Section: Introductionmentioning

confidence: 99%

A New Type of Single Valued Neutrosophic Covering Rough Set Model

Wang

Zhang

2019

Symmetry

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“…In 2018, Chatterjee et al [38] integrated the opinions of both decision-makers and the company's stake to select the best supplier; these opinions were taken as fuzzy soft sets and integrated by the rough approximation theory. In 2019, to handle all types of uncertainty in data to simultaneously exploit the advantages of rough sets and neutrosophic soft sets, Al-Quran et al [39] introduced a new rough set model based on a neutrosophic soft set. Riaz et al [40] in 2020 used a neutrosophic soft rough set to introduce the notion of a neutrosophic soft rough topology, and Ayub et al [41] in 2020 introduced a pair of two soft sets, viz.…”

Section: Introductionmentioning

confidence: 99%

New Soft Rough Set Approximations

Alkhazaleh¹,

Marei²

2021

IJFIS

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The soft rough set model was introduced by Fing in 2011 and can be considered as a generalized rough set model, in which an interesting connection was established between two mathematical approaches to vagueness: rough sets and soft sets. It was also shown that Pawlak's rough set model can be viewed as a special case of soft rough sets. There are two problems with this model in using this concept in real-life applications. The first problem is that some soft rough sets are not contained in their upper approximations, which contradicts Pawlak's thoughts. The second problem is that the boundary region of any considered set, in the soft rough set model, must be decreased to make it possible to take a true decision of any application problem. In this study, the soft rough set model is modified to solve these problems. The basic properties of the modified approximations are introduced and supported with propositions and illustrative examples. Modified concepts can be viewed as a general mathematical model for qualitative and quantitative real-life problems. A comparison between the suggested approach to soft rough sets and the traditional soft rough set model is provided.

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“…T (e j )(x i )), e j is a cos t parameter (24) Step 3: Compute the determinacy degree vector ψ t = (ψ 1 , ψ 2 , . .…”

Section: Algorithm For Neutrosophic Soft Sets In Stochastic Multi-crimentioning

confidence: 99%

“…Karaaslan [21] introduced the possibility of neutrosophic soft sets by assigning probability to the three function values and defined related properties and operations. In addition, the concepts of single-valued neutrosophic refined soft sets [22], generalized neutrosophic soft expert sets [23], and neutrosophic soft rough sets [24] were presented successively.…”

Section: Introductionmentioning

confidence: 99%

Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory

2019

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To address issues involving inconsistencies, this paper proposes a stochastic multi-criteria group decision making algorithm based on neutrosophic soft sets, which includes a pair of asymmetric functions: Truth-membership and false-membership, and an indeterminacy-membership function. For integrating an inherent stochastic, the algorithm expresses the weights of decision makers and parameter subjective weights by neutrosophic numbers instead of determinate values. Additionally, the algorithm is guided by the prospect theory, which incorporates psychological expectations of decision makers into decision making. To construct the prospect decision matrix, this research establishes a conflict degree measure of neutrosophic numbers and improves it to accommodate the stochastic multi-criteria group decision making. Moreover, we introduce the weighted average aggregation rule and weighted geometric aggregation rule of neutrosophic soft sets. Later, this study presents an algorithm for neutrosophic soft sets in the stochastic multi-criteria group decision making based on the prospect theory. Finally, we perform an illustrative example and a comparative analysis to prove the effectiveness and feasibility of the proposed algorithm.

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A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

Cited by 14 publications

References 31 publications

A New Type of Single Valued Neutrosophic Covering Rough Set Model

A New Type of Single Valued Neutrosophic Covering Rough Set Model

New Soft Rough Set Approximations

Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory

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