New Multigranulation Neutrosophic Rough Set with Applications

Bo, Chunxin; Zhang, Xiao­hong; Shao, Songtao; Smarandache, Florentín

doi:10.3390/sym10110578

Cited by 9 publications

(9 citation statements)

References 29 publications

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“…To illustrate the features of our model, we compare it with traditional rough approach [5,33], neutrosophic rough set approaches [10,[23][24][25], and fuzzy and intuitionistic fuzzy rough soft approaches [34][35][36].…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, all properties of traditional rough set approximations will be satisfied. We continue our discussion by comparing the proposed neutrosophic soft rough approach with other approaches which combine rough set to neutrosophic set [10,[23][24][25]. It can be seen that these approaches have the inadequacy of the parametrization tool to facilitate the representation of parameters, while the soft set in the proposed model can represent the problem parameters in a more complete manner.…”

Section: Traditional Rough Properties Neutrosophic Soft Rough Propertiesmentioning

confidence: 99%

“…Smarandache [16,17] proposed neutrosophic set to handle problems containing imprecise, incomplete, uncertain and indeterminate data. Neutrosophic sets progressed rapidly to neutrosophic oversets, neutrosophic undersets, neutrosophic offsets [18], neutrosophic cubic sets [19], neutrosophic and generalised neutrosophic soft sets [20][21][22], neutrosophic rough sets [23][24][25][26], neutrosophic vague sets [27,28] and complex neutrosophic sets [29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

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A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

2019

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To handle indeterminate and incomplete data, neutrosophic logic/set/probability were established. The neutrosophic truth, falsehood and indeterminacy components exhibit symmetry as the truth and the falsehood look the same and behave in a symmetrical way with respect to the indeterminacy component which serves as a line of the symmetry. Soft set is a generic mathematical tool for dealing with uncertainty. Rough set is a new mathematical tool for dealing with vague, imprecise, inconsistent and uncertain knowledge in information systems. This paper introduces a new rough set model based on neutrosophic soft set to exploit simultaneously the advantages of rough sets and neutrosophic soft sets in order to handle all types of uncertainty in data. The idea of neutrosophic right neighborhood is utilised to define the concepts of neutrosophic soft rough (NSR) lower and upper approximations. Properties of suggested approximations are proposed and subsequently proven. Some of the NSR set concepts such as NSR-definability, NSR-relations and NSR-membership functions are suggested and illustrated with examples. Further, we demonstrate the feasibility of the newly rough set model with decision making problems involving neutrosophic soft set. Finally, a discussion on the features and limitations of the proposed model is provided.

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Section: Discussionmentioning

confidence: 99%

Section: Traditional Rough Properties Neutrosophic Soft Rough Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

2019

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“…Zavareh M. and Maggioni V. proposes an approach to analyze water quality data that is based on rough set theory [15]. Bo C. studies multigranulation neutrosophic rough sets (MNRSs) and their applications in multi-attribute group decision-making [16]. Akram M., Ali G. and Alsheh N. O. introduce notions of soft rough m-polar fuzzy sets and m-polar fuzzy soft rough sets as novel hybrid models for soft computing, and investigate some of their fundamental properties [17].…”

Section: Introductionmentioning

confidence: 99%

Decision-Making Method based on Mixed Integer Linear Programming and Rough Set: A Case Study of Diesel Engine Quality and Assembly Clearance Data

Chang

Yuan

et al. 2019

Sustainability

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The purpose of this paper is to establish a decision-making system for assembly clearance parameters and machine quality level by analyzing the data of assembly clearance parameters of diesel engine. Accordingly, we present an extension of the rough set theory based on mixed-integer linear programming (MILP) for rough set-based classification (MILP-FRST). Traditional rough set theory has two shortcomings. First, it is sensitive to noise data, resulting in a low accuracy of decision systems based on rough sets. Second, in the classification problem based on rough sets, the attributes cannot be automatically determined. MILP-FRST has the advantages of MILP in resisting noisy data and has the ability to select attributes flexibly and automatically. In order to prove the validity and advantages of the proposed model, we used the machine quality data and assembly clearance data of 29 diesel engines of a certain type to validate the proposed model. Experiments show that the proposed decision-making method based on MILP-FRST model can accurately determine the quality level of the whole machine according to the assembly clearance parameters.

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“…Yao et al [21] studied the rough set models under the multi-granulation approximation space. Now the MRS model has been used widely and has produced some interesting results [22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Non-Dual Multi-Granulation Neutrosophic Rough Set with Applications

Zhang

Shao

2019

Symmetry

Self Cite

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Multi-attribute decision-making (MADM) is a part of management decision-making and an important branch of the modern decision theory and method. MADM focuses on the decision problem of discrete and finite decision schemes. Uncertain MADM is an extension and development of classical multi-attribute decision making theory. When the attribute value of MADM is shown by neutrosophic number, that is, the attribute value is complex data and needs three values to express, it is called the MADM problem in which the attribute values are neutrosophic numbers. However, in practical MADM problems, to minimize errors in individual decision making, we need to consider the ideas of many people and synthesize their opinions. Therefore, it is of great significance to study the method of attribute information aggregation. In this paper, we proposed a new theory—non-dual multi-granulation neutrosophic rough set (MS)—to aggregate multiple attribute information and solve a multi-attribute group decision-making (MGDM) problem where the attribute values are neutrosophic numbers. First, we defined two kinds of non-dual MS models, intersection-type MS and union-type MS. Additionally, their properties are studied. Then the relationships between MS, non-dual MS, neutrosophic rough set (NRS) based on neutrosophic intersection (union) relationship, and NRS based on neutrosophic transitive closure relation of union relationship are outlined, and a figure is given to show them directly. Finally, the definition of non-dual MS on two universes is given and we use it to solve a MGDM problem with a neutrosophic number as the attribute value.

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New Multigranulation Neutrosophic Rough Set with Applications

Cited by 9 publications

References 29 publications

A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

Decision-Making Method based on Mixed Integer Linear Programming and Rough Set: A Case Study of Diesel Engine Quality and Assembly Clearance Data

Non-Dual Multi-Granulation Neutrosophic Rough Set with Applications

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