摘要 :
Smarandache (1998) initiated neutrosophic sets (NSs) as a new mathematical tool for dealing with problems involving incomplete, indeterminant and inconsistent knowledge. By simplifying NSs, Smarandache (1998) and Wang et al. (2010...
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Smarandache (1998) initiated neutrosophic sets (NSs) as a new mathematical tool for dealing with problems involving incomplete, indeterminant and inconsistent knowledge. By simplifying NSs, Smarandache (1998) and Wang et al. (2010) proposed the concept of single valued neutrosophic sets (SVNSs) and studied some properties of SVNSs. In this paper, we mainly investigate the topological structures of single valued neutrosophic rough sets which is constructed by combining SVNSs and rough sets. Firstly, we introduce the concept of single valued neutrosophic topological spaces. Then, we discuss the relationships between single valued neutrosophic approximation spaces and single valued neutrosophic topological spaces. Concretely, a reflexive and transitive single valued neutrosophic relation can induce a single valued neutrosophic topological space such that its single valued neutrosophic interior and closure operators are the lower and upper approximation operators induced by this single valued neutrosophic relation, respectively. Conversely, a single valued neutrosophic interior (closure, respectively) operator derived from a single valued neutrosophic topological space is just the single valued neutrosophic lower (upper, respectively) approximation operator derived from a single valued neutrosophic approximation space under some conditions. Finally, we show there exists a one-to-one correspondence between the set of all reflexive and transitive single valued neutrosophic relations and the set of all single valued neutrosophic rough topologies.
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摘要 :
The notion of simple bipolar quadripartition is presented valuable neutrosophic set. Some basic set theoretic terminologies, operations and properties of bipolar quadripartitioned single valued neutrosophic set are given here. Als...
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The notion of simple bipolar quadripartition is presented valuable neutrosophic set. Some basic set theoretic terminologies, operations and properties of bipolar quadripartitioned single valued neutrosophic set are given here. Also different types of distances, similarity measures and entropy measure are discussed. Finally a decision making problem using the similarity measure technique of bipolar quadripartitioned single valued neutrosophic sets has been solved.
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摘要 :
Smarandache initiated neutrosophic sets (NSs) as a tool for handling undetermined information. Wang et al. proposed single valued neutrosophic sets (SVNSs) that is an especial NSs and can be used expediently to deal with real-worl...
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Smarandache initiated neutrosophic sets (NSs) as a tool for handling undetermined information. Wang et al. proposed single valued neutrosophic sets (SVNSs) that is an especial NSs and can be used expediently to deal with real-world problems. In this paper, we propose single valued neutrosophic rough sets by combining single valued neutrosophic sets and rough sets. We study the hybrid model by constructive and axiomatic approaches. Firstly, by using the constructive approach, we propose the lower/upper single valued neutrosophic approximation operators and illustrate the connections between special single valued neutrosophic relations (SVNRs) and the lower/upper single valued neutrosophic approximation operators. Then, by using the axiomatic approach, we discuss the operator-oriented axiomatic characterizations of single valued neutrosophic rough sets. We obtain that different axiom sets of the lower/upper single valued neutrosophic set-theoretic operators guarantee the existence of different classes of SVNRs which produce the same operators. Finally, we introduce single valued neutrosophic rough sets on two-universes and an algorithm of decision making based on single valued neutrosophic rough sets on two-universes, and use an illustrative example to demonstrate the application of the proposed model.
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摘要 :
A notion of Quadripartitioned Single Valued Neutrosophic Sets (QSVNS) is introduced and a theoretical study on various set-theoretic operations on them has been carried out. The definitions of distance, similarity measure and entr...
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A notion of Quadripartitioned Single Valued Neutrosophic Sets (QSVNS) is introduced and a theoretical study on various set-theoretic operations on them has been carried out. The definitions of distance, similarity measure and entropy have been proposed. Finally an application of the proposed similarity measure in a problem pertaining to pattern recognition has been shown.
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The information based on the tripartite (truth, indeterminacy, and falsity) can be described by single-valued neutrosophic numbers, but the linguistic information based on these tripartite cannot be represented by single-valued ne...
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The information based on the tripartite (truth, indeterminacy, and falsity) can be described by single-valued neutrosophic numbers, but the linguistic information based on these tripartite cannot be represented by single-valued neutrosophic numbers. To overcome this obstacle, linguistic single-valued neutrosophic numbers are characterized independently by the truth, indeterminacy, and falsity linguistic variables. In this paper, some new operations are introduced to increase the richness of linguistic fusion based on the linguistic single-valued neutrosophic approach. The Hamming distance-based formula is proposed to measure the distance between two linguistic single-valued neutrosophic numbers. Afterwards, we initiate the theory of linguistic single-valued neutrosophic soft (LSVNS) set by combining linguistic single-valued neutrosophic set and soft set. Meanwhile, the different computational functions and desirable properties of LSVNS sets are studied. Furthermore, we construct the framework of LSVNS technique for order preference by similarity to ideal solution (TOPSIS) and then present a game theory model based on this framework. Finally, we give an outstanding example to validate the practicality and effectiveness of the proposed LSVNS TOPSIS-based game theory model.
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The target of this study is to observe some of the algebraic structures of a single valued neutrosophic set. So, we introduce the concept of a neutrosophic submodule of a given classical module and investigate some of the crucial ...
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The target of this study is to observe some of the algebraic structures of a single valued neutrosophic set. So, we introduce the concept of a neutrosophic submodule of a given classical module and investigate some of the crucial properties and characterizations of the proposed concept.
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摘要 :
The target of this study is to observe some of the algebraic structures of a single valued neutrosophic set. So, we introduce the concept of a neutrosophic submodule of a given classical module and investigate some of the crucial ...
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The target of this study is to observe some of the algebraic structures of a single valued neutrosophic set. So, we introduce the concept of a neutrosophic submodule of a given classical module and investigate some of the crucial properties and characterizations of the proposed concept.
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摘要 :
Since everything in the world is full of indeterminacy so, the neutrosophic becomes appear and found their place into research. The purpose of this paper is twofold: first, it focuses on some important notions such as neutrosophic...
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Since everything in the world is full of indeterminacy so, the neutrosophic becomes appear and found their place into research. The purpose of this paper is twofold: first, it focuses on some important notions such as neutrosophic set, neutrosophic logic, neutrosophic measure, neutrosophic integral, and a single valued neutrosophic set (SVNS). Second, the most important part of the paper is related to the neutrosophic applications. There exists a lot of application in all field such as in information technology, information system and decision support system for example, relational database systems, semantic web services, financial data set detection, new economy's growth, decline analysis and etc... These notion and application may help the researcher in making algorithm to solve problems.
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摘要 :
Smarandache initiated neutrosophic sets (NSs) which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. In order to apply NSs conveniently, single valued neutrosophic sets (SVNSs) were p...
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Smarandache initiated neutrosophic sets (NSs) which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. In order to apply NSs conveniently, single valued neutrosophic sets (SVNSs) were proposed by Wang et al. In this paper, we propose single valued neutrosophic relations (SVNRs) and study their properties. The notions of anti-reflexive kernel, symmetric kernel, reflexive closure, and symmetric closure of a SVNR are introduced, respectively. Their accurate calculate formulas and some properties are explored. Some examples are also given. Finally, single valued neutrosophic relation mappings and inverse single valued neutrosophic relation mappings are introduced, and some interesting properties are also obtained.
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摘要 :
Neutrosophic set (NS) theory was originally established by Smarandache for handling indeterminate and inconsistent information. In this paper, we introduce single valued neutrosophic refined rough sets by combining single valued n...
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Neutrosophic set (NS) theory was originally established by Smarandache for handling indeterminate and inconsistent information. In this paper, we introduce single valued neutrosophic refined rough sets by combining single valued neutrosophic refined sets with rough sets and further study the hybrid model from two perspectives-constructive viewpoint and axiomatic viewpoint. We also give single valued neutrosophic refined rough sets on two universes and an available algorithm for handling multi-attribute decision making problem based on single valued neutrosophic refined rough sets on two universes. In addition, we illustrate the validity of the single valued neutrosophic refined rough set model by an example.
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