Subsethood measure for single valued neutrosophic sets

Şahin, Rıdvan; Küçük, Ahmet

doi:10.3233/ifs-141304

Cited by 107 publications

(59 citation statements)

References 15 publications

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“…As simplified forms of neutrosophic sets, Smarandache [10], Wang et al [11,12] and Ye [13] introduced single-valued neutrosophic sets (SVNSs) and interval neutrosophic sets (INSs), and simplified neutrosophic sets (SNSs) as subclasses of neutrosophic sets for easy engineering applications. Since then, SVNSs, INSs, and SNSs have been widely applied to various areas, such as image processing [14][15][16], decision-making [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], clustering analyses [33,34], medical diagnoses [35,36], and fault diagnoses [37]. Recently, Ali et al [38] and Jun et al [39] have extended cubic sets to the neutrosophic sets and proposed the concepts of neutrosophic cubic sets (NCSs), including internal NCSs and external NCSs, subsequently introducing some logic operations of NCSs, such as the P-union, P-intersection, R-union, and R-intersection of NCSs.…”

Section: Introductionmentioning

confidence: 99%

Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

2017

Symmetry

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Abstract:The neutrosophic cubic set can contain much more information to express its interval neutrosophic numbers and single-valued neutrosophic numbers simultaneously in indeterminate environments. Hence, it is a usual tool for expressing much more information in complex decision-making problems. Unfortunately, there has been no research on similarity measures of neutrosophic cubic sets so far. Since the similarity measure is an important mathematical tool in decision-making problems, this paper proposes three cosine measures between neutrosophic cubic sets based on the included angle cosine of two vectors, distance, and cosine functions, and investigates their properties. Then, we develop a cosine measures-based multiple attribute decision-making method under a neutrosophic cubic environment in which, from the cosine measure between each alternative (each evaluated neutrosophic cubic set) and the ideal alternative (the ideal neutrosophic cubic set), the ranking order of alternatives and the best option can be obtained, corresponding to the cosine measure values in the decision-making process. Finally, an illustrative example about the selection problem of investment alternatives is provided to illustrate the application and feasibility of the developed decision-making method.

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Section: Introductionmentioning

confidence: 99%

Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

2017

Symmetry

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“…On comparing with the existing neutrosophic decision making strategies [26][27][28][29][33][34][35][64][65][66][67][68][69], we see that the decision information used in the proposed NC-TODIM strategy is NC numbers, which comprises of interval neutrosophic information and single-valued neutrosophic information simultaneously; whereas the decision information in the existing literature is either SVNSs or INSs. Since NC numbers comprises of much more information, the NC numbers based on the TODIM strategy proposed in this paper is more elegant, typical and more general in applications, while the existing neutrosophic decision-making strategies cannot deal with the NC number decision-making problem developed in this paper.…”

Section: Comparative Analysis and Discussionmentioning

confidence: 97%

NC-TODIM-Based MAGDM under a Neutrosophic Cubic Set Environment

Pramanik¹,

Dalapati

Alam

et al. 2017

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Abstract:A neutrosophic cubic set is the hybridization of the concept of a neutrosophic set and an interval neutrosophic set. A neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets has been reported in the current literature. In the present paper, we propose the score and accuracy functions for neutrosophic cubic sets and prove their basic properties. We also develop a strategy for ranking of neutrosophic cubic numbers based on the score and accuracy functions. We firstly develop a TODIM (Tomada de decisao interativa e multicritévio) in the neutrosophic cubic set (NC) environment, which we call the NC-TODIM. We establish a new NC-TODIM strategy for solving multi attribute group decision making (MAGDM) in neutrosophic cubic set environment. We illustrate the proposed NC-TODIM strategy for solving a multi attribute group decision making problem to show the applicability and effectiveness of the developed strategy. We also conduct sensitivity analysis to show the impact of ranking order of the alternatives for different values of the attenuation factor of losses for multi-attribute group decision making strategies.

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“…Recently, SNSs (INSs, and SVNSs) have been widely applied in many areas [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], such as decision-making, image processing, medical diagnosis, fault diagnosis, and clustering analysis. Especially, many researchers [7,[29][30][31][32][33][34][35][36] have developed various aggregation operators, like simplified neutrosophic weighted aggregation operators, simplified neutrosophic prioritized aggregation operators, single-valued neutrosophic normalized weighted Bonferroni mean operators, generalized neutrosophic Hamacher aggregation operators, generalized weighted aggregation operators, interval neutrosophic prioritized ordered weighted average operators, interval neutrosophic Choquet integral operators, interval neutrosophic exponential weighted aggregation operators, and so on, and applied them to decision-making problems with SNS/SVNS/INS information.…”

Section: Introductionmentioning

confidence: 99%

Some Single-Valued Neutrosophic Dombi Weighted Aggregation Operators for Multiple Attribute Decision-Making

Chen

2017

Symmetry

112

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Abstract:The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators for neutrosophic sets by the extension of the Dombi operations, this paper firstly presents the Dombi operations of single-valued neutrosophic numbers (SVNNs) based on the operations of the Dombi T-norm and T-conorm, and then proposes the single-valued neutrosophic Dombi weighted arithmetic average (SVNDWAA) operator and the single-valued neutrosophic Dombi weighted geometric average (SVNDWGA) operator to deal with the aggregation of SVNNs and investigates their properties. Because the SVNDWAA and SVNDWGA operators have the advantage of good flexibility with the operational parameter, we develop a multiple attribute decision-making (MADM) method based on the SVNWAA or SVNWGA operator under a SVNN environment. Finally, an illustrative example about the selection problem of investment alternatives is given to demonstrate the application and feasibility of the developed approach.Keywords: single-valued neutrosophic number; Dombi operation; single-valued neutrosophic Dombi weighted arithmetic average (SVNDWAA) operator; single-valued neutrosophic Dombi weighted geometric average (SVNDWGA) operator; multiple attribute decision-making

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Subsethood measure for single valued neutrosophic sets

Cited by 107 publications

References 15 publications

Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

NC-TODIM-Based MAGDM under a Neutrosophic Cubic Set Environment

Some Single-Valued Neutrosophic Dombi Weighted Aggregation Operators for Multiple Attribute Decision-Making

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