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

Lu, Zhikang; Ye, Jun

doi:10.3390/sym9070121

Cited by 40 publications

(29 citation statements)

References 38 publications

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“…On comparing with cosine measures of NCSs [49], we observe that the proposed NC-TODIM involves multiple decision makers, while in [49] only a single decision maker is involved. This shows that [49] cannot deal with group decision making, while the proposed NC-TODIM strategy is more sophisticated as it can deal with single as well as group decision making in the NCS environment.…”

Section: Comparative Analysis and Discussionmentioning

confidence: 99%

“…In the same study, Pramanik et al [48] developed a new MAGDM strategy in the NCS environment. Lu and Ye [49] proposed cosine measures between NCSs and established their basic properties. In the same study, Lu and Ye [49] proposed three new cosine measures-based MADM strategies under a NCS environment.…”

Section: Introductionmentioning

confidence: 99%

“…In the literature, there are only six strategies [44,[48][49][50][51][52] for MADM and MAGDM in NCS environment. However, we say that none of them is generally superior to all others.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Comparative Analysis and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Pramanik¹,

Dalapati

Alam

et al. 2017

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“…After that, the concept of a neutrosophic cubic set (including the internal neutrosophic cubic set and external neutrosophic cubic set), where a neutrosophic cubic number (a basic element in a neutrosophic cubic set) is composed of both the interval neutrosophic number and the single-valued neutrosophic number, and the distance measure of neutrosophic cubic sets were proposed and applied to pattern recognition [19,20]. Then, decision-making methods with neutrosophic cubic information were put forward based on grey relational analysis [21] and cosine measures [22], respectively.…”

Section: Introductionmentioning

confidence: 99%

Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Method

2017

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Abstract:To describe both certain linguistic neutrosophic information and uncertain linguistic neutrosophic information simultaneously in the real world, this paper originally proposes the concept of a linguistic neutrosophic cubic number (LNCN), including an internal LNCN and external LNCN. In LNCN, its uncertain linguistic neutrosophic number consists of the truth, indeterminacy, and falsity uncertain linguistic variables, and its linguistic neutrosophic number consists of the truth, indeterminacy, and falsity linguistic variables to express their hybrid information. Then, we present the operational laws of LNCNs and the score, accuracy, and certain functions of LNCN for comparing/ranking LNCNs. Next, we propose a LNCN weighted arithmetic averaging (LNCNWAA) operator and a LNCN weighted geometric averaging (LNCNWGA) operator to aggregate linguistic neutrosophic cubic information and discuss their properties. Further, a multiple attribute decision-making method based on the LNCNWAA or LNCNWGA operator is developed under a linguistic neutrosophic cubic environment. Finally, an illustrative example is provided to indicate the application of the developed method.

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“…In the same study, Pramanik et al [29] developed a new MAGDM method in 50 neutrosophic cubic set environment. Lu and Ye [30] proposed cosine measures between 51 neutrosophic cubic sets and proved their basic properties. In the same study, Lu and Ye [30] 52…”

mentioning

confidence: 99%

NC-TODIM Based MAGDM under Neutrosophic Cubic Set Environment

Pramanik¹,

Dalapati²,

Alam³

et al. 2017

Preprint

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Neutrosophic cubic set is the hybridization of the concept of neutrosophic set and interval 9 neutrosophic set. Neutrosophic cubic set has the capacity to express the hybrid information of both 10 the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly 11 defined, little research on the operations and applications of neutrosophic cubic sets appear in the 12 current literature. In the present paper we propose the score, accuracy functions for neutrosophic 13 cubic sets and prove their basic properties. We firstly develop TODIM method in neutrosophic cubic 14 set environment, which we call NC-TODIM. We establish a new NC-TODIM method in 15 neutrosophic cubic set environment for solving MAGDM in neutrosophic cubic set environment 16 problems. We illustrate the proposed NC-TODIM method for solving a MAGDM problem to show 17 applicability and effectiveness of the developed method. We also conduct sensitivity analysis to 18show the impact of ranking order of the alternatives for different values of attenuation factor of 19 losses for multi-attribute group decision making problem. 20Keywords: neutrosophic cubic set; single valued neutrosophic set; interval neutrosophic set; multi 21 attribute group decision making; TODIM method; NC-TODIM 22

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

Cited by 40 publications

References 38 publications

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

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

Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Method

NC-TODIM Based MAGDM under Neutrosophic Cubic Set Environment

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