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Open AccessFeature PaperArticle
Information 2017, 8(3), 110; doi:10.3390/info8030110

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

Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
Received: 25 August 2017 / Revised: 6 September 2017 / Accepted: 6 September 2017 / Published: 8 September 2017
(This article belongs to the Special Issue Neutrosophic Information Theory and Applications)
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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. View Full-Text
Keywords: linguistic neutrosophic cubic number; score function; accuracy function; certain function; linguistic neutrosophic cubic number weighted arithmetic averaging (LNCNWAA) operator; linguistic neutrosophic cubic number weighted geometric averaging (LNCNWGA) operator; decision-making linguistic neutrosophic cubic number; score function; accuracy function; certain function; linguistic neutrosophic cubic number weighted arithmetic averaging (LNCNWAA) operator; linguistic neutrosophic cubic number weighted geometric averaging (LNCNWGA) operator; decision-making
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Ye, J. Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Method. Information 2017, 8, 110.

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