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Open AccessArticle

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

by Zhikang Lu and Jun Ye *
Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
*
Author to whom correspondence should be addressed.
Symmetry 2017, 9(7), 121; https://doi.org/10.3390/sym9070121
Received: 26 June 2017 / Revised: 9 July 2017 / Accepted: 11 July 2017 / Published: 18 July 2017
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
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. View Full-Text
Keywords: neutrosophic cubic set; decision-making; similarity measure; cosine measure; interval neutrosophic set; single-valued neutrosophic set neutrosophic cubic set; decision-making; similarity measure; cosine measure; interval neutrosophic set; single-valued neutrosophic set
MDPI and ACS Style

Lu, Z.; Ye, J. Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making. Symmetry 2017, 9, 121.

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