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Information 2017, 8(3), 107; doi:10.3390/info8030107

Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods

1
Department of Computer Science, Shaoxing University, 508 Huancheng West Road, Shaoxing, Zhejiang 312000, China
2
Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, Zhejiang 312000, China
*
Author to whom correspondence should be addressed.
Received: 11 August 2017 / Revised: 31 August 2017 / Accepted: 31 August 2017 / Published: 1 September 2017
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Abstract

Linguistic neutrosophic numbers (LNN) is presented by Fang and Ye in 2017, which can describe the truth, falsity, and indeterminacy linguistic information independently. In this paper, the LNN and the Bonferroni mean operator are merged together to propose a LNN normalized weighted Bonferroni mean (LNNNWBM) operator and a LNN normalized weighted geometric Bonferroni mean (LNNNWGBM) operator and the properties of these two operators are proved. Further, multi-attribute group decision methods are introduced based on the proposed LNNNWBM and LNNNWGBM operators, and then an example is provided to demonstrate the application and validity of the proposed methods. In addition, in order to consider the effect of the parameters p and q on the decision results, different pairs of parameter values are employed to verify the decision results. View Full-Text
Keywords: linguistic neutrosophic numbers (LNN); LNN normalized weighted Bonferroni mean (LNNNWBM) operator; LNN normalized weighted geometric Bonferroni mean (LNNNWGBM) operator; group decision-making linguistic neutrosophic numbers (LNN); LNN normalized weighted Bonferroni mean (LNNNWBM) operator; LNN normalized weighted geometric Bonferroni mean (LNNNWGBM) operator; group 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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MDPI and ACS Style

Fan, C.; Ye, J.; Hu, K.; Fan, E. Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods. Information 2017, 8, 107.

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