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Axioms 2018, 7(1), 12; https://doi.org/10.3390/axioms7010012

NN-Harmonic Mean Aggregation Operators-Based MCGDM Strategy in a Neutrosophic Number Environment

1
Department of Mathematics, Jadavpur University, Kolkata-700032 West Bengal, India
2
Department of Mathematics, Nandalal Ghosh B.T. College, Panpur, PO-Narayanpur, and District: North 24 Parganas, Pin-743126 West Bengal, India
3
Mathematics & Science Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Received: 18 November 2017 / Revised: 9 February 2018 / Accepted: 11 February 2018 / Published: 23 February 2018
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making)
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Abstract

A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine the unknown weight of the criteria. We define the neutrosophic number harmonic mean operators and prove their basic properties. Then, we develop two novel multi-criteria group decision-making (MCGDM) strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility, applicability, and effectiveness of the two proposed strategies. Sensitivity analysis with the variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the results obtained from the proposed strategies with the results obtained from the existing strategies in the literature. View Full-Text
Keywords: neutrosophic number; neutrosophic number harmonic mean operator (NNHMO); neutrosophic number weighted harmonic mean operator (NNWHMO); cosine function; score function; multi-criteria group decision-making neutrosophic number; neutrosophic number harmonic mean operator (NNHMO); neutrosophic number weighted harmonic mean operator (NNWHMO); cosine function; score function; multi-criteria group decision-making
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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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Mondal, K.; Pramanik, S.; Giri, B.C.; Smarandache, F. NN-Harmonic Mean Aggregation Operators-Based MCGDM Strategy in a Neutrosophic Number Environment. Axioms 2018, 7, 12.

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