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Symmetry 2019, 11(2), 180; https://doi.org/10.3390/sym11020180

Group Decision Making Based on Triangular Neutrosophic Cubic Fuzzy Einstein Hybrid Weighted Averaging Operators

1
Department of mathematics, Hazara University Mansehra, Dhodial 21130, Pakistan
2
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Pakistan
3
Mathematics Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Received: 17 December 2018 / Revised: 22 January 2019 / Accepted: 28 January 2019 / Published: 2 February 2019
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Abstract

In this paper, a new concept of the triangular neutrosophic cubic fuzzy numbers (TNCFNs), their score and accuracy functions are introduced. Based on TNCFNs, some new Einstein aggregation operators, such as the triangular neutrosophic cubic fuzzy Einstein weighted averaging (TNCFEWA), triangular neutrosophic cubic fuzzy Einstein ordered weighted averaging (TNCFEOWA) and triangular neutrosophic cubic fuzzy Einstein hybrid weighted averaging (TNCFEHWA) operators are developed. Furthermore, their application to multiple-attribute decision-making with triangular neutrosophic cubic fuzzy (TNCF) information is discussed. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness. View Full-Text
Keywords: triangular neutrosophic cubic fuzzy number; Einstein t-norm; arithmetic averaging operator; Multi-attribute decision making; numerical application triangular neutrosophic cubic fuzzy number; Einstein t-norm; arithmetic averaging operator; Multi-attribute decision making; numerical application
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Fahmi, A.; Amin, F.; Khan, M.; Smarandache, F. Group Decision Making Based on Triangular Neutrosophic Cubic Fuzzy Einstein Hybrid Weighted Averaging Operators. Symmetry 2019, 11, 180.

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