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Spherical Fuzzy Logarithmic Aggregation Operators Based on Entropy and Their Application in Decision Support Systems

1
School of Economic and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(7), 628; https://doi.org/10.3390/e21070628
Received: 2 June 2019 / Revised: 20 June 2019 / Accepted: 23 June 2019 / Published: 26 June 2019
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Abstract

Keeping in view the importance of new defined and well growing spherical fuzzy sets, in this study, we proposed a novel method to handle the spherical fuzzy multi-criteria group decision-making (MCGDM) problems. Firstly, we presented some novel logarithmic operations of spherical fuzzy sets (SFSs). Then, we proposed series of novel logarithmic operators, namely spherical fuzzy weighted average operators and spherical fuzzy weighted geometric operators. We proposed the spherical fuzzy entropy to find the unknown weights information of the criteria. We study some of its desirable properties such as idempotency, boundary and monotonicity in detail. Finally, the detailed steps for the spherical fuzzy decision-making problems were developed, and a practical case was given to check the created approach and to illustrate its validity and superiority. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our proposed method. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative. View Full-Text
Keywords: spherical fuzzy sets; logarithmic spherical operational laws; logarithmic spherical aggregation operators; entropy; multi-criteria group decision making (MCGDM) problems spherical fuzzy sets; logarithmic spherical operational laws; logarithmic spherical aggregation operators; entropy; multi-criteria group decision making (MCGDM) problems
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Jin, Y.; Ashraf, S.; Abdullah, S. Spherical Fuzzy Logarithmic Aggregation Operators Based on Entropy and Their Application in Decision Support Systems. Entropy 2019, 21, 628.

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