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Open AccessArticle

Unified Fuzzy Divergence Measures with Multi-Criteria Decision Making Problems for Sustainable Planning of an E-Waste Recycling Job Selection

1
Department of Mathematics, National Institute of Technology, Warangal 506004, Telangana, India
2
Center for Sustainable Supply Chain Engineering, Department of Technology and Innovation, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark
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Department of Mathematics, Govt College Jaitwara, Satna 485221, M P, India
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Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam
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Faculty of Business Administration, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam
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Department of Quantitative Methods, School of Business, King Faisal University, Al-Hasa 31982, Saudi Arabia
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Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar 125001, Haryana, India
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 90; https://doi.org/10.3390/sym12010090 (registering DOI)
Received: 30 October 2019 / Revised: 18 December 2019 / Accepted: 27 December 2019 / Published: 2 January 2020
In the literature of information theory and fuzzy set doctrine, there exist various prominent measures of divergence; each possesses its own merits, demerits, and disciplines of applications. Divergence measure is a tool to compute the discrimination between two objects. Particularly, the idea of divergence measure for fuzzy sets is significant since it has applications in several areas viz., process control, decision making, image segmentation, and pattern recognition. In this paper, some new fuzzy divergence measures, which are generalizations of probabilistic divergence measures are introduced. Next, we review two different generalizations of the following measures. Firstly, directed divergence (Kullback–Leibler or Jeffrey invariant) and secondly, Jensen difference divergence, based on these measures, we develop a class of unified divergence measures for fuzzy sets (FSs). Then, a method based on divergence measure for fuzzy sets (FSs) is proposed to evaluate the multi-criteria decision-making (MCDM) problems under the fuzzy atmosphere. Lastly, an illustrative example of the recycling job selection problem of sustainable planning of the e-waste is presented to demonstrate the reasonableness and usefulness of the developed method. View Full-Text
Keywords: divergence measure; entropy; fuzzy set; multi-criteria decision making; recycling job selection; e-waste divergence measure; entropy; fuzzy set; multi-criteria decision making; recycling job selection; e-waste
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Rani, P.; Govindan, K.; Mishra, A.R.; Mardani, A.; Alrasheedi, M.; Hooda, D.S. Unified Fuzzy Divergence Measures with Multi-Criteria Decision Making Problems for Sustainable Planning of an E-Waste Recycling Job Selection. Symmetry 2020, 12, 90.

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