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Symmetry 2019, 11(1), 39; https://doi.org/10.3390/sym11010039

Probabilistic Linguistic Aggregation Operators Based on Einstein t-Norm and t-Conorm and Their Application in Multi-Criteria Group Decision Making

1
School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 610054, China
2
Center for West African Studies, University of Electronic Science and Technology of China, Chengdu 610054, China
*
Author to whom correspondence should be addressed.
Received: 8 December 2018 / Revised: 22 December 2018 / Accepted: 24 December 2018 / Published: 2 January 2019
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Abstract

One of the major problems of varied knowledge-based systems has to do with aggregation and fusion. Pang’s probabilistic linguistic term sets denotes aggregation of fuzzy information and it has attracted tremendous interest from researchers recently. The purpose of this article is to deal investigating methods of information aggregation under the probabilistic linguistic environment. In this situation we defined certain Einstein operational laws on probabilistic linguistic term elements (PLTESs) based on Einstein product and Einstein sum. Consequently, we develop some probabilistic linguistic aggregation operators, notably the probabilistic linguistic Einstein average (PLEA) operators, probabilistic linguistic Einstein geometric (PLEG) operators, weighted probabilistic linguistic Einstein average (WPLEA) operators, weighted probabilistic linguistic Einstein geometric (WPLEG) operators. These operators extend the weighted averaging operator and the weighted geometric operator for the purpose of aggregating probabilistic linguistic terms values respectively. Einstein t-norm and Einstein t-conorm constitute effective aggregation tools and they allow input arguments to reinforce each other downwardly and upwardly respectively. We then generate various properties of these operators. With the aid of the WPLEA and WPLEG, we originate the approaches for the application of multiple attribute group decision making (MAGDM) with the probabilistic linguistic term sets (PLTSs). Lastly, we apply an illustrative example to elucidate our proposed methods and also validate their potentials. View Full-Text
Keywords: Einstein t-norm; Einstein t-conorm; PLTSs; multiple attribute group decision-making; entropy; operational laws; Einstein aggregation operator; Shannon entropy Einstein t-norm; Einstein t-conorm; PLTSs; multiple attribute group decision-making; entropy; operational laws; Einstein aggregation operator; Shannon entropy
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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Agbodah, K.; Darko, A.P. Probabilistic Linguistic Aggregation Operators Based on Einstein t-Norm and t-Conorm and Their Application in Multi-Criteria Group Decision Making. Symmetry 2019, 11, 39.

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