Z probabilistic linguistic term sets and its application in multi-attribute group decision making

In multiattribute group decision-making (MAGDM), due to quantity, fuzziness, and complexity of evaluation linguistic information on commodities, traditional distance measures need to be extended to the integration of evaluation information under a multigranular probabilistic linguistic environment. A more reasonable method is proposed to deal with the missing value in the evaluation information. On the basis of the generalized distance measures and filling in the missing evaluation information, some novel distance measures between two multigranular probabilistic linguistic term sets (PLTSs) are presented in this paper. Based on these distance measures, three extended decision-making (DM) algorithms based on TOPSIS, the extended TOPSIS, and VIKOR are proposed, which are MGPL-TOPSIS, MGPL-ETOPSIS, and MGPL-VIKOR, respectively. The case analyses on purchasing a car are provided to illustrate the application of the extended multiattribute group decision-making (MAGDM) algorithms. Then, sensitivity analyses based on PT are proposed as well. In particular, the extended TOPSIS method is presented. These results demonstrate the novelty, feasibility, and rationality of the distance measures between two multigranular PLTSs proposed in this paper.

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Distance‐based multicriteria group decision‐making approach with probabilistic linguistic term sets

Expert Systems ◽

10.1111/exsy.12352 ◽

2018 ◽

Vol 36 (2) ◽

pp. e12352 ◽

Cited By ~ 30

Author(s):

Xiaokang Wang ◽

Jianqiang Wang ◽

Hongyu Zhang

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Linguistic Term ◽

Probabilistic Linguistic Term Sets ◽

Multicriteria Group Decision Making

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

Symmetry ◽

10.3390/sym11010039 ◽

2019 ◽

Vol 11 (1) ◽

pp. 39 ◽

Cited By ~ 5

Author(s):

Kobina Agbodah ◽

Adjei Peter Darko

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Information Aggregation ◽

Aggregation Operators ◽

Weighted Averaging ◽

Knowledge Based ◽

Multiple Attribute ◽

Linguistic Term ◽

Probabilistic Linguistic Term Sets

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.

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