A projection method for multiple attribute group decision making with probabilistic linguistic term sets

2018 ◽  
Vol 10 (9) ◽  
pp. 2515-2528 ◽  
Author(s):  
Xiaofang Zhang ◽  
Xunjie Gou ◽  
Zeshui Xu ◽  
Huchang Liao
Keyword(s):  
Decision Making ◽  
Projection Method ◽  
Group Decision Making ◽  
Group Decision ◽  
Multiple Attribute ◽  
Linguistic Term ◽  
Probabilistic Linguistic Term Sets

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

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 39 ◽  
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.

scholarly journals Probabilistic Hybrid Linguistic Approaches for Multiple Attribute Group Decision Making with Decision Hesitancy and the Prioritization of Attribute Relationships

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 235
Author(s):  
Junling Zhang ◽  
Ying Hong ◽  
Xiaowen Qi ◽  
Changyong Liang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Weighted Average ◽  
Distance Measures ◽  
Distance Measurements ◽  
Information Distortion ◽  
Multiple Attribute ◽  
Wide Range ◽  
Linguistic Term

Focusing on ill-structured multiple attribute decision-making (MADM) problems, including decision hesitancy and attribute prioritization relationships, this paper investigates appropriate approaches for decision making. Firstly, we introduce the probabilistic hybrid linguistic term set (P-HLTS) for capturing probabilistic preferences about possible linguistic labels belonging to a wide range of hesitant linguistic term sets. Entropy and distance measurements for P-HLTS are developed without arbitrary complementing operations. To facilitate decision making with attribute prioritization relationships, we present a probabilistic uncertain balanced linguistic-prioritized weighted average (PUBL-PWA) operator and the probabilistic uncertain balanced linguistic-induced prioritized ordered weighted average (PUBL-IPOWA) operator. In terms of the strength of the above tools, we further construct two multiple attribute group decision-making (MAGDM) approaches under P-HLTS environments, namely, an approach for decision-making situations where attribute prioritization relationships are known in advance and the relative importance of decision makers (DMs) or decision-making units (DMUs) is not required for consideration, and second approach for decision-making situations where both attribute prioritization relationships and the weighted vectors of DMs or DMUs are explicitly unknown. In general, our proposed approaches are more flexible and practical when considering heterogeneous opinions, avoiding information distortion brought about by complementing operation-based distance measures. Furthermore, illustrative application studies are conducted to verify our developed approaches.

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