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

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.

A survey of group decision making methods in Healthcare Industry 4.0: bibliometrics, applications, and directions

“…To express the hesitancy and preference of DMs clearly, classic probabilistic linguistic term sets (PLTSs) were applied to represent qualitative data such as the criteria of medical products suppliers, the condition of patients, and the healthcare situation of hospitals [ 26 , 104 – 109 ]. Probabilistic linguistic preference relation whose elements were PLTSs was used to collect the preference of individuals in [ 35 , 110 – 112 ].…”

“…To improve the quality of hospital services, it is necessary to evaluate hospitals and doctors regularly. [ 120 , 163 , 191 ] evaluated the healthcare service quality of doctors and nurses, while [ 31 , 41 , 57 , 78 , 104 , 141 ] assessed the performance of hospitals. Considering that it is crucial to determine the prioritisation of patients when there are lots of them, [ 51 , 116 , 174 , 196 ] discussed the problem of patients' prioritisation systems.…”