As an effective aggregation tool, power average (PA) allows the input arguments being aggregated to support and reinforce each other, which provides more versatility in the information aggregation process. Under the probabilistic linguistic term environment, we deeply investigate the new power aggregation (PA) operators for fusing the probabilistic linguistic term sets (PLTSs). In this paper, we firstly develop the probabilistic linguistic power average (PLPA), the weighted probabilistic linguistic power average (WPLPA) operators, the probabilistic linguistic power geometric (PLPG) and the weighted probabilistic linguistic power geometric (WPLPG) operators. At the same time, we carefully analyze the properties of these new aggregation operators. With the aid of the WPLPA and WPLPG operators, we further design the approaches for the application of multi-criteria group decision-making (MCGDM) with PLTSs. Finally, we use an illustrated example to expound our proposed methods and verify their performances.

Stakeholders have become worried about the environmental problems of agricultural production activities. Therefore, there is pressure on smallholder farmers to observe environmental regulations and embed sustainable green technologies in their production. The literature on green production has thoroughly emphasized the critical role of behavioral factors in adopting environmental sustainability practices. We develop a probabilistic linguistic preference selection index method to assess the behavioral constructs that promote the adoption of agricultural green production technologies (AGPTs) among smallholder rice farmers in an emerging economy. The result shows that the five most-important factors promoting the adoption of AGPTs include knowledge (0.828), perceived cost and benefit (0.819), descriptive norm (0.810), moral and environmental concern (0.809), and injunctive norm (0.807). The study findings offer insightful directions for examining rice farmers’ decisions on the adoption of AGPTs. Our findings imply that policymakers should consider multiple behavioral factors when designing policies that promote AGPTs. This study enriches farmers’ adoption decisions by modeling the uncertainties in the decision-making process.

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.