Selection of a solar water heater for large-scale group decision making with hesitant fuzzy linguistic preference relations based on the best-worst method

Due to the promotion of sustainable development policies, solar water heaters have quickly occupied the market. Choosing the best-performing solar water heater has become a popular group decision-making problem. This paper presents a best-worst large-scale group decision making (LSGDM) approach based on hesitant fuzzy linguistic preference relations (HFLPRs) and applies it to the selection of solar water heaters. First, we establish an optimization model to normalize hesitant fuzzy linguistic term sets (HFLTSs) with diverse lengths. Then, a satisfaction degree function based on the additive consistency of HFLPRs is proposed, and the fluctuation deviation level of HFLPRs is described. Next, we develop a clustering process combining the satisfaction degree and fluctuation deviation level to classify large-scale experts into several subgroups. The clustering algorithm not only improves the fusion of subgroups but also enhances the satisfaction of subgroups. Moreover, a best-worst model based on the credibility measure of subgroups is presented to determine the weights of the subgroups. Finally, a numerical example of a solar water heater which involves normalizing the HFLPRs given by 20 experts into HFLTSs with a length of 3, clustering the 20 experts into 7 subgroups with weights of 0.5153, 0.2125, 0.1332, 0.0155, 0.0854, 0.0287 and 0.0094, and selecting P1 as the most satisfactory alternative and a comparative analysis are utilized to demonstrate the availability of the proposed method.