An approach based on linguistic spherical fuzzy sets for public evaluation of shared bicycles in China

In the context of the booming sharing economy, shared bicycles as an important part of the sharing economy have been studied by many scholars, and these researches mainly focus on the socioeconomic characteristics of users and the system design level of shared bicycles, it is very necessary to study the evaluation method of shared bicycles which is a typical multi-attribute decision- making (MADM) problem. Firstly, the linguistic spherical fuzzy numbers (Lt-SFNs) is proposed to express the public's language evaluation information. Compared with the linguistic intuitionistic fuzzy numbers (LIFNs) and the linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs), Lt-SFNs have a wider information expression range. Then, in order to integrate the language evaluation information, the linguistic spherical fuzzy weighted averaging (Lt-SFSWA) operator is proposed, which can aggregate the group linguistic evaluation information. Further, the MABAC (MultiAttributive Border Approximation area Comparison) method is extended to the linguistic spherical fuzzy environment and the Lt-SFS-MABAC method is proposed, which can process linguistic evaluation information and select an optimal alternative from a plurality of alternatives. At the same time, the TODIM (an acronym in Portuguese of Interactive and Multicriteria Decision Making) method is extended to the linguistic spherical fuzzy environment and the Lt-SFS-TODIM method is proposed. Lastly, we conducted sensitivity analysis and comparative analysis of the Lt-SFS-MABAC method, the Lt-SFS-TODIM method and the Lt-SFSWA method. The results show that the Lt-SFS-MABAC method is sensitive to weights, decision makers can use the Lt-SFS-MABAC method to make a realistic evaluation based on the actual environment.