A Best-Worst multi-attribute decision-making (MADM) method based on a new possibility degree is put forward to deal with MADM problems with probabilistic linguistic evaluation information. Firstly, a new possibility degree for pairwise comparisons with probabilistic linguistic term sets (PLTSs) is defined. Secondly, starting from the new possibility degree, two different ideas of Best-Worst Method (BWM) for getting the optimal attribute weights are put forward. Thirdly, combining the new probabilistic linguistic possibility degree and the two BWM ideas, two optimization models for determining the attribute weights are constructed, respectively. Moreover, consistency ratios for two new BWM models are proposed to check the reliability of the pairwise comparisons. Meanwhile, the state of optimal solutions for the new BWM models is analyzed. Finally, a new Best-Worst MADM method under probabilistic linguistic information is presented, which is applied to a practical example of selecting optimal green enterprises. Some comparative analyses are given to show the rationality and validity of the proposed method.INDEX TERMS Multi-attribute decision-making (MADM), probabilistic linguistic term sets (PLTSs), possibility degree, attribute weight, Best-Worst Method (BWM), green evaluation.

The evaluation of sustainable rural tourism potential is a key work in sustainable rural tourism development. Due to the complexity of the rural tourism development situation and the limited cognition of people, most of the assessment problems for sustainable rural tourism potential are highly uncertain, which brings challenges to the characterisation and measurement of evaluation information. Besides, decision-makers (DMs) usually do not exhibit complete rationality in the practical evaluation process. To tackle such problems, this paper proposes a new behaviour multi-attribute group decision-making (MAGDM) method with probabilistic linguistic terms sets (PLTSs) by integrating Wasserstein distance measure into TODIM (an acronym in Portuguese of interactive and multicriteria decision making) method. Firstly, a new Wasserstein-based distance measure with PLTSs is defined, and some properties of the proposed distance are developed. Secondly, based on the correlation coefficient among attributes and standard deviation of each attribute, an attribute weight determination method (called PL-CRITIC method) is proposed. Subsequently, a Wasserstein distance-based probabilistic linguistic TODIM method is developed. Finally, the proposed method is applied to the evaluation of sustainable rural tourism potential, along with sensitivity and comparative analyses, as a means of illustrating the effectiveness and advantages of the new method.