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Transforming and decision-making based on probabilistic linguistic term sets with comparative linguistic expressions and incomplete assessments

The probabilistic linguistic term sets (PLTSs) are widely used in decision-making, due to its convenience of evaluation, and allowances of probability information. However, there are still some cases where it is not convenient to give an evaluation using the PLTS gramma. Sometimes the evaluators can only give a comparative relationship between alternatives, sometimes evaluators may have difficulty understanding all the alternatives and cannot give a complete assessment. Therefore, we propose a method to transform the comparative linguistic expressions (CLEs) into PLTSs, and the comparison objects of CLEs are alternatives evaluated by PLTSs. And the probability distribution has been adjusted to make the transformation more in line with common sense. Then, a method to correct the deviation is proposed, allowing alternatives to be compared in the case of incomplete assessment. Combining the above two methods, we propose a decision-making method when both CLEs and incomplete assessments coexist. With the study in this paper, the limitations of PLTS-based evaluation and decision-making are reduced and the flexibility of using PLTS is improved.