Abstract
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.
Highlights
In many cases, it is difficult to describe alternatives quantitatively, but the use of words or sentences can be more flexible
In order to overcome the problems mentioned above, this paper aim to address the situation where comparative linguistic expressions (CLEs) may be mixed in the evaluation, and the situation where incomplete assessments are caused by a lack of comprehensive understanding of alternatives, proposed transforming and decision-making methods
The rest of this paper is arranged as follows: Section 2 reviews the basic research related to this paper; In Section 3, we introduce the method of transforming CLE into probabilistic linguistic term sets (PLTSs), revise the transformed result; Section 4 introduce the comparison when the incomplete assessments exist in evaluation; The process of decision making when both CLEs and incomplete assessments coexist is presented in Section 5; Section 6 shows an example that illustrates the content of this research
Summary
It is difficult to describe alternatives quantitatively, but the use of words or sentences can be more flexible. In [43], the PL-TODIM (PLTS-based TODIM) method considering the DMs’ psychological factors has been proposed by Zhang et al The proposed approach captures the uncertainties, and takes the DMs’ noncomplete rationality into consideration These studies mainly focus on the rational determination of weights, and cannot deal with the mixed assessment with both linguistic term and comparative relationship. In many cases that do not require thoughtful evaluation, evaluators prefer to use the simple comparative expression like “I can’t give the evaluation or comparison of LeBron’s physical talent with linguistic terms, but he has better physical talent than Kobe”, or “Class 1 is better than Class 2” This kind of CLE can directly express the relationship between alternatives, and can make a more realistic assessment sometimes.
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