Probabilistic Linguistic Term Set With Interval Uncertainty

The probabilistic linguistic term set (PLTS), composed by linguistic terms and their probabilities, is effective to represent uncertain evaluations. Considering that interval probability is more powerful than the precise form in describing uncertainty, this study introduces the PLTS with interval probabilities. Based on belief and plausibility measures, in this article, we discuss how to translate complex qualitative evaluations, which may be composed by both interval probabilities and interval linguistic terms, to the PLTS with interval probabilities. Utility-based translation approaches are proposed, which further shows the ability of the PLTS with interval probabilities in representing quantitative information. In addition, a probabilistic linguistic dominance method is developed to compare PLTSs. Integrating optimization models with the Dempster–Shafer theory, we present an aggregation method to estimate the maximum and minimum PLTSs obtained from the combination. Furthermore, a multicriteria decision-making method is introduced considering both the comprehensive evaluations of alternatives and the ability to achieve the tolerance and expectation values of criteria. The applicability of the proposed approach is illustrated by a case study of shelter selection.