The probabilistic linguistic term set is a powerful technique in representing linguistic evaluations of individuals or groups in the process of decision making. The aim of this paper is to propose a strongly robust method to solve multi-experts multi-criteria decision making problems with linguistic evaluations. To enrich the computation and to improve the measures of probabilistic linguistic term set, we firstly define an expectation function of it. In addition, we advance three kinds of probabilistic linguistic distance measures reflecting on the difference of linguistic terms and probabilities at the same time to make up for the defects of the existing distance measures, and then propose the similarity and correlation measures. Integrating the subjective opinions with the correlation coefficients between criteria, we put forward a combined weight determining method. The robustness of the ranking method, MULTIMOORA, is enhanced by the improved Borda rule. Based on these research findings, a probabilistic linguistic MULTIMOORA method is proposed. Finally, the developed method is applied to an empirical example concerning the selection of shared karaoke television brands. The effectiveness of the proposed method is verified by some comparative analyses.

The hesitant fuzzy linguistic term set (HFLTS) is an effective tool to express the experts' subjective evaluations in the processes of decision making. To solve the problem with both qualitative and quantitative criteria in the context of HFLTSs and the crisp weights of criteria being unknown, this paper proposes a new multi-criteria decision making method. Firstly, some formulas are developed to convert the quantitative data into the hesitant fuzzy linguistic elements. Then, motivated by the ORESTE method, we develop a new global preference score function to aggregate the criterion weights and criterion values, both of which are expressed as hesitant fuzzy linguistic elements. To get the real relation between alternatives, three preference intensity formulas are proposed and a hesitant fuzzy linguistic indifference threshold is introduced. In what follows, we establish a conflict test framework after a detailed research on the threshold values. On these bases, a new hesitant fuzzy linguistic ORESTE method is developed and the calculation process of this method is described. Furthermore, a case study on supplier selection is given to illustrate the method. Finally, some comparative analyses with other methods are conducted to show the practicability and reliability of the proposed method.

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.