Limited interval-valued probabilistic linguistic term sets in evaluating airline service quality

The probabilistic linguistic term set (PLTS) is a useful tool and has been widely applied to deal with uncertain information for decision-making problems. It allows the experts to evaluate the alternatives by linguistic terms with corresponding probability information. In practice, the experts are difficult to provide complete probability information because of the complexity of the decision-making environment and limited cognition of the experts. In such cases, we need to normalize the probability information. To avoid information loss in the normalization process of PLTSs, this paper proposes the concept called limited interval-valued probabilistic linguistic term sets (l-IVPLTSs) by introducing the membership degree. First, we present the concept of l-IVPLTSs, and provide the basic operation laws and aggregation operators for l-IVPLTSs. Then, the membership degree is determined by the deviation degree based on a programming model. Furthermore, the extended possibility degree and the PROMETHEE II method under the limited interval-valued probabilistic linguistic environment are given, based on which, the whole multi-criteria group decision making (MCGDM) process with l-IVPLTSs is presented. Finally, the proposed method is applied to a case about evaluation of airline service quality. Discussions and analyses about the results are further conducted to verify the rationality of our approach.