Affiliations: School of Mathematics and Statistics, Anhui Normal University, Anhui Province, China
Correspondence:
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Corresponding author. Hui Zhang, School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, Anhui Province, China. E-mail: huizhang@mail.ahnu.edu.cn.
Abstract: The probabilistic linguistic term sets (PLTSs) allow experts to express their preferences on one linguistic term over another. However, when the probability of linguistic term given is internal number nor numerical value. The PLTS is no way to express it. Therefore, Bai et al. proposed the definition of uncertain probabilistic linguistic term set (UPLTS). In this paper, we first propose a priority degree method for interval number and possibility degree method for PLTS. Second, based on the above mentioned two methods, we propose a new possibility degree method for UPLTS to solve the problem of Bai et al’s possibility degree method. Third, we propose two aggregation operators for UPLTSs, which are uncertain probabilistic linguistic geometric Bonferroni mean (UPLGBM) operator and weighted uncertain probabilistic linguistic geometric Bonferroni mean (WUPLGBM) operator, and theirs properties. Then, based on possibility degree method for UPLTS and UPLGBM (WUPLGBM) operator, we propose a multi-criteria decision-making method for UPLTSs. Finally, we illustrate the relationship between Bai et al’s decision-making method and our method by an example. The result show that our method is more rational than Bai et al’s method.
Keywords: Probabilistic linguistic term sets, priority degree method for interval
number, possibility degree method for PLTS, uncertain probabilistic linguistic term set, possibility
degree method for UPLTS, UPLGBM operator, WUPLGBM operator
