Multi-attribute decision-making based on dual probabilistic interval-valued intuitionistic hesitant fuzzy weighted heronian mean aggregation operator

Probabilistic interval-valued intuitionistic hesitant fuzzy sets (PIVIHFSs) can well describe the evaluation information of decision-makers (DMs) in multi-attribute decision-making (MADM) problems. However, PIVIHFSs only depict the situation where both membership and non-membership information occur with equal probability while ignoring the situations of non-equal possibility due to DMs' subjective preferences. In this paper, we develop dual probabilistic interval-valued intuitionistic hesitant fuzzy sets (DPIVIHFSs) concept based on the truncated normal distribution. The DPIVIHFSs overcome the shortcomings of PIVIHFSs and are more interpretable. Then, the operations and ranking method of DPIVIHFSs are introduced. Furthermore, we studyMADMmethods in dual probabilistic interval-valued intuitionistic hesitant fuzzy environments by aggregation operators (AOs). We propose a series of AOs including the DPIVIHF heronian mean (DPIVIHFHM) operator and the DPIVIHF weighted heronian mean (DPIVIHFWHM) operator. The basic properties of the presented are discussed and proved. Finally, a novel method for solving the MADM problem is proposed based on the DPIVIHFWHM operator and a numerical example of express company selection strategy is used to illustrate the effectiveness of the method. The proposed method in this article can capture more fuzzy and uncertain information when solving MADM problems and have a wider application range.