| Summary: | In investment selection problems, the existence of contingency and uncertainty may result in the loss of attribute information. Then, how to make proper investment decision-making will be a tricky proposition. In this work, a multiattribute group decision making (MAGDM) method based on the generalized probabilistic hesitant fuzzy Bonferroni mean (GPHFBM) operator is constructed, which enables decision-makers to select the proper parameters in decision-making process. Firstly, the GPHFBM operator is proposed by combining the Bonferroni mean operator and Archimedean norm. Secondly, five excellent properties of the GPHFBM operator are discussed in detail. In view of applications, we further develop some special aggregation operators for GPHFBM with the various values of parameters <em>b</em>, <em>d</em> and additive operators <em>g</em>(<em>t</em>). Finally, we propose a probabilistic hesitant fuzzy MAGDM method based on the GPHFBM operator to analyze the aggregated information. A case study of the investment of social insurance funds is given to depict the validity and reasonability of the proposed method. Ultimately, the company <em>X</em><sub>4 </sub>is selected as the investment company with the best comprehensive indicator.
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