Abstract
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 b, d and additive operators g(t). 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 X4 is selected as the investment company with the best comprehensive indicator.
Highlights
N o where p( xi ) =|γi ∈ p( xi ), cγi ∈ [0, 1], ∑γi ∈ p( xi ) cγi = 1 is the probabilistic hesitant fuzzy element (PHFE). γi denotes the possible membership degrees of the element x ∈ X, and cγi is the probability associated with γi
Note 1 The elements in PHFE are arranged in descending order, where γi indicates the element corresponding to the k-th membership degree of γi
Considering the importance of attribute weights, we further introduce the generalized probabilistic hesitant fuzzy weighted Bonferroni mean (GPHFWBM) operator
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. HFSs has some advantages in expressing decision-making, they cannot be accurate in depicting the original decision information and avoiding the loss of information In this regard, several researchers have taken the idea of probability into consideration in the hesitant fuzzy environment, some of them focused on information aggregation. None of the probabilistic hesitant fuzzy information aggregation operators described above take into account the situation that is often present in investment decision-making problems, namely that there is usually some interconnection between the decision-making information provided. A new group decision-making method is presented by aggregating BM operators under a probabilistic hesitant fuzzy environment, which has the following advantages: (1).
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