Motivated by bipolar fuzzy (\(B_{p}\)F) sets (\(B_{p}\)FSs) and picture fuzzy sets (\(P_{c}\)FSs), we introduced the aggregation operators for the novel extension of \(P_{c}\)FSs named as bipolar picture fuzzy sets (B\(P_{c}\)FSs). Firstly, various arithmetic rules, scores and accuracy functions of the B\(P_{c}\)FSs are presented. Secondly, some aggregation operators of B\(P_{c}\)FSs are constructed to accumulate the bipolar picture fuzzy (B\(P_{c}\)F) data. Thirdly, the features of these aggregation operators are penned and then based on these aggregation operators a multiple criteria decision-making (MCDM) approach is developed to resolve the vague data. In the end, an illustrated example of the investment of money is put forward to show the authenticity and efficacy of the suggested approach. Moreover, B\(P_{c}\)F-TOPSIS, B\(P_{c}\)F-VIKOR, and sensitivity analysis (SA) have been used to provide the strength and practicality of the proposed MCDM model.

受双极模糊（\（B_ {p} \） FS ）集（\（B_ {p} \） FS）和图片模糊集（\（P_ {c} \） FS）的启发，我们引入了聚合算子\（P_ {c} \） FS的新颖扩展，称为双极图片模糊集（B \（P_ {c} \） FS）。首先，给出了B \（P_ {c} \） FS的各种算术规则，分数和准确性函数。其次，构造一些B \（P_ {c} \） FS的聚合算子，以累积双极性图片模糊（B \（P_ {c} \）F）数据。第三，确定了这些聚合算子的特征，然后基于这些聚合算子，开发了一种多准则决策（MCDM）方法来解决模糊数据。最后，给出了货币投资的一个示例，以表明所建议方法的真实性和有效性。此外，已使用B \（P_ {c} \） F-TOPSIS，B \（P_ {c} \） F-VIKOR和敏感性分析（SA）来提供所提出的MCDM模型的强度和实用性。