The rough set (RS) and multi-granulation rough set (MGRS) theories have been successfully extended to accommodate preference analysis by substituting the equivalence relation (ER) with the dominance relation (DR). On the other hand, bipolarity refers to the explicit handling of positive and negative aspects of data. In this paper, with the help of bipolar fuzzy preference relation (BFPR) and bipolar fuzzy preference \(\delta \)-covering (BFP\(\delta \)C), we put forward the idea of BFP\(\delta \)C based optimistic multi-granulation bipolar fuzzy rough set (BFP\(\delta \)C-OMG-BFRS) model and BFP\(\delta \)C based pessimistic multi-granulation bipolar fuzzy rough set (BFP\(\delta \)C-PMG-BFRS) model. We examine several significant structural properties of BFP\(\delta \)C-OMG-BFRS and BFP\(\delta \)C-PMG-BFRS models in detail. Moreover, we discuss the relationship between BFP\(\delta \)C-OMG-BFRS and BFP\(\delta \)C-PMG-BFRS models. Eventually, we apply the BFP\(\delta \)C-OMG-BFRS model for solving multi-criteria decision-making (MCDM). Furthermore, we demonstrate the effectiveness and feasibility of our designed approach by solving a numerical example. We further conduct a detailed comparison with certain existing methods. Last but not least, theoretical studies and practical examples reveals that our suggested approach dramatically enriches the MGRS theory and offers a novel strategy for knowledge discovery, which is practical in real-world circumstances.

通过用优势关系 (DR) 代替等价关系 (ER)，粗糙集 (RS) 和多粒度粗糙集 (MGRS) 理论已成功扩展到适应偏好分析。另一方面，双极性是指对数据的积极和消极方面的明确处理。本文借助双极模糊偏好关系(BFPR)和双极模糊偏好\(\delta\) -覆盖(BFP \(\delta\) C)，提出了BFP \(\delta\)的思想)基于 C 的乐观多粒双极模糊粗糙集 (BFP \(\delta \) C-OMG-BFRS) 模型和 BFP \(\delta \)基于 C 的悲观多粒双极模糊粗糙集 (BFP \(\delta \) C-PMG-BFRS)模型。我们详细研究了 BFP \(\delta \) C-OMG-BFRS 和 BFP \(\delta \) C-PMG-BFRS 模型的几个重要结构特性。此外，我们还讨论了BFP \(\delta \) C-OMG-BFRS 和BFP \(\delta \) C-PMG-BFRS 模型之间的关系。最终，我们应用 BFP \(\delta \) C-OMG-BFRS 模型来解决多标准决策（MCDM）。此外，我们通过解决数值例子证明了我们设计方法的有效性和可行性。我们进一步与某些现有方法进行详细比较。最后但并非最不重要的一点是，理论研究和实际例子表明，我们提出的方法极大地丰富了 MGRS 理论，并提供了一种新颖的知识发现策略，这在现实环境中是实用的。