Huang Zhehuang, Li Jinjin
IEEE Trans Neural Netw Learn Syst. 2022 May 27;PP. doi: 10.1109/TNNLS.2022.3175922.
Fuzzy β covering (FBC) has attracted considerable attention in recent years. Nevertheless, as the basic information granularity of FBC, fuzzy β neighborhood does not satisfy reflexivity, which may lead to instability in classification learning and decision-making. Although a few studies have involved reflexive fuzzy β neighborhoods, they only focus on a single fuzzy covering and cannot effectively deal with the information representation and information fusion of multiple fuzzy coverings. Moreover, there is a lack of investigation on noise-tolerant uncertainty measures for FBC, as well as their application in feature selection. Motivated by these issues, we investigate a noise-tolerant variable precision discrimination index (VPDI) by means of a new reflexive fuzzy covering neighborhood. To this end, fuzzy ɣ neighborhood with reflexivity is introduced to characterize the information fusion of a fuzzy covering family. An uncertainty measure called fuzzy ɣ neighborhood discrimination index is then presented to reflect the discriminatory power of fuzzy covering families. Some variants of the uncertainty measure, such as variable precision joint discrimination index, variable precision conditional discrimination index, and variable precision mutual discrimination index, are then put forth by means of fuzzy decision. These VPDIs can be used as an evaluation metric for a family of fuzzy coverings. Finally, the knowledge reduction of fuzzy covering decision systems is addressed from the point of keeping the discriminatory power, and a heuristic feature selection algorithm is designed by means of the variable precision conditional discrimination index. The experiments on 16 public datasets exhibit that the proposed algorithm can effectively reduce redundant features and achieve competitive results compared with six state-of-the-art feature selection algorithms. Moreover, it demonstrates strong robustness to the interference of random noise.
模糊β覆盖（FBC）近年来受到了广泛关注。然而，作为FBC的基本信息粒度，模糊β邻域不满足自反性，这可能导致分类学习和决策中的不稳定性。尽管有一些研究涉及自反模糊β邻域，但它们仅关注单个模糊覆盖，无法有效处理多个模糊覆盖的信息表示和信息融合。此外，缺乏对FBC的抗噪不确定性度量及其在特征选择中的应用的研究。受这些问题的启发，我们通过一种新的自反模糊覆盖邻域研究了一种抗噪可变精度判别指数（VPDI）。为此，引入具有自反性的模糊γ邻域来刻画模糊覆盖族的信息融合。然后提出了一种称为模糊γ邻域判别指数的不确定性度量，以反映模糊覆盖族的判别能力。通过模糊决策提出了该不确定性度量的一些变体，如可变精度联合判别指数、可变精度条件判别指数和可变精度互判别指数。这些VPDI可以用作模糊覆盖族的评估指标。最后，从保持判别能力的角度探讨了模糊覆盖决策系统的知识约简，并通过可变精度条件判别指数设计了一种启发式特征选择算法。在16个公共数据集上的实验表明，与六种最先进的特征选择算法相比，所提出的算法可以有效地减少冗余特征并取得有竞争力的结果。此外，它对随机噪声的干扰表现出很强的鲁棒性。
