Single-parameter decision-theoretic rough set

Decision-theoretic rough sets (DTRSs), which can be considered as generalized rough set models produced by Bayesian risk minimum and three-way decisions (3WD) theories, have achieved fruitful results in risk decision-making problems. Nevertheless, the parameter determination of decision-theoretic rough sets is a challenging problem in practical applications, which narrows the generalization and development of these models. In this paper, a methodology to determine the parameters for DTRS and 3WD is proposed to improve their practicability. First, a data-driven loss function matrix is introduced based on the significance and the probability of the sample. Subsequently, a generalized rough set model named single-parameter decision-theoretic rough set (SPDTRS) is put forward based on the proposed loss function matrix. The main feature of the proposed model is that there is only one parameter that should be preset rather than the two or six parameters in the traditional DTRS models. Finally, some experiments on the University of California Irvine (UCI) and Knowledge Extraction based on Evolutionary Learning (KEEL) data sets are conducted to illustrate the effectiveness of the proposed methodology. (C) 2020 Elsevier Inc. All rights reserved.

决策理论粗糙集（DTRSs）可被视为由贝叶斯风险最小化和三分决策（3WD）理论产生的广义粗糙集模型，在风险决策问题中取得了丰硕成果。然而，决策理论粗糙集的参数确定在实际应用中是一个具有挑战性的问题，这限制了这些模型的推广和发展。本文提出了一种确定DTRS和3WD参数的方法以提高其实用性。首先，基于样本的重要性和概率引入一个数据驱动的损失函数矩阵。随后，基于所提出的损失函数矩阵提出了一个名为单参数决策理论粗糙集（SPDTRS）的广义粗糙集模型。所提模型的主要特点是只需预设一个参数，而不是传统DTRS模型中的两个或六个参数。最后，在加州大学欧文分校（UCI）和基于进化学习的知识提取（KEEL）数据集上进行了一些实验，以说明所提方法的有效性。（C）2020爱思唯尔公司。保留所有权利。