Attribute reduction for the double-quantitative rough set model based on logical difference of precision and grade
ZHANG Xian-yong
1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, China; 2. Department of Computer Science and Technology, Tongji University, Shanghai 201804, China
Abstract:Double quantification has a fundamental function to completely describe the approximate space in rough set theory, and the rough set model based on logical difference of precision and grade serves as a basic double-quantitative model. According to this model, this paper aims to deeply explore its attribute reduction in the two-category case. First, by virtue of the model approximations, basic properties of two-region preservation are discussed, and the reduct regarding two-region preservation is proposed and investigated. Then, by virtue of both the variable precision approximations and graded approximations, the reduct regarding four-region preservation is defined, and the hierarchical relationship between both reducts is obtained. Finally, both reducts and their hierarchy are illustrated by a statistical decision table. For double-quantitative attribute reduction, the reducts regarding two-region and four-region preservation exhibit generalization and fundamentality/guidance, respectively, thus providing some basic thoughts.
张贤勇. 精度与程度逻辑差双量化粗糙集模型的属性约简[J]. 系统工程理论与实践, 2015, 35(11): 2925-2931.
ZHANG Xian-yong. Attribute reduction for the double-quantitative rough set model based on logical difference of precision and grade. Systems Engineering - Theory & Practice, 2015, 35(11): 2925-2931.
[1] Pawlak Z. Rough sets[J]. International Journal of Computer and Information Sciences, 1982, 11:341-356. [2] Yao Y Y, Deng X F. Quantitative rough sets based on subsethood measures[J]. Information Sciences, 2014, 267:306-322. [3] Ziarko W. Variable precision rough set model[J]. Journal of Computer and System Sciences, 1993, 46(1):39-59. [4] Yao Y Y, Lin T Y. Generalization of rough sets using modal logics[J]. Intelligent Automation and Soft Computing, 1996, 2(2):103-120. [5] Liu J N K, Hu Y X, He Y L. A set covering based approach to find the reduct of variable precision rough set[J]. Information Sciences, 2014, 275:83-100. [6] Yang Y Y, Chen D G, Dong Z. Novel algorithms of attribute reduction with variable precision rough set model[J]. Neurocomputing, 2014, 139(2):336-344. [7] Inuiguchi M, Yoshioka Y, Kusunoki Y. Variable-precision dominance-based rough set approach and attribute reduction[J]. International Journal of Approximate Reasoning, 2009, 50(8):1199-1214. [8] Wang J Y, Zhou J. Research of reduct features in the variable precision rough set model[J]. Neurocomputing, 2009, 72:2643-2648. [9] Mi J S, Wu W Z, Zhang W X. Approaches to knowledge reduction based on variable precision rough set model[J]. Information Sciences, 2004, 159(3-4):255-272. [10] Yao Y Y. The superiority of three-way decision in probabilistic rough set models[J]. Information Sciences, 2011, 181:1080-1096. [11] Yao Y Y, Lin T Y. Graded rough set approximations based on nested neighborhood systems[C]//Proceedings of 5th European Congress on Intelligent Techniques and Soft Computing, Aachen, Verlag Mainz, 1997:196-200. [12] Liu C H, Miao D Q, Zhang N, et al. Graded rough set model based on two universes and its properties[J]. Knowledge-Based Systems, 2012, 33:65-72. [13] Zhang X Y, Mo Z W, Xiong F, et al. Comparative study of variable precision rough set model and graded rough set model[J]. International Journal of Approximate Reasoning, 2012, 53(1):104-116. [14] Zhang X Y, Miao D Q. Two basic double-quantitative rough set models of precision and grade and their investigation using granular computing[J]. International Journal of Approximate Reasoning, 2013, 54(8):1130-1148. [15] Zhang X Y, Miao D Q. Quantitative information architecture, granular computing and rough set models in the double-quantitative approximation space on precision and grade[J]. Information Sciences, 2014, 268:147-168. [16] 张贤勇, 莫智文, 熊方. 精度与程度的逻辑差粗糙集模型及其算法[J]. 系统工程理论与实践, 2011, 31(12):2394-2399.Zhang Xianyong, Mo Zhiwen, Xiong Fang. Rough set model based on logical difference operation of precision and grade and its algorithms[J]. Systems Engineering-Theory & Practice, 2011, 31(12):2394-2399.