多粒度近似空间中基于“逻辑或”算子的双量化粗糙集模型
Double Quantitative Rough Set Model Based on Logical Disjunct Operation in Multi-Granulation Approximate Space
DOI: 10.12677/ORF.2017.74016, PDF, HTML, XML, 下载: 1,426  浏览: 2,495  科研立项经费支持
作者: 陈华峰, 沈玉玲：重庆电讯职业学院，基础部，重庆；瞿先平：重庆电讯职业学院，基础部，重庆；重庆理工大学，计算机科学与工程学院，重庆
关键词: 多粒度近似空间；逻辑或；变精度粗糙集；程度粗糙集；双量化；Multi-Granulation Approximate Space； Logical Disjunct Operation； Variable Precision Rough Set； Graded Rough Set； Double Quantitative
摘要: 变精度粗糙集和程度粗糙集都是在单粒度近似空间中，基于不可分辨关系的扩展粗糙集模型。从信息量化角度来说，变精度粗糙集描述了近似空间中的相对量化信息，程度粗糙集则用于对绝对量化信息的表示中，而多粒度近似空间作为一种广义的近似空间，是对经典近似空间的自然扩张。为了在多粒度近似空间中研究同时具有信息的相对量化和绝对量化特征的粗糙集模型，本文通过“逻辑或”算子将变精度粗糙集和程度粗糙集在多粒度近似空间中结合起来，建立了“逻辑或”双量化多粒度粗糙集模型。并对该模型的粗糙集区域，以及所具有的一些基本数学性质进行了深入的讨论，为多粒度近似空间中基于粗糙集理论的知识发现，提供了新的研究方法。
Abstract: Both the variable precision rough set and graded rough set are the generalized rough set models based on indiscernibility relation in single granulation approximate space. In the viewpoint of information quantitative, the variable precision rough set describes relative quantitative infor-mation, while graded rough set is used to represent the absolute quantitative information in ap-proximate space. The multi-granulation approximate space as a generalized approximate space is a natural expansion of classical approximation space. In order to study the rough set model that include characteristics of variable precision rough set and graded rough set. We combine them into a double-quantitative multi-granulation rough set model based on logical disjunct operation. Furthermore, the rough set regions and some basic mathematical properties of the proposed model are discussed in detail. This research provides a novel approach to knowledge discovery in multi-granulation approximate space based on rough set theory.
文章引用：陈华峰, 沈玉玲, 瞿先平. 多粒度近似空间中基于“逻辑或”算子的双量化粗糙集模型[J]. 运筹与模糊学, 2017, 7(4): 152-162. https://doi.org/10.12677/ORF.2017.74016

参考文献

[1] Pawlak, Z. (1982) Rough Sets. International Journal of Computer and Information Sciences, 11, 341-356.
https://doi.org/10.1007/BF01001956
[2] Pawlak, Z. and Skowron, A. (2007) Rudiments of Rough Sets. Information Sciences, 177, 3-27.
https://doi.org/10.1016/j.ins.2006.06.003
[3] Yao, Y.Y. and Deng, X.F. (2014) Quantitative Rough Sets Based on Subsethood Measures. Information Sciences, 267, 306-322.
https://doi.org/10.1016/j.ins.2014.01.039
[4] Ziarko, W. (1993) Variable Precision Rough Set Model. Journal of Computer and System Sciences, 46, 39-59.
[5] Yao, Y.Y. and Lin, T.Y. (1996) Generalization of Rough Sets Using Modal Logics. Intelligent Automatic and Soft Computing, 2, 103-120.
https://doi.org/10.1080/10798587.1996.10750660
[6] 张文修, 吴伟志, 梁吉业, 等. 粗糙集理论与方法[M]. 北京: 科学出版社, 2001.
[7] Xu, W.H., Liu, S.H. and Wang, Q.R. (2010) The First Type of Grade Rough Set Based on Rough Membership Function. 2010 Seventh International Conference System and Knowledge Discovery (FSKD), 1922-1926.
https://doi.org/10.1109/FSKD.2010.5569459
[8] Zhang, X.Y., Mo, Z.W., Xiong, F., et al. (2012) Comparative Study of Variable Precision Rough Set Model and Graded Rough Set Model. International Journal of Approximate Reasoning, 53, 104-116.
https://doi.org/10.1016/j.ijar.2011.10.003
[9] 张贤勇, 熊方, 莫志文. 精度与程度的逻辑或粗糙集模型[J]. 模式识别与人工智能, 2009, 17(9): 151-155.
[10] 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.
[11] Zhang, X.Y. and Miao, D.Q. (2013) Two Basic Dou-ble-Quantitative Rough Set Models of Precision and Grade and Their Investigations Using Granular Computing. In-ternational Journal of Approximate Reasoning, 54, 1130-1148.
https://doi.org/10.1016/j.ijar.2013.02.005
[12] 李蒙蒙, 徐伟华. 优势关系下变精度与程度“逻辑且”粗糙模糊集[J]. 计算机科学与探索, 2016, 10(2): 277-284.
[13] Qian, Y.H., Liang, J.Y., Yao, Y.Y., et al. (2010) MGRS: A Multi-Granulation Rough Set. Information Sciences, 180, 949-970.
https://doi.org/10.1016/j.ins.2009.11.023
[14] Qian, Y.H., Liang, J.Y. and Dang, C.Y. (2010) Incomplete Multi-Granulation Rough Set. IEEE Transactions on Systems, Man & Cybernetics Part A, 40, 420-431.
https://doi.org/10.1109/TSMCA.2009.2035436
[15] 窦慧莉, 吴陈, 杨习贝, 等. 可变精度多粒度粗糙集模型[J]. 江苏科技大学学报(自然科学版), 2012, 26(1): 65-69.
[16] 吴志远, 钟培华, 胡建根. 程度多粒度粗糙集[J]. 模糊系统与数学, 2014, 28(3): 165-172.
[17] 沈家兰, 汪小燕, 申元霞, 等. 可变程度多粒度粗糙集[J]. 小型微型计算机系统, 2016, 37(5): 1012-1016.

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