Descriptive Method on Data Association Based on Granulation Trees
YAN Shuo1, YAN Lin2
1.School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044 2.College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007
Abstract To study the data association, a data set is divided into different hierarchy granules. Consequently, a hierarchy structure called a granulation tree is obtained. Then, grounded on the granular hierarchy information in the granulation tree, the numerical representation of granularity and the data connections determined by association data, a definition of the data association between two granulation trees is introduced. In this paper, the upper approximation is taken as an operator. With the granule corresponding to the operation of the upper approximation, a theorem is established, and it is used to investigate whether two data are associated with each other. The investigation bases the close degree of the association on the numerical information of granular. Therefore, a method taking granulation trees as the basis to describe the data association is presented. The characteristics of the hierarchy granules and the numerical representation of granularity contained in the method provide a way of research on granular computing. The discussion on a specific example shows the application value of the granulation tree method.
[1] Zhang J B, Li T R, Chen H M. Composite Rough Sets for Dynamic Data Mining. Information Sciences, 2014, 257: 81-100 [2] Zhang J B, Li T R, Ruan D. Neighborhood Rough Sets for Dynamic Data Mining. International Journal of Intelligent Systems, 2012, 27(4): 317-342 [3] Hońko P. Association Discovery from Relational Data via Granular Computing. Information Sciences, 2013, 234: 136-149 [4] Merigó J M. The Probabilistic Weighted Average and Its Application in Multiperson Decision Making. International Journal of Intelligent Systems, 2012, 27(5): 457-476 [5] She Y H. On the Rough Consistency Measures of Logic Theories and Approximate Reasoning in Rough Logic. International Journal of Approximate Reasoning, 2014, 55(1): 486-499 [6] Yan L, Yan S. Granular Reasoning and Decision System′s Decomposition. Journal of Software, 2012, 7(3): 683-690 [7] Yan L, Liu Q. Researches on Granular Reasoning Based on Granular Space // Proc of the IEEE International Conference on Granular Computing. Hangzhou, China, 2008: 706-711 [8] Yan L, Liu Q. Granular Resolution and Granular Reasoning // Proc of the IEEE International Conference on Granular Computing. Nanchang, China, 2009: 668-671 [9] Tagarelli A. Exploring Dictionary-Based Semantic Relatedness in Labeled Tree Data. Information Sciences, 2013, 220: 244-268 [10]Cozman F G. Independence for Full Conditional Probabilities: Structure, Factorization, Non-uniqueness, and Bayesian Networks. International Journal of Approximate Reasoning, 2013, 54(9): 1261-1278 [11] Jia X Y, Liao W H, Tang Z M. Minimum Cost Attribute Reduction in Decision-Theoretic Rough Set Models. Information Sciences, 2013, 219: 151-167 [12] McAllister R A, Angryk R A. Abstracting for Dimensionality Reduction in Text Classification. International Journal of Intelligent Systems, 2013, 28(2): 115-138 [13] Li J H, Mei C L, Lü Y J. Incomplete Decision Contexts: Approximate Concept Construction, Rule Acquisition and Knowledge Reduction. International Journal of Approximate Reasoning, 2013, 54(1): 149-165 [14] Yan L. Fundamentals of Mathematical Logic and Granular Computing. Beijing, China: Science Press, 2007 (in Chinese) (闫 林.数理逻辑基础与粒计算.北京:科学出版社, 2007) [15] Pedrycz W. Granular Computing: Analysis and Design of Intelligent Systems. Boca Raton, USA: CRC Press, 2013 [16] Skowron A, Stepaniuk J, Swiniarski R. Modeling Rough Granular Computing Based on Approximation Spaces. Information Sciences, 2012, 184(1): 20-43 [17] Yan L, Song J P. Granular Trees Based on Different Data Sets and Their Modeling Applications. Computer Science, 2014, 41(3): 258-262 (in Chinese) (闫 林,宋金鹏.数据集的粒化树及其建模应用.计算机科学, 2014, 41(3): 258-262) [18] Pawlak Z. Rough Set: Theoretical Aspects of Reasoning about Data. Dordrecht, The Netherlands: Kluwer Academic Publishers, 1992 [19] Fan T F. Rough Set Analysis of Relational Structures. Information Sciences, 2013, 221: 230-244
2015, Vol. 28 
