Rough Set Approximations in Multi-scale Interval Information Systems

With the view point of granular computing, the notion of a granule may be interpreted as one of the numerous small particles forming a larger unit. There are different granules at different levels of scale in data sets having hierarchical structures. Human beings often observe objects or deal with data hierarchically structured at different levels of granulations. And in real-world applications, there may exist multiple types of data in interval information systems. Therefore, the concept of multi-scale interval information systems is first introduced in this paper. The lower and upper approximations in multi-scale interval information systems are then defined, and the accuracy and the roughness are also explored. Monotonic properties of these rough set approximations with different levels of granulations are analyzed with illustrative examples.

[1]  Yiyu Yao,et al.  MGRS: A multi-granulation rough set , 2010, Inf. Sci..

[2]  Manfred M. Fischer,et al.  A Rough Set Approach for the Discovery of Classification Rules in Interval-Valued Information Systems , 2008, Int. J. Approx. Reason..

[3]  Yiyu Yao,et al.  Granular Computing Based on Rough Sets, Quotient Space Theory, and Belief Functions , 2003, ISMIS.

[4]  Wei-Zhi Wu,et al.  Rule acquisition in consistent multi-scale decision systems , 2011, 2011 Eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD).

[5]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[6]  Liang Liu,et al.  Decision rule mining using classification consistency rate , 2013, Knowl. Based Syst..

[7]  Y. Yao,et al.  Stratified rough sets and granular computing , 1999, 18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.99TH8397).

[8]  Jiye Liang,et al.  Knowledge structure, knowledge granulation and knowledge distance in a knowledge base , 2009, Int. J. Approx. Reason..

[9]  Yiyu Yao,et al.  A Partition Model of Granular Computing , 2004, Trans. Rough Sets.

[10]  Jiye Liang,et al.  Interval ordered information systems , 2008, Comput. Math. Appl..

[11]  Wei-Zhi Wu,et al.  Knowledge Acquisition in Inconsistent Multi-scale Decision Systems , 2011, RSKT.

[12]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[13]  Yee Leung,et al.  Theory and applications of granular labelled partitions in multi-scale decision tables , 2011, Inf. Sci..

[14]  Wei-Zhi Wu,et al.  Multi-granulation rough sets in multi-scale information systems , 2013, 2013 International Conference on Machine Learning and Cybernetics.

[15]  Wei-Zhi Wu,et al.  Rough Set Approximations Based on Granular Labels , 2009, RSFDGrC.

[16]  Wei-Zhi Wu,et al.  Granular Computing Based on a Generalized Approximation Space , 2007, RSKT.

[17]  Yee Leung,et al.  Clustering by Scale-Space Filtering , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Shusaku Tsumoto,et al.  Automated extraction of hierarchical decision rules from clinical databases using rough set model , 2003, Expert Syst. Appl..

[19]  C. Maria Keet,et al.  A Formal Theory of Granularity , 2008 .

[20]  Yee Leung,et al.  Optimal scale selection for multi-scale decision tables , 2013, Int. J. Approx. Reason..

[21]  Chris Cornelis,et al.  Attribute selection with fuzzy decision reducts , 2010, Inf. Sci..

[22]  Wei-Zhi Wu,et al.  Approaches to knowledge reduction based on variable precision rough set model , 2004, Inf. Sci..

[23]  Y. Yao.  Information granulation and rough set approximation , 2001 .

[24]  Yiyu Yao,et al.  Comparison of Rough-Set and Interval-Set Models for Uncertain Reasoning , 1996, Fundam. Informaticae.

[25]  Andrzej Bargiela,et al.  Toward a Theory of Granular Computing for Human-Centered Information Processing , 2008, IEEE Transactions on Fuzzy Systems.

[26]  Wei-Zhi Wu,et al.  On knowledge acquisition in multi-scale decision systems , 2013, Int. J. Mach. Learn. Cybern..

[27]  Lotfi A. Zadeh,et al.  Fuzzy sets and information granularity , 1996 .

[28]  Chen Wei-min.  Rough Set Theory and Granular Computing , 2006 .

[29]  Qinghua Hu,et al.  Mixed feature selection based on granulation and approximation , 2008, Knowl. Based Syst..

[30]  L. Zadeh,et al.  Data mining, rough sets and granular computing , 2002 .

[31]  Thomas Bittner,et al.  A Theory of Granular Partitions , 2003, Foundations of Geographic Information Science.

[32]  Witold Pedrycz,et al.  Granular computing: an introduction , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).