An Improved Variable Tolerance RSM with a Proportion Threshold

Authors: Chen Wu, Youquan Xu, Dandan Li, Ronghua Yang, Lijuan Wang

Abstract:

In rough set models, tolerance relation, similarity relation and limited tolerance relation solve different situation problems for incomplete information systems in which there exists a phenomenon of missing value. If two objects have the same few known attributes and more unknown attributes, they cannot distinguish them well. In order to solve this problem, we presented two improved limited and variable precision rough set models. One is symmetric, the other one is non-symmetric. They all use more stringent condition to separate two small probability equivalent objects into different classes. The two models are needed to engage further study in detail. In the present paper, we newly form object classes with a different respect comparing to the first suggested model. We overcome disadvantages of non-symmetry regarding to the second suggested model. We discuss relationships between or among several models and also make rule generation. The obtained results by applying the second model are more accurate and reasonable.

Keywords: Incomplete information system, rough set, symmetry, variable precision.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125633

References:

[1] Z. Pawlak, "Rough sets". International Journal of Parallel Programming 11 (5),1982: 341–356.
[2] Z. Pawlak, “Rough sets and intelligent data analysis”, Information Sciences. 147 (2002), pp.1-12.
[3] M. Kryszkiewicz, “Rough set approach to incomplete information systems,” Information Science,112(1), 1998, 39-49
[4] J. Stefanowski, S. A. Tsouki, “Incomplete information tables and rough classification,” Computational Intelligence, 17(3), 2001, 545-566
[5] G. Y. Wang, “Extension of rough set under incomplete information systems,” Journal of Computer Research and Development, 39(10), 2002, 1238-1243
[6] X. B. Yang, “Rough set model based on variable parameter classification in incomplete information systems,” Systems Engineering-Theory & Practice, 28(5), 2008, 116-121
[7] X. B. Yang, J. Y. Yang, “Incomplete Information System and Rough Set Theory,” Science Press, 2011, 9
[8] Y. Y. Yao, “Probabilistic rough set approximations,” International Journal of Approximate Reasoning, 49 (2008), 255-271
[9] Y. H. Qian, J. Y. Liang, “Approximation reduction in inconsistent incomplete decision tables,” Knowledge-Based Systems, 23 (2010), 427-433
[10] W. G. Yin, M. Y. Lu, “Variable precision rough set based decision tree classifier”. Journal of Intelligent and Fuzzy Systems, 23 (2012), 61-70
[11] L. J. Wang, C. Wu, “A limited and variable precision rough model with symmetry,” Journal of Jiangnan University (Natural Science Edition), 6(6), 2007, 825-829
[12] W. M. Ma, “Probabilistic rough set over two universes and rough entropy,” International Journal of Approximate Reasoning, 6, 2012, 608-619
[13] Tzung-Pei H, “Learning rules from incomplete training examples by rough sets,” Expert Systems with Application, 2002, 22: 285-293
[14] Ning Shan, Wojciech Ziarko, “Data-based acquisition and incremental modification of classification rules,” Computational Intelligence.1995, 11(2):357-370.