Study on conditions of neighborhoods forming a partition

A rough set is basically an approximation representation of the given data. The representation is expressed in two subsets defined on the data set: the upper and lower approximations. As well known, there are many different definitions about the two approximations. An open question regarding rough set is how to characterize the conditions for a neighborhood of a data item using the upper and lower approximations to form a partition of the universe U of the data. In this paper, we address this open question by defining two special operators, and there are some significant results about them.

[1]  Ivo Düntsch,et al.  Rough Set Data Analysis , 2000 .

[2]  Yan Gao,et al.  On Covering Rough Sets , 2007, RSKT.

[3]  D. Mohanty.  ROUGH SET ON GENERALIZED COVERING APPROXIMATION SPACES , 2010 .

[4]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[5]  N. D. Thuan,et al.  Covering Rough Sets From a Topological Point of View , 2012, ArXiv.

[6]  Shusaku Tsumoto,et al.  Rough Set Data Analysis , 2009, Encyclopedia of Complexity and Systems Science.

[7]  Xiaole Bai,et al.  Axiomatization and conditions for neighborhoods in a covering to form a partition , 2011, Inf. Sci..

[8]  Wen-Xiu Zhang,et al.  Measuring roughness of generalized rough sets induced by a covering , 2007, Fuzzy Sets Syst..

[9]  Hui Liu,et al.  Study of definable subsets in covering approximation spaces of rough sets , 2011, 2011 IEEE International Conference on Information Reuse & Integration.

[10]  William Zhu,et al.  On Three Types of Covering-Based Rough Sets , 2014, IEEE Transactions on Knowledge and Data Engineering.

[11]  William Zhu,et al.  Relationship among basic concepts in covering-based rough sets , 2009, Inf. Sci..

[13]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[14]  L. Polkowski.  Rough Sets: Mathematical Foundations , 2013 .

[15]  Zhaowen Li,et al.  Definable Subsets in Covering Approximation Spaces , 2011 .

[17]  Fei-Yue Wang,et al.  Reduction and axiomization of covering generalized rough sets , 2003, Inf. Sci..

[18]  Ivo Düntsch,et al.  Logical and algebraic techniques for rough set data analysis , 2000 .

[19]  Urszula Wybraniec-Skardowska,et al.  Extensions and Intentions in the Ruogh Set Theory , 1998, Inf. Sci..

[20]  Daowu Pei,et al.  On definable concepts of rough set models , 2007, Inf. Sci..

[21]  Andrzej Skowron,et al.  Rough sets: Some extensions , 2007, Inf. Sci..

[22]  Ping Zhu,et al.  Covering rough sets based on neighborhoods: An approach without using neighborhoods , 2009, Int. J. Approx. Reason..

[23]  D. Mohanty.  Dependency on Rough Set Approximation Spaces , 2010 .

[24]  Tongjun Li,et al.  Rough Set Models on Granular Structures and Rule Induction , 2011 .

[25]  Yiyu Yao,et al.  Relational Interpretations of Neigborhood Operators and Rough Set Approximation Operators , 1998, Inf. Sci..

[26]  Jianguo Tang,et al.  Covering-based Rough sets Based on the Refinement of Covering-element , 2011 .

[27]  L. Fu.  The Minimal Description of Formal Concept Analysis , 2010 .

[28]  T. Y. Lin,et al.  Neighborhood systems and relational databases , 1988, CSC '88.

[29]  Jinjin Li,et al.  Some Separations in Covering Approximation Spaces , 2010 .