Properties of the Second Type of Covering-Based Rough Sets

To deal with the vagueness and granularity in information systems, researchers proposed several methods such as fuzzy theory and rough set theory. This paper studies a class of covering-based generalized rough sets. In this setting, a covering can generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied. We investigate conditions for a covering under which these properties hold for the second type of covering-based lower and upper approximation operations

[1]  John N. Mordeson,et al.  Rough set theory applied to (fuzzy) ideal theory , 2001, Fuzzy Sets Syst..

[2]  Yiyu Yao,et al.  A Comparative Study of Fuzzy Sets and Rough Sets , 1998 .

[3]  Yiyu Yao,et al.  On Generalizing Pawlak Approximation Operators , 1998, Rough Sets and Current Trends in Computing.

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

[5]  Yiyu Yao,et al.  Subsystem Based Generalizations of Rough Set Approximations , 2005, ISMIS.

[6]  Tsau Young Lin,et al.  Rough Approximate Operators: Axiomatic Rough Set Theory , 1993, RSKD.

[7]  Fei-Yue Wang,et al.  Relationships among three types of covering rough sets , 2006, 2006 IEEE International Conference on Granular Computing.

[8]  Yiyu Yao,et al.  Constructive and Algebraic Methods of the Theory of Rough Sets , 1998, Inf. Sci..

[9]  William Zhu,et al.  Topological approaches to covering rough sets , 2007, Inf. Sci..

[10]  Fei-Yue Wang,et al.  Axiomatic Systems of Generalized Rough Sets , 2006, RSKT.

[11]  Daniel Vanderpooten,et al.  A Generalized Definition of Rough Approximations Based on Similarity , 2000, IEEE Trans. Knowl. Data Eng..

[12]  Guilong Liu.  The transitive closures of matrices over distributive lattices , 2006, 2006 IEEE International Conference on Granular Computing.

[13]  Fei-Yue Wang,et al.  On the abstraction of conventional dynamic systems: from numerical analysis to linguistic analysis , 2005, Inf. Sci..

[14]  Ewa Orlowska,et al.  Semantic Analysis of Inductive Reasoning , 1986, Theor. Comput. Sci..

[15]  Fei-Yue Wang,et al.  A New Type of Covering Rough Set , 2006, 2006 3rd International IEEE Conference Intelligent Systems.

[16]  Fei-Yue Wang,et al.  Binary Relation Based Rough Sets , 2006, FSKD.

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

[18]  Wei-Zhi Wu,et al.  Rough set approximations VS. measurable spaces , 2006, 2006 IEEE International Conference on Granular Computing.

[19]  Marzena Kryszkiewicz,et al.  Rules in Incomplete Information Systems , 1999, Inf. Sci..

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

[21]  Zheng Pei,et al.  The Relationship Among Several Knowledge Reduction Approaches , 2005, FSKD.

[22]  William Zhu,et al.  Recognition in software watermarking , 2006, MCPS '06.

[23]  Marzena Kryszkiewicz,et al.  Rough Set Approach to Incomplete Information Systems , 1998, Inf. Sci..

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

[25]  Fei-Yue Wang,et al.  Covering Based Granular Computing for Conflict Analysis , 2006, ISI.

[26]  F. Zhu,et al.  Logical properties of rough sets , 2000, Proceedings Fourth International Conference/Exhibition on High Performance Computing in the Asia-Pacific Region.

[27]  William Zhu,et al.  Extraction in software watermarking , 2006, MM&Sec '06.

[28]  Qing Liu,et al.  Semantic analysis of rough logical formulas based on granular computing , 2006, 2006 IEEE International Conference on Granular Computing.