Rough variables with values in measurable spaces

An X-valued rough variable is introduced as a measurable function from a rough space to a measurable space X. Based on the concept of X-valued rough variables, some properties of X-valued rough variables are studied. Furthermore, the concept of χ-convergence is presented, and χ-convergence of X-valued rough variables is discussed.

[1]  Andrzej Skowron,et al.  Rough sets and Boolean reasoning , 2007, Inf. Sci..

[2]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[3]  Wojciech Ziarko,et al.  Variable Precision Rough Set Model , 1993, J. Comput. Syst. Sci..

[4]  Wen-Xiu Zhang,et al.  An axiomatic characterization of a fuzzy generalization of rough sets , 2004, Inf. Sci..

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

[6]  Bijan Davvaz,et al.  Roughness in rings , 2004, Inf. Sci..

[7]  Mohamed Quafafou,et al.  alpha-RST: a generalization of rough set theory , 2000, Inf. Sci..

[8]  Z. Pawlak,et al.  Rough set approach to multi-attribute decision analysis , 1994 .

[9]  Van-Nam Huynh,et al.  A roughness measure for fuzzy sets , 2005, Inf. Sci..

[10]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[11]  Zdzislaw Pawlak,et al.  Rough Set Theory and its Applications to Data Analysis , 1998, Cybern. Syst..

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

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

[14]  Dominik Slezak,et al.  The investigation of the Bayesian rough set model , 2005, Int. J. Approx. Reason..

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

[16]  José Edison Cabral,et al.  Fraud detection in electrical energy consumers using rough sets , 2004, 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04CH37583).

[17]  T. Medhat,et al.  Rough set theory for topological spaces , 2005, Int. J. Approx. Reason..