Fuzzy Approximating Spaces

Relationships between fuzzy relations and fuzzy topologies are deeply researched. The concept of fuzzy approximating spaces is introduced and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained.

[1]  Sankar K. Pal,et al.  Soft data mining, computational theory of perceptions, and rough-fuzzy approach , 2004, Inf. Sci..

[2]  Dexue Zhang,et al.  Fuzzy preorder and fuzzy topology , 2006, Fuzzy Sets Syst..

[3]  J. Kortelainen.  On relationship between modified sets, topological spaces and rough sets , 1994 .

[4]  Guo-Jun Wang,et al.  An axiomatic approach of fuzzy rough sets based on residuated lattices , 2009, Comput. Math. Appl..

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

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

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

[8]  Yiyu Yao,et al.  Two views of the theory of rough sets in finite universes , 1996, Int. J. Approx. Reason..

[9]  Qingguo Li,et al.  Topological structure of generalized rough sets , 2012, Comput. Math. Appl..

[10]  C. L. Chang,et al.  Fuzzy topological spaces , 1968 .

[11]  L. Kuncheva.  Fuzzy rough sets: application to feature selection , 1992 .

[12]  William Zhu,et al.  The algebraic structures of generalized rough set theory , 2008, Inf. Sci..

[13]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[14]  D. Vanderpooten.  Similarity Relation as a Basis for Rough Approximations , 1995 .

[15]  Lingyun Yang,et al.  Topological properties of generalized approximation spaces , 2011, Inf. Sci..

[16]  S. Nanda,et al.  Fuzzy rough sets , 1992 .

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

[18]  Zheng Pei,et al.  On the topological properties of fuzzy rough sets , 2005, Fuzzy Sets Syst..

[19]  Andrzej Skowron,et al.  Tolerance Approximation Spaces , 1996, Fundam. Informaticae.

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

[21]  L. Zadeh.  Fuzzy Topology. I. Neighborhood Structure of a Fuzzy Point and Moore-Smith Convergence* , 2003 .

[22]  Anna Maria Radzikowska,et al.  A comparative study of fuzzy rough sets , 2002, Fuzzy Sets Syst..

[23]  Salvatore Greco,et al.  Fuzzy Similarity Relation as a Basis for Rough Approximations , 1998, Rough Sets and Current Trends in Computing.

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

[25]  Li Zheng,et al.  Topology vs generalized rough sets , 2011, Int. J. Approx. Reason..

[26]  YongXuan Huang,et al.  Topology Theory on Rough Sets , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[27]  Wei-Zhi Wu,et al.  Generalized fuzzy rough sets , 2003, Inf. Sci..

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

[29]  R. Lowen.  Fuzzy topological spaces and fuzzy compactness , 1976 .