The relationship between L-fuzzy rough set and L-topology

Various fuzzy generalizations of rough approximations have been proposed in the literature. This paper is devoted to the discussion of the relationship between L-fuzzy rough sets and L-topologies on an arbitrary universe. Finally, one-to-one correspondence between the set of all reflexive, transitive L-relations and the set of all Alexandrov L-topologies is obtained.

[1]  Nehad N. Morsi,et al.  Axiomatics for fuzzy rough sets , 1998, Fuzzy Sets Syst..

[2]  J. Goguen.  L-fuzzy sets , 1967 .

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

[4]  Chris Cornelis,et al.  Fuzzy rough sets: beyond the obvious , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[5]  Alexander P. Sostak,et al.  Axiomatic Foundations Of Fixed-Basis Fuzzy Topology , 1999 .

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

[7]  Yee Leung,et al.  On characterizations of (I, J)-fuzzy rough approximation operators , 2005, Fuzzy Sets Syst..

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

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

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

[11]  Qingguo Li,et al.  Construction of rough approximations in fuzzy setting , 2007, Fuzzy Sets Syst..

[12]  Z. Pawlak.  Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[13]  Zhudeng Wang,et al.  Note on "Generalized rough sets based on reflexive and transitive relations" , 2009, Inf. Sci..

[14]  J. Recasens,et al.  UPPER AND LOWER APPROXIMATIONS OF FUZZY SETS , 2000 .

[15]  Zheng Pei,et al.  Generalized rough sets based on reflexive and transitive relations , 2008, Inf. Sci..

[16]  Constantine Tsinakis,et al.  The Structure of Residuated Lattices , 2003, Int. J. Algebra Comput..

[17]  Weixian Xie,et al.  Fuzzy complete lattices , 2009, Fuzzy Sets Syst..

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

[19]  Ulrich Höhle,et al.  Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory , 1998 .

[20]  R. P. Dilworth,et al.  Residuated Lattices. , 1938, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Qi-Ye Zhang,et al.  Continuity in quantitative domains , 2005, Fuzzy Sets Syst..

[22]  Radim Belohlávek,et al.  Fuzzy Galois Connections , 1999, Math. Log. Q..

[23]  Lei Fan,et al.  A New Approach to Quantitative Domain Theory , 2001, MFPS.

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

[25]  Anna Maria Radzikowska,et al.  Characterisation of main classes of fuzzy relations using fuzzy modal operators , 2005, Fuzzy Sets Syst..

[26]  R. Belohlávek.  Fuzzy Closure Operators , 2001 .

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

[28]  Anna Maria Radzikowska,et al.  Fuzzy Rough Sets Based on Residuated Lattices , 2004, Trans. Rough Sets.

[29]  Jari Kortelainen,et al.  A unifying study between modal-like operators, topologies and fuzzy sets , 2007, Fuzzy Sets Syst..

[30]  Helmut Thiele,et al.  On Axiomatic Characterizations of Fuzzy Approximation Operators , 2000, Rough Sets and Current Trends in Computing.