Textures and covering based rough sets

This paper introduces the relations between covering and dicovering in the framework of rough sets. The natural counterpart of a covering in textures is given by a family of pairs of sets which is called a dicovering. This leads us to two dual concepts which are called star and co-star of a set, respectively. Here, we define dicovering approximation space and we discuss on covering and dicovering based rough sets. In this context, star corresponds to the upper approximation operator defined by Zakowski and co-star corresponds to the lower approximation operator studied by Pomykala, Yao, and Zhu and Wang.

[1]  Murat Diker,et al.  Stone-C˘ech Compactifications of Ditopological Texture Spaces , 2009 .

[2]  Yiyu Yao,et al.  On Generalizing Rough Set Theory , 2003, RSFDGrC.

[3]  W. Zakowski.  APPROXIMATIONS IN THE SPACE (U,π) , 1983 .

[4]  Lawrence M. Brown,et al.  Fuzzy sets as texture spaces, I. Representation theorems , 2000, Fuzzy Sets Syst..

[5]  Murat Diker,et al.  One-point compactifications of ditopological texture spaces , 2004, Fuzzy Sets Syst..

[6]  Daowu Pei,et al.  A generalized model of fuzzy rough sets , 2005, Int. J. Gen. Syst..

[7]  Piero Pagliani.  A Pure Logic-Algebraic Analysis of Rough Top and Rough Bottom Equalities , 1993, RSKD.

[8]  Lawrence M. Brown,et al.  RELATIONS AND CORELATIONS BETWEEN LATTICES OF FUZZY SUBSETS , 2005 .

[9]  Murat Diker,et al.  Interior and closure operators on texture spaces - I: Basic concepts and Cech closure operators , 2010, Fuzzy Sets Syst..

[10]  E. Bryniarski.  A calculus of rough sets of the first order , 1989 .

[11]  Senol Dost,et al.  Ditopological texture spaces and fuzzy topology, I. Basic concepts , 2004, Fuzzy Sets Syst..

[12]  Murat Diker,et al.  Textural approach to generalized rough sets based on relations , 2010, Inf. Sci..

[13]  Zbigniew Bonikowski,et al.  Algebraic Structures of Rough Sets , 1993, RSKD.

[15]  Murat Diker,et al.  Textures and Fuzzy Rough Sets , 2011, Fundam. Informaticae.

[16]  Murat Diker,et al.  Paracompactness and Full Normality in Ditopological Texture Spaces , 1998 .

[17]  Mustafa Demirci,et al.  Textures and C-spaces , 2007, Fuzzy Sets Syst..

[18]  James F. Peters,et al.  Categories of Direlations and Rough Set Approximation Operators , 2010 .

[19]  Siegfried Gottwald,et al.  Fuzzy Sets and Fuzzy Logic , 1993 .

[20]  Lawrence M. Brown,et al.  Sequentially dinormal ditopological texture spaces and dimetrizability , 2008 .

[21]  Murat Diker,et al.  A Wallman-type compactification of texture spaces , 2006, Fuzzy Sets Syst..

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

[23]  Mihir K. Chakraborty,et al.  A Geometry of Approximation , 2009 .

[24]  Li Jin-in.  Rough Sets and Subsets of a Topological Space , 2005 .

[25]  Murat Diker,et al.  Interior and closure operators on texture spaces - II: Dikranjan-Giuli closure operators and Hutton algebras , 2010, Fuzzy Sets Syst..

[26]  XU Zhong-yin,et al.  On the Properties of Covering Rough Sets Model , 2005 .

[27]  Murat Diker,et al.  Ditopological texture spaces and intuitionistic sets , 1998, Fuzzy Sets Syst..

[28]  Wei-Zhi Wu,et al.  On axiomatic characterizations of three pairs of covering based approximation operators , 2010, Inf. Sci..

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

[30]  Diker,et al.  Definability and Textural Rough Set Algebras , 2010 .

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

[32]  Lawrence M. Brown,et al.  Di-uniform texture spaces , 2003 .

[33]  Ivan Kramosil.  Fuzzy Sets and Fuzzy Logic --Foundations of Applications from a Mathematical Point of View , 1995 .

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