On characterization of fuzzy rough sets based on pseudo-operations

The main purpose of this paper is to present a general framework for the study of fuzzy rough approximation operators based on pseudo-operations. In this paper, using the pseudo-operation, the pseudo-generalized fuzzy rough sets are presented and some properties of the pseudo fuzzy rough approximation operators are investigated. Meanwhile, connections between the proposed pseudo fuzzy rough approximation operators and the existing fuzzy rough approximation operators are also discussed.

[1]  Zhudeng Wang,et al.  On fuzzy rough sets based on tolerance relations , 2010, Inf. Sci..

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

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

[4]  Yan Gao,et al.  On Covering Rough Sets , 2007, RSKT.

[5]  Qionghai Dai,et al.  A novel approach to fuzzy rough sets based on a fuzzy covering , 2007, Inf. Sci..

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

[7]  Riemann-Stieltjes Type Integral based on Generated Pseudo-Operations , 2006 .

[8]  Wei-Zhi Wu,et al.  Constructive and axiomatic approaches of fuzzy approximation operators , 2004, Inf. Sci..

[9]  Guilong Liu,et al.  Axiomatic systems for rough sets and fuzzy rough sets , 2008, Int. J. Approx. Reason..

[10]  T. Y. Lin,et al.  Neighborhood systems and relational databases , 1988, CSC '88.

[11]  E. Pap,et al.  CHAPTER 30 – Generalized Derivatives* , 2002 .

[12]  Chen Degang,et al.  A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets , 2007 .

[13]  Degang Chen,et al.  Fuzzy rough set theory for the interval-valued fuzzy information systems , 2008, Inf. Sci..

[14]  Endre Pap,et al.  Handbook of measure theory , 2002 .

[15]  Didier Dubois,et al.  Putting Rough Sets and Fuzzy Sets Together , 1992, Intelligent Decision Support.

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

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

[18]  Qinghua Hu,et al.  A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets , 2007, Inf. Sci..

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

[20]  Endre Pap,et al.  Generalized pseudo-convolution in the theory of probabilistic metric spaces, information, fuzzy numbers, optimization, system theory , 1999, Fuzzy Sets Syst..

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

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

[23]  J. Aczél,et al.  Lectures on Functional Equations and Their Applications , 1968 .

[24]  E. Pap,et al.  Pseudo-Laplace transform , 1998 .

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

[26]  Generalization of the Jensen’s inequality for pseudo-integral , 2008 .

[27]  A. Floren,et al.  ' " ' " ' " . " ' " " " " " ' " ' " " " " " : ' " 1 , 2001 .

[28]  E. Pap CHAPTER 35 – Pseudo-Additive Measures and Their Applications , 2002 .

[29]  Wen-Xiu Zhang,et al.  Measuring roughness of generalized rough sets induced by a covering , 2007, Fuzzy Sets Syst..

[30]  Hideo Tanaka,et al.  Fuzzy integrals based on pseudo-additions and multiplications , 1988 .

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

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

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

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

[35]  Katar ´ ina Lendelova ON THE PSEUDO-LEBESGUE-STIELTJES INTEGRAL , 2006 .

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

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

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

[39]  Jun Li,et al.  Pseudo-optimal measures , 2010, Inf. Sci..

[40]  Degang Chen,et al.  Fuzzy rough set theory for the interval-valued fuzzy information systems , 2008, Inf. Sci..

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

[42]  Yee Leung,et al.  Generalized fuzzy rough sets determined by a triangular norm , 2008, Inf. Sci..

[43]  Zengtai Gong,et al.  The further investigation of covering-based rough sets: Uncertainty characterization, similarity measure and generalized models , 2010, Inf. Sci..

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

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

[46]  Endre Pap,et al.  Generalization of the Jensen’s inequality for pseudo-integral , 2008, 2008 6th International Symposium on Intelligent Systems and Informatics.

[47]  William Zhu,et al.  Generalized rough sets based on relations , 2007, Inf. Sci..

[48]  Yee Leung,et al.  Generalized fuzzy rough approximation operators based on fuzzy coverings , 2008, Int. J. Approx. Reason..

[49]  Guilong Liu,et al.  Generalized rough sets over fuzzy lattices , 2008, Inf. Sci..

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