Roughness Bounds in Set-oriented Rough Set Operations

Roughness is an important indicator for the uncertainty of a rough set. This paper analyses the roughness bounds for set-oriented rough set operations. A bound of the roughness of the union between two set-oriented rough sets could be determined by the roughness of the two operand set-oriented sets. In most cases, a bound could also be found for a difference set between two set-oriented rough sets. However, the roughness of the operand sets can not uniquely bound the roughness of their intersection set. The results presented here show that a bound of the set operation can be determined from their operand's roughnesses under some operations. We provide an example to show the derived bounds from operand's roughness.

[1]  Qiang Shen,et al.  Centre for Intelligent Systems and Their Applications Fuzzy Rough Attribute Reduction with Application to Web Categorization Fuzzy Rough Attribute Reduction with Application to Web Categorization Fuzzy Sets and Systems ( ) – Fuzzy–rough Attribute Reduction with Application to Web Categorization , 2022 .

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

[3]  Didier Dubois,et al.  Fuzzy relation equations and causal reasoning , 1995, Fuzzy Sets Syst..

[4]  Zdzislaw Pawlak,et al.  Rough sets and intelligent data analysis , 2002, Inf. Sci..

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

[6]  Amin Mousavi,et al.  Double-faced rough sets and rough communication , 2002, Inf. Sci..

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

[8]  Yiyu Yao.  Combination of Rough and Fuzzy Sets Based on α-Level Sets , 1997 .

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

[10]  A. Wiweger.  On topological rough sets , 1989 .

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

[12]  Andrzej Skowron,et al.  Rough Sets: A Tutorial , 1998 .

[13]  Huaguang Zhang,et al.  Two new operators in rough set theory with applications to fuzzy sets , 2004, Inf. Sci..

[14]  U. Wybraniec-Skardowska.  On a generalization of approximation space , 1989 .

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

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

[17]  Slavka Bodjanova,et al.  Alpha-bounds of fuzzy numbers , 2003, Inf. Sci..

[18]  Jesús Manuel Fernández Salido,et al.  Rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations , 2003, Fuzzy Sets Syst..

[19]  Henri Prade,et al.  A logical approach to interpolation based on similarity relations , 1997, Int. J. Approx. Reason..

[20]  Sankar K. Pal,et al.  Roughness of a Fuzzy Set , 1996, Inf. Sci..

[21]  T. Iwiński.  Algebraic approach to rough sets , 1987 .