On the compact computational domain of fuzzy-rough sets

Based on some properties of fuzzy t-norm and t-conorm operators, the concept of fuzzy-rough sets on compact computational domain has been put forward. Various mathematical properties of this new definition of fuzzy-rough sets are discussed from pattern classification viewpoint. It is established that the proposed approach identifies various patterns in the sense of fuzzy-roughness, in addition to providing deeper insight into various concepts of fuzzy-rough sets.

[1]  Andrzej Skowron,et al.  Rough-Fuzzy Hybridization: A New Trend in Decision Making , 1999 .

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

[3]  Witold Pedrycz,et al.  Shadowed sets: representing and processing fuzzy sets , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[4]  R. Słowiński.  Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory , 1992 .

[5]  Isak Gath,et al.  Unsupervised Optimal Fuzzy Clustering , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  James C. Bezdek,et al.  On cluster validity for the fuzzy c-means model , 1995, IEEE Trans. Fuzzy Syst..

[7]  Sudarsan Nanda,et al.  Fuzziness in rough sets , 2000, Fuzzy Sets Syst..

[8]  Roman Słowiński,et al.  Intelligent Decision Support , 1992, Theory and Decision Library.

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

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

[11]  B. Yegnanarayana,et al.  Rough-fuzzy membership functions , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[12]  Zdzislaw Pawlak,et al.  Rough sets, decision algorithms and Bayes' theorem , 2002, Eur. J. Oper. Res..

[13]  Rajen B. Bhatt,et al.  On fuzzy-rough sets approach to feature selection , 2005, Pattern Recognit. Lett..

[14]  Van-Nam Huynh,et al.  An approach to roughness of fuzzy sets , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

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

[16]  M. Shaw,et al.  Induction of fuzzy decision trees , 1995 .

[17]  Mauro Barni,et al.  Comments on "A possibilistic approach to clustering" , 1996, IEEE Trans. Fuzzy Syst..

[18]  Manish Sarkar,et al.  Fuzzy-rough membership functions , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

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

[20]  James M. Keller,et al.  A possibilistic approach to clustering , 1993, IEEE Trans. Fuzzy Syst..

[21]  Zdzislaw Pawlak.  Rough classification , 1999, Int. J. Hum. Comput. Stud..