Rough sets, neighborhood systems and granular computing

Granulation of a universe involves grouping of similar elements into granules. With granulated views, we deal with approximations of concepts, represented by subsets of the universe, in terms of granules. This paper examines the problem of approximations with respect to various granulations of the universe. The granulation structures used by both rough set theory and neighborhood systems, and the corresponding approximation structures, are studied.

[1]  Lotfi A. Zadeh,et al.  Fuzzy sets and information granularity , 1996 .

[2]  A. Macallum.  The University of Toronto , 1907, Nature.

[3]  A. Skowron,et al.  Towards adaptive calculus of granules , 1998 .

[4]  T. Y. Lin,et al.  NEIGHBORHOOD SYSTEMS AND APPROXIMATION IN RELATIONAL DATABASES AND KNOWLEDGE BASES , 1989 .

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

[6]  Salvatore Greco,et al.  Fuzzy Similarity Relation as a Basis for Rough Approximations , 1998, Rough Sets and Current Trends in Computing.

[7]  Yiyu Yao,et al.  Generalization of Rough Sets using Modal Logics , 1996, Intell. Autom. Soft Comput..

[8]  D. Vanderpooten.  Similarity Relation as a Basis for Rough Approximations , 1995 .

[9]  Z. Pawlak.  Granularity of knowledge, indiscernibility and rough sets , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[10]  Yiyu Yao.  Granular Computing using Neighborhood Systems , 1999 .

[11]  Y. Yao,et al.  Generalized Rough Set Models , 1998 .

[12]  Y. Yao,et al.  Stratified rough sets and granular computing , 1999, 18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.99TH8397).

[13]  Yiyu Yao,et al.  On Generalizing Pawlak Approximation Operators , 1998, Rough Sets and Current Trends in Computing.

[14]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[15]  Sadaaki Miyamoto,et al.  Rough Sets and Current Trends in Computing , 2012, Lecture Notes in Computer Science.