alpha-RST: a generalization of rough set theory

The paper presents a transition from the crisp rough set theory to a fuzzy one, called Alpha Rough Set Theory or, in short, a-RST. All basic concepts or rough set theory are extended, i.e., information system, indiscernibility, dependency, reduction, core, definability, approximations and boundary. The resulted theory takes into account fuzzy data and allows the approximation of fuzzy concepts. Besides, the control of knowledge granularity is natural in a-RST which is based on a parameterized indiscernibility relation. a-RST is developed to recognize non-deterministic relationships using notions as a-dependency, a-reduct and so forth. On the other hand, we introduce a notion of relative dependency as an alternative of the absolute definibility presented in rough set theory. The extension a-RST leads naturally to the new concept of alpha rough sets which represents sets with fuzzy non-empty boundaries. ” 2000 Elsevier Science Inc. All rights reserved.

[1]  Z. Pawlak,et al.  Decision analysis using rough sets , 1994 .

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

[3]  J. Bezdek,et al.  Fuzzy partitions and relations; an axiomatic basis for clustering , 1978 .

[4]  Jerzy W. Grzymala-Busse,et al.  The Rule Induction System LERS-a version for personal computers in Foun-dations of Computing and Dec , 1993 .

[5]  R. Słowiński.  A generalization of the indiscernibility relation for rough set analysis of quantitative information , 1992 .

[6]  L. Valverde,et al.  An Inquiry into Indistinguishability Operators , 1984 .

[7]  S. Ovchinnikov.  Similarity relations, fuzzy partitions, and fuzzy orderings , 1991 .

[8]  W. Ziarko,et al.  An application of DATALOGIC/R knowledge discovery tool to identify strong predictive rules in stock market data , 1993 .

[9]  Enrique Ruspini,et al.  A theory of fuzzy clustering , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[10]  Vijay V. Raghavan,et al.  Exploiting Upper Approximation in the Rough Set Methodology , 1995, KDD.

[11]  L. Zadeh,et al.  An Introduction to Fuzzy Logic Applications in Intelligent Systems , 1992 .

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

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

[14]  R. Słowiński,et al.  Rough sets analysis of diagnostic capacity of vibroacoustic symptoms , 1992 .

[15]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[16]  S. K. Michael Wong,et al.  Ruzzy Representations in Rough Set Approximations , 1993, RSKD.

[17]  Keki B. Irani,et al.  Multi-interval discretization of continuos attributes as pre-processing for classi cation learning , 1993, IJCAI 1993.

[18]  Roman Slowinski,et al.  Handling Various Types of Uncertainty in the Rough Set Approach , 1993, RSKD.

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

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

[21]  Earl Cox,et al.  The fuzzy systems handbook , 1994 .

[22]  Roman Slowinski,et al.  Sensitivity Analysis of Rough Classification , 1990, Int. J. Man Mach. Stud..

[23]  Wojciech Ziarko,et al.  Variable Precision Rough Set Model , 1993, J. Comput. Syst. Sci..

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

[25]  John Harris,et al.  An Introduction to Fuzzy Logic Applications , 2000 .

[26]  Jerzy W. Grzymala-Busse,et al.  Rough sets : New horizons in commercial and industrial AI , 1995 .

[27]  Bart Kosko,et al.  Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence , 1991 .

[28]  Usama M. Fayyad,et al.  Multi-Interval Discretization of Continuous-Valued Attributes for Classification Learning , 1993, IJCAI.

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

[30]  C. Zopounidis,et al.  Rough-Set Sorting of Firms According to Bankruptcy Risk , 1994 .

[31]  B. C. Brookes,et al.  Information Sciences , 2020, Cognitive Skills You Need for the 21st Century.

[32]  D. Dubois,et al.  Twofold fuzzy sets and rough sets—Some issues in knowledge representation , 1987 .