Approximation Algebra and Framework

Generalized approximation algebras and approximation algebras are defined as a theoretical counterpart of all the situations where a "lower" and an "upper" mapping are used. Some models of these structures are discusse, among them rough sets, fuzzy rough sets and possibility theory. Generalized approximation framework and approximation framework are also introduced as an abstraction of all those cases where several approximations are possibile on the same element. Also in this case some examples are given.

[1]  Yiyu Yao,et al.  Interpretation of Belief Functions in The Theory of Rough Sets , 1998, Inf. Sci..

[2]  M. Inuiguchi.  Generalizations of Rough Sets and Rule Extraction , 2004, Trans. Rough Sets.

[3]  Yiyu Yao,et al.  ON MODELING UNCERTAINTY WITH INTERVAL STRUCTURES , 1995, Comput. Intell..

[4]  Didier Dubois,et al.  The logical view of conditioning and its application to possibility and evidence theories , 1990, Int. J. Approx. Reason..

[5]  Gianpiero Cattaneo,et al.  Investigation about Time Monotonicity of Similarity and Preclusive Rough Approximations in Incomplete Information Systems , 2004, Rough Sets and Current Trends in Computing.

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

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

[8]  Yiyu Yao,et al.  A Decision Theoretic Framework for Approximating Concepts , 1992, Int. J. Man Mach. Stud..

[9]  Gianpiero Cattaneo,et al.  Abstract Approximation Spaces for Rough Theories , 2008 .

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

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

[12]  Davide Ciucci,et al.  A Unifying Abstract Approach for Rough Models , 2008, RSKT.

[13]  Ronald R. Yager,et al.  Classic Works of the Dempster-Shafer Theory of Belief Functions , 2010, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[14]  Jouni Järvinen.  On the Structure of Rough Approximations , 2002, Fundam. Informaticae.

[15]  Gianpiero Cattaneo,et al.  Lattices with Interior and Closure Operators and Abstract Approximation Spaces , 2009, Trans. Rough Sets.

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

[17]  Md. Aquil Khan,et al.  Multiple-Source Approximation Systems: Membership Functions and Indiscernibility , 2008, RSKT.

[18]  Gianpiero Cattaneo,et al.  Generalized Rough Sets (Preclusivity Fuzzy-Intuitionistic (BZ) Lattices) , 1997, Stud Logica.

[19]  Mohamed M. E. Abd El-Monsef,et al.  Decision Analysis via Granulation Based on General Binary Relation , 2007, Int. J. Math. Math. Sci..

[20]  Yiyu Yao,et al.  Probabilistic rough set approximations , 2008, Int. J. Approx. Reason..

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

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

[23]  Wojciech Ziarko,et al.  Probabilistic approach to rough sets , 2008, Int. J. Approx. Reason..

[24]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[25]  Chris Cornelis,et al.  Fuzzy Rough Sets: The Forgotten Step , 2007, IEEE Transactions on Fuzzy Systems.

[26]  Didier Dubois,et al.  Possibility Theory, Probability Theory and Multiple-Valued Logics: A Clarification , 2001, Annals of Mathematics and Artificial Intelligence.

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

[28]  C. Cornelis,et al.  Vaguely Quantified Rough Sets , 2009, RSFDGrC.

[29]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.