Rough Sets and Vague Concept Approximation: From Sample Approximation to Adaptive Learning

We present a rough set approach to vague concept approximation. Approximation spaces used for concept approximation have been initially defined on samples of objects (decision tables) representing partial information about concepts. Such approximation spaces defined on samples are next inductively extended on the whole object universe. This makes it possible to define the concept approximation on extensions of samples. We discuss the role of inductive extensions of approximation spaces in searching for concept approximation. However, searching for relevant inductive extensions of approximation spaces defined on samples is infeasible for compound concepts. We outline an approach making this searching feasible by using a concept ontology specified by domain knowledge and its approximation. We also extend this approach to a framework for adaptive approximation of vague concepts by agents interacting with environments. This paper realizes a step toward approximate reasoning in multiagent systems (MAS), intelligent systems, and complex dynamic systems (CAS).

[1]  Stephen Read,et al.  Thinking about logic : an introduction to the philosophy oflogic , 1995 .

[2]  Nada Lavrac,et al.  The Multi-Purpose Incremental Learning System AQ15 and Its Testing Application to Three Medical Domains , 1986, AAAI.

[3]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[4]  Andrzej Skowron,et al.  Approximate Reasoning in Distributed Environments , 2004 .

[5]  Andrzej Skowron,et al.  Rough set approach to pattern extraction from classifiers, In: Proceedings of the Workshop on Rough Sets in Knowledge Discovery and Soft Computing at ETAPS’2003 , 2003 .

[6]  Jon Rigelsford,et al.  Rough Neural Computing: Techniques for Computing with Words , 2004 .

[7]  Peter Stone,et al.  Layered learning in multiagent systems - a winning approach to robotic soccer , 2000, Intelligent robotics and autonomous agents.

[8]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[9]  Leslie M. Marx,et al.  Adaptive Learning and Iterated Weak Dominance , 1999 .

[10]  Arkadiusz Wojna,et al.  Constraint Based Incremental Learning of Classification Rules , 2000, Rough Sets and Current Trends in Computing.

[11]  Sandip Sen,et al.  Learning and Adaption in Multi-Agent Systems , 2006 .

[12]  Leo Breiman,et al.  Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author) , 2001, Statistical Science.

[13]  Jan Pavelka,et al.  On Fuzzy Logic III. Semantical completeness of some many-valued propositional calculi , 1979, Math. Log. Q..

[14]  Andrzej Skowron,et al.  Approximation Spaces and Information Granulation , 2004, Trans. Rough Sets.

[15]  Andrzej Skowron,et al.  On-Line Elimination of Non-relevant Parts of Complex Objects in Behavioral Pattern Identification , 2005, PReMI.

[16]  Michael Luck,et al.  Agent technology, Computing as Interaction , 2005 .

[17]  Malik Ghallab,et al.  Chapter 14 – Temporal Planning , 2004 .

[18]  James F. Peters,et al.  Rough Sets: Trends and Challenges , 2003, RSFDGrC.

[19]  Stephen Read,et al.  Thinking about logic , 1994 .

[20]  Richard S. Sutton,et al.  Introduction to Reinforcement Learning , 1998 .

[21]  Karl Tuyls,et al.  An Overview of Cooperative and Competitive Multiagent Learning , 2005, LAMAS.

[22]  Karen Holtzblatt.  Designing for the Mobile Device: Experiences, Challenges, and Methods , 2005 .

[23]  Christian Lebiere,et al.  Cognition and Multi-Agent Interaction: From Cognitive Modeling to Social Simulation , 2006 .

[24]  Paolo Traverso,et al.  Automated Planning: Theory & Practice , 2004 .

[25]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning - II , 1975, Inf. Sci..

[26]  Andrzej Skowron,et al.  Rough Sets and Vague Concepts , 2004, Fundam. Informaticae.

[27]  Jan G. Bazan.  Behavioral Pattern Identification Through Rough Set Modeling , 2005, Fundam. Informaticae.

[28]  Marcin Szczuka,et al.  Rough Sets in KDD , 2005 .

[29]  Bart Selman,et al.  A general stochastic approach to solving problems with hard and soft constraints , 1996, Satisfiability Problem: Theory and Applications.

[30]  Sinh Hoa Nguyen,et al.  Regularity analysis and its applications in data mining , 2000 .

[31]  P. Grünwald.  The Minimum Description Length Principle (Adaptive Computation and Machine Learning) , 2007 .

[32]  Leo Breiman,et al.  Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author) , 2001 .

[33]  R. Słowiński,et al.  Learning Decision Rules from Similarity Based Rough Approximations , 1998 .

[34]  J. Sutherland.  The Quark and the Jaguar , 1994 .

[35]  Amy McGovern.  Autonomous Discovery of Abstractions through Interaction with an Environment , 2002, SARA.

[36]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[37]  Andrzej Skowron,et al.  Information Granules and Rough-Neural Computing , 2004 .

[38]  Stefan Edelkamp,et al.  Automated Planning: Theory and Practice , 2007, Künstliche Intell..

[39]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[40]  Z. Pawlak,et al.  Rough membership functions , 1994 .

[41]  Andrzej Skowron,et al.  Calculi of Approximation Spaces , 2006, Fundam. Informaticae.

[42]  Lotfi A. Zadeh,et al.  Fuzzy logic = computing with words , 1996, IEEE Trans. Fuzzy Syst..

[43]  James F. Peters,et al.  Reinforcement Learning with Approximation Spaces , 2006, Fundam. Informaticae.

[44]  S. Tsumoto,et al.  Rough set methods and applications: new developments in knowledge discovery in information systems , 2000 .

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

[46]  Andrzej Skowron,et al.  Transactions on Rough Sets III , 2005, Trans. Rough Sets.

[47]  Tuan Trung Nguyen,et al.  Rough Set Approach to Domain Knowledge Approximation , 2003, Fundam. Informaticae.

[48]  René J. Jorna,et al.  Planning in intelligent systems : aspects, motivations, and methods , 2006 .

[49]  Andrzej Skowron,et al.  Tolerance Approximation Spaces , 1996, Fundam. Informaticae.

[50]  Christophe G. Giraud-Carrier,et al.  A Note on the Utility of Incremental Learning , 2000, AI Commun..

[51]  D. Ruppert.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2004 .

[52]  L. A. ZADEH,et al.  The concept of a linguistic variable and its application to approximate reasoning - I , 1975, Inf. Sci..

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

[54]  Andrzej Skowron,et al.  Rough Sets in Knowledge Discovery 2: Applications, Case Studies, and Software Systems , 1998 .

[55]  Dominik Slezak,et al.  Approximate Entropy Reducts , 2002, Fundam. Informaticae.

[56]  Michael Luck,et al.  Agent technology, Computing as Interaction: A Roadmap for Agent Based Computing , 2005 .

[57]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[58]  Andrzej Skowron,et al.  Rough Sets and Higher Order Vagueness , 2005, RSFDGrC.

[59]  Jerzy W. Grzymala-Busse,et al.  Transactions on Rough Sets I , 2004, Lecture Notes in Computer Science.

[60]  Thomas G. Dietterich.  Machine-Learning Research Four Current Directions , 1997 .

[61]  Andrzej Skowron,et al.  Modelling Complex Patterns by Information Systems , 2005, Fundam. Informaticae.

[62]  Tuan Trung Nguyen.  Eliciting Domain Knowledge in Handwritten Digit Recognition , 2005, PReMI.

[63]  Paul R. Milgrom,et al.  Adaptive and sophisticated learning in normal form games , 1991 .

[64]  Andrzej Skowron,et al.  Rough mereology: A new paradigm for approximate reasoning , 1996, Int. J. Approx. Reason..

[65]  R. Keefe.  Theories of vagueness , 2000 .

[66]  Richard S. Sutton,et al.  Reinforcement Learning: An Introduction , 1998, IEEE Trans. Neural Networks.

[67]  Andrzej Skowron,et al.  Ontological Framework for Approximation , 2005, RSFDGrC.

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

[69]  Andrzej Skowron,et al.  Classifiers Based on Approximate Reasoning Schemes , 2004, MSRAS.

[70]  Andrew G. Barto,et al.  Autonomous discovery of temporal abstractions from interaction with an environment , 2002 .

[71]  Thomas G. Dietterich.  Hierarchical Reinforcement Learning with the MAXQ Value Function Decomposition , 1999, J. Artif. Intell. Res..

[72]  Andrew W. Moore,et al.  Reinforcement Learning: A Survey , 1996, J. Artif. Intell. Res..

[73]  Thomas G. Dietterich.  Machine-Learning Research , 1997, AI Mag..

[74]  James F. Peters,et al.  Rough Set Approach to Pattern Extraction from Classifiers , 2003, RSKD.

[75]  Zbigniew Suraj,et al.  The Synthesis Problem of Concurrent Systems Specified by Dynamic Information Systems , 1998 .

[76]  Andrzej Skowron,et al.  Rough Mereological Calculi of Granules: A Rough Set Approach To Computation , 2001, Comput. Intell..

[77]  Andrzej Skowron,et al.  Layered Learning for Concept Synthesis , 2004, Trans. Rough Sets.