Calculi of Approximation Spaces

• Autorzy: Skowron A. , Stepaniuk J. , Peters J. , Swinarski R.
• Języki publikacji: EN

Abstrakty

EN

This paper considers the problem of how to establish calculi of approximation spaces. Approximation spaces considered in the context of rough sets were introduced by Zdzisaw Pawlak more than two decades ago. In general, a calculus of approximation spaces is a system for combining, describing, measuring, reasoning about, and performing operations on approximation spaces. An approach to achieving a calculus of approximation spaces that provides a basis for approximating reasoning in distributed systems of cooperating agents is considered in this paper. Examples of basic concepts are given throughout this paper to illustrate how approximation spaces can be beneficially used in many settings, in particular for complex concept approximation. The contribution of this paper is the presentation of a framework for calculi of approximation spaces useful for approximate reasoning by cooperating agents.

Słowa kluczowe

EN

rough sets; approximation space; concept approximations; learning; approximate reasoning

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2006
• Tom: Vol. 72, nr 1-3
• Strony: 363--378
• Opis fizyczny: bibliogr. 52 poz.

Twórcy

autor

Skowron A.

autor

Stepaniuk J.

autor

Peters J.

autor

Swinarski R.

• Department of Computer Science, Białystok University of technology, Wiejska 45A, 15-351 Białystok, Poland,

Bibliografia

• [1] Albus, J.S., Meystel, A. M.: Engineering of mind: An introduction to the science of intelligent systems. John Wiley, New York, 2001.
• [2] Anderson, J.R.: Rules of the Mind. Lawrence Erlbaum, Hillsdale, NJ, 1993.
• [3] Barwise, J., Seligman, J.: Information Flow: The Logic of Distributed Systems. Cambridge University Press Tracts in Theoretical Computer Science 44, 1997.
• [4] Bazan, J., Peters, J., F., Skowron, A.: Behavioral pattern identification through rough set modelling. In: LNAI 3642, Springer, Heidelberg, 2005, 688-697.
• [5] Bazan, J., Skowron, A.: Classifiers based on approximate reasoning schemes. In: Dunin-Kęplicz, B., Jankowski A., Skowron A., and Szczuka M., (Eds.), Monitoring, Security, and Rescue Techniques in Multiagent Systems MSRAS, Advances in Soft Computing. Springer, Heidelberg, 2005, 191-202.
• [6] Bazan, J., Nguyen, S. Hoa, Nguyen, H. Son, Skowron, A.: Rough set methods in approximation of hierarchical concepts. Proc. of RSCTC'2004, LNAI 3066, Springer, Heidelberg, 2004, 346-355.
• [7] Gomolinska, A.: Rough validity, confidence, and coverage of rules in approximation spaces. LNCS 3400, Transactions on Rough Sets III, Springer, Heidelberg, 2005, 57-81.
• [8] Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. Springer-Verlag, Heidelberg, 2003.
• [9] Kieras, D., Meyer, D.E.: An overview of the EPIC architecture for cognition and performance with application to human-computer interaction. Human-Computer Interaction 12: 391-438, 1997.
• [10] Langley, P., Laird, J.E.: Cognitive architectures: Research issues and challenges. Technical Report, Institute for the Study of Learning and Expertise, Palo Alto, CA, 2002.
• [11] Leibniz, G.W., Opuscles et fragments inedits de Leibniz, edited by L. Couturat. Paris, 1903, 256.
• [12] Luck, M., McBurney, P., Preist, Ch.: Agent Technology: Enabling Next Generation. A Roadmap for Agent Based Computing, Agent Link, 2003.
• [13] Łukasiewicz, J.: Die logischen Grundlagen derWahrscheinlichkeitsrechnung, Kraków 1913. In: Borkowski, L. (ed.), Jan Łukasiewicz - SelectedWorks. North Holland, Amsterdam, Polish Scientific Publishers,Warsaw, 1970.
• [14] Meyer, D. E., Kieras, D. E.: A computational theory of executive cognitive processes and multiple-task performance: Part 1. Basic mechanisms. Psychological Review 104: 3-65, 1997.
• [15] Meyer, D. E., Kieras, D. E.: A computational theory of executive control processes and human multiple-task performance: Part 2. Accounts of Psychological Refractory-Period Phenomena. Psychological Review 104: 749-791, 1997.
• [16] Newell, A.: (1990). Unified Theories of Cognition. Cambridge, Harvard University Press, MA, 1980.
• [17] Nguyen, S. Hoa, Bazan, J., Skowron, A., Nguyen, H. Son: Layered learning for concept synthesis. Transactions on Rough Sets I: LNCS Journal Subline, LNCS 3100, Springer, Heidelberg, 2004, 187-208
• [18] Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht, 1991.
• [19] Peters, J. F.: Approximation spaces for hierarchical intelligent behavioral system models. In B.D. Kęplicz, A. Jankowski, A. Skowron, M. Szczuka (Eds.), Monitoring, Security and Rescue Techniques in Multiagent Systems, Advances in Soft Computing, Physica-Verlag, Heidelberg, 2004, 13-30.
• [20] Peters, J.F.: Rough ethology: Towards a biologically-inspired study of collective behavior in intelligent systems with approximation spaces. LNAI 3400, Transactions on Rough Sets III: 153-174, Springer, Heidelberg, 2005.
• [21] Peters, J. F. : Approximation space for intelligent system design patterns. Engineering Applications of Artificial Intelligence 17(4): 1-8, 2004.
• [22] Peters, J.F., Henry, C.: Reinforcement learning with approximation spaces. Fundamenta Informaticae, 2006 (to appear).
• [23] Peters, J. F., Skowron, A., Stepaniuk, J., Ramanna, S.: Towards an ontology of approximate reason. Fundamenta Informaticae 51(1-2), 157-173, 2002.
• [24] Peters, J. F., Henry, C., Ramanna, S.: Reinforcement learning with pattern-based rewards. In Proc. Fourth Int. IASTED Conf. Computational Intelligence (CI 2005), Calgary, Alberta, Canada (4-6 July 2005) 267-272.
• [25] Peters, J.F.: Approximation spaces in off-policy Monte Carlo learning. Plenary paper in T. Burczynski, W. Cholewa, W. Moczulski (Eds.), Recent Methods in Artificial Intelligence Methods, AI-METH Series, Gliwice, 2005, 139-144.
• [26] Peters, J.F., Henry, C., Lockery, D., Borkowski, M., Ramanna, S.: Approximation spaces for swarms that learn. In T. Burczynski,W. Cholewa,W.Moczulski (Eds.), RecentMethods in Artificial IntelligenceMethods, AI-METH Series, Gliwice, 2005, 135-138.
• [27] Pal, S.K., Polkowski, L., Skowron, A. (Eds.): Rough-Neural Computing: Techniques for Computing with Words. Springer-Verlag, Berlin, 2004.
• [28] Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning. International Journal Approximate Reasoning 15(4): 333-365, 1996.
• [29] Polkowski, L., Skowron, A.: Towards adaptive calculus of granules. In: [51], 201-227.
• [30] Precup,D.: Temporal Abstraction in Reinforcement Learning. Ph.D. thesis, Supervisor: R.S. Sutton, Department of Computer Science, University of Massachusetts, 2000.
• [31] Rummery, G.A.: Problem Solving with Reinforcement Learning. Ph.D. Thesis, Cambridge University, 1995.
• [32] Skowron,A.: Toward intelligent systems: Calculi of information granules. Bulletin of the Rough Set Society, 5(1-2): 9-30, 2001.
• [33] Skowron, A., Swiniarski, R.W.: Information granulation and pattern recognition. In: [27], 2004, 599-636.
• [34] Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27: 245-253, 1996.
• [35] Skowron, A., Stepaniuk, J.: Information granules: Towards foundations of granular computing. International Journal of Intelligent Systems 16(1): 57-86, 2001.
• [36] Skowron, A., Stepaniuk, J.: Information granules and rough-neural computing. In: [27], 43-84.
• [37] Skowron, A., Stepaniuk, J., Peters, J.F.: Rough sets and infomorphisms: Towards approximation of relations in distributed environments. Fundamenta Informaticae 54(1-2): 263-277, 2003.
• [38] Skowron, A., Stepaniuk, J.: Constrained sums of information systems. In: Proc. RSCTC 2004, LNCS 3066, Springer, Heidelberg, 2004, 300-309.
• [39] Skowron, A., Synak, P., Complex patterns. Fundamenta Informaticae 60(1-4): 351-366, 2004.
• [40] Skowron, A., Swiniarski, R., Synak, P: Approximation spaces and information granulation. Transactions on Rough Sets III: LNCS Journal Subline, LNCS 3400, Springer, Heidelberg, 2005, 175-189.
• [41] Skowron, A., Stepaniuk, J. (2005). Ontological framework for approximation. In: D. ślęzak, G. Wang, M. Szczuka, I. Düntsch, Y.Y. Yao (Eds.), Proceedings of the 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC'2005), Regina, Canada, August 31-September 3, 2005, Part I, LNAI 3641, Springer, Heidelberg, 718-727.
• [42] Staab, S., Studer, R., (Eds.): Handbook on Ontologies. International Handbooks on Information Systems, Springer, Heidelberg, 2004.
• [43] Stepaniuk, J.: Rough relations and logics. In: L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 1. Methodology and Applications, Physica Verlag, Heidelberg, 1998, 248-260.
• [44] Stepaniuk, J.: Knowledge discovery by application of rough set models. In: L. Polkowski, S. Tsumoto, T.Y. Lin (Eds.), Rough Set Methods and Applications. New Developments in Knowledge Discovery in Information Systems, Physica-Verlag, Heidelberg, 2000, 137-233.
• [45] Stone, P.: Layered Learning in Multi-Agent Systems: A Winning Approach to Robotic Soccer. MIT Press, Cambridge,MA, 2000.
• [46] Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. TheMIT Press, Cambridge,MA, 1998.
• [47] Tarski, A., Introduction to logic and to the methodology of deductive sciences, Oxford University Press, NY, 1965, IV, 68-78.
• [48] Tinbergen, N.: On aims and methods of ethology, Zeitschrift für Tierpsychologie 20: 410-433, 1963.
• [49] Veloso, M.M., Carbonell, J.G.: Derivational analogy in PRODIGY: Automating case acquisition, storage, and utilization. Machine Learning 10: 249-278, 1993.
• [50] C.J.C.H. Watkins, Learning from Delayed Rewards. Ph.D. Thesis, supervisor: Richard Young, King's College, University of Cambridge, UK, May, 1989.
• [51] Zadeh, L.A., Kacprzyk, J. (Eds.): Computing with Words in Information/Intelligent Systems 1-2, Physica-Verlag, Heidelberg, 1999.
• [52] Ziarko,W., Variable precision rough set model, Journal of Computer and System Sciences 46: 39-59, 1993.