Synthesis of Decision Systems from Data Tables

  • Andrzej Skowron
  • Lech Polkowski


We discuss two basic questions related to the synthesis of decision algorithms.

The first question can be formulated as follows: what strategies can be used in order to discover the decision rules from experimental data? Answering this question, we propose to build these strategies on the basis of rough set methods and Boolean reasoning techniques. We present some applications of these methods for extracting decision rules from decision tables used to represent experimental data.

The second question can be formulated as follows: what is a general framework for approximate reasoning in distributed systems? Answering this question, we assume that distributed systems are organized on rough mereological principles in order to assembly (construct) complex objects satisfying a given specification in a satisfactory degree. We discuss how this approach can be used for building the foundations for approximate reasoning. Our approach is based on rough mereology, the recently developed extension of mereology of Leśniewski.


Decision Rule Decision Table Tolerance Relation Decision Class Approximate Reasoning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Aarts E., Korst J., “Simulated Annealing and Boltzmann Machines”, Wiley, New York 1989.MATHGoogle Scholar
  2. [2]
    Anderberg M.R., “Cluster Analysis for Applications”, Academic Press, New York 1973.MATHGoogle Scholar
  3. [3]
    Bazan J., Skowron A., Synak P., “Discovery of Decision Rules from Experimental Data”, Soft Computing, T.Y. Lin, A.M. Wildberger (eds.), Simulation Councils, San Diego 1995, pp. 276–279.Google Scholar
  4. [4]
    Bazan J., Skowron A., Synak P., “Dynamic Reducts as a Tool for Extracting Laws from Decision Tables”, Proc. of the Symp. on Methodologies for Intelligent Systems, Charlotte, NC, October 16–19, 1994, Lecture Notes in Arificial Intelligence 869, Springer-Verlag, Berlin 1994, pp. 346–355.Google Scholar
  5. [5]
    Bazan J., Nguyen S.H., Nguyen T.T., Skowron A., Stepaniuk J., “Applications of Modal Logics and Rough Sets for Classifying Objects”, In: Second World Conference on Fundamentals of Artificial Intelligence, De Glas M., Pawlak Z. (eds.), 3–7 July 1995, Angkor, Paris 1995, pp. 15–26.Google Scholar
  6. [6]
    Bazan J., Skowron A., “Dynamic Reducts and Stable Coverings of the Objects Set”, in preparation.Google Scholar
  7. [7]
    Bouckaert R.R., “;Properties of Bayesian Belief Networks Learning Algorithm”, In: Proc. of the 10-th Conf. on Uncertainty in AI, University of Washington, Seattle 1994, de Mantarnas R.L., Poole D. (eds.) Morgan Kaufmann, San Franciso 1994, pp. 102–109.Google Scholar
  8. [8]
    Brown E.M., “Boolean Reasoning”, Kluwer, Dordrecht 1990.MATHGoogle Scholar
  9. [9]
    Dubois D., Prade H., Yager R.R., “Readings in Fuzzy Sets and Intelligent Systems”, Morgan Kaufmann, San Mateo 1993.Google Scholar
  10. [10]
    Freeman J.D., Skapura D.M., “Neural Networks: Algorithms, Applications and Programming Techniques”, Addison Wesley, Reading, MA 1992.Google Scholar
  11. [11]
    Garey M.S., Johnson D.S., “Computers and Intractability”, W.M. Freeman, New York 1979.MATHGoogle Scholar
  12. [12]
    Goldberg D.E., “Genetic Algorithms in Search Optimization and Machine Learning”, Addison-Wesley, Reading, MA 1989.MATHGoogle Scholar
  13. [13]
    Holland J.H., “Adaptation in Natural and Artificial Systems”, The MIT Press, Cambridge, MA 1993.Google Scholar
  14. [14]
    Market Data, manuscript from Hughes Research Laboratories.Google Scholar
  15. [15]
    Komorowski J., Polkowski L., Skowron A., “Towards a Rough Mereology - Based Logic for Approximate Solution Synthesis. Part 1”, Studia Logica, to appear.Google Scholar
  16. [16]
    Low B.T.,: Neural-Logic Belief Networks - a Tool for Knowledge Representation and Reasoning”, Proc. of the 5-th IEEE International Conference on Tools with Artificial Intelligence, Boston 1993, pp. 34–37.Google Scholar
  17. [17]
    Lenarcik A., Piasta Z., “Deterministic Rough Classifiers”, ICS Research Report 46/94, Warsaw University of Technology 1994.Google Scholar
  18. [18]
    Lesniewski S., “Foundations of the General Theory of Sets” (in Polish), Moscow, 1916; also in: Surma, Srzednicki, Barnett, Rickey (eds.), “Stanislaw Lesniewski Collected Works”, Kluwer. Dordrecht 1992, pp. 128–173.Google Scholar
  19. [19]
    Michie D., Spiegelhalter D.J., Taylor C.C., “Machine Learning: Neural and Statistical Classification”, Ellis Horwood, New York 1994.Google Scholar
  20. [20]
    Michalski R., Tecuci G., “Machine Learning. A Multistrategy Approach vol.IV”, Morgan Kaufmann, San Mateo 1994.Google Scholar
  21. [21]
    Mollestad T., Skowron A., “Learning Propositional Default Rules Using Rough Set Approach”, In: Proc. of the Fifth Scandinavian Conference on Artifical Intelligence SCAI - 95, Aamodt A., Komorowski J. (eds.), IOS Press, Amsterdam 1995, pp.208–219.Google Scholar
  22. [22]
    Nadler M., Smith E.P., “Pattern Recognition Engineering”, Wiley, New York 1993.MATHGoogle Scholar
  23. [23]
    Pao Y.H., “Adaptive Pattern Recognition and Neural Networks”, Addison Wesley, Reading, MA 1989.MATHGoogle Scholar
  24. [24]
    Payne J.W., Bettman, Johnson E.J., “The Adaptive Decision Maker”, Cambridge University Press, Cambridge 1993.Google Scholar
  25. [25]
    Pawlak Z., “Rough Sets: Theoretical Aspects of Reasoning About Data”, Kluwer, Dordrecht 1991.MATHGoogle Scholar
  26. [26]
    Pawlak Z., Skowron A., “A Rough Set Approach for Decision Rules Generation”, ICS Research Report 23/93, Warsaw University of Technology 1993, Proc. of the IJCAF93 Workshop: The Management of Uncertainty in AI, France 1993.Google Scholar
  27. [27]
    Pearl J., “Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Beliefs”, Morgan Kaufmann 1988.Google Scholar
  28. [28]
    Pogonowski, J., “Tolerance Spaces with Applications to Linguistics”, UAM Press, Poznan 1981.Google Scholar
  29. [29]
    Polkowski L., Skowron A., “Decision Support Systems: A Rough Set Approach”, pp. 1–312 (manuscript).Google Scholar
  30. [30]
    Polkowski L., Skowron A., “Introducing Rough Mereological Controllers: Rough Quality Control”, Soft Computing, T.Y. Lin, A.M. Wildberger (eds.), Simulation Councils, San Diego 1995, pp. 240–243.Google Scholar
  31. [31]
    Polkowski L., Skowron A., “Rough Mereology”, Proc. of Lecture Notes in Artificial Intelligence 869, Springer-Verlag, Berlin 1994, pp. 85–94.Google Scholar
  32. [32]
    Polkowski L., Skowron A.: Analytical Morphology: Mathematical Morphology of Rough Sets”, ICS Research Report 22/94, Warsaw University of Techology 1994, also in: Fund. Informaticae, to appear.Google Scholar
  33. [33]
    L.Polkowski, Skowron A., “Adaptive Decision-Making by Systems of Cooperating Intelligent Agents Organized on Rough Mereological Principles”, ICS Research Report 71/94, Warsaw University of Techology 1994, also in: Intelligent Automation and Soft Computing, to appear.Google Scholar
  34. [34]
    Polkowski L., Skowron A., “Rough Mereology: Logic of Rough Inclusion”, ICS Research Report 16/94, Warsaw University of Technology 1994.Google Scholar
  35. [35]
    Serra J., “Image Analysis and Mathematical Morphology”, Academic Press, New York 1982.MATHGoogle Scholar
  36. [36]
    Shafer G., Pearl J., “Readings in Uncertainty Reasoning”, Morgan Kaufmann, San Mateo 1990.Google Scholar
  37. [37]
    Skowron, A. and Rauszer C., “The Discernibility Matrices and Functions in Information Systems”, In: R. Slowiriski (ed.): Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory. Kluwer, Dordrecht 1992, pp. 331–362.Google Scholar
  38. [38]
    Skowron A., “A Synthesis of Decision Rules: Applications of Discernibility Matrices”, Proc. of the Conf. Intelligent Information Systems, Augustow, June 7–11, 1993, pp. 30–46.Google Scholar
  39. [39]
    Skowron A., “Boolean Reasoning for Decision Rules Generation”, Proc. of the 7-th International Symposium ISMIS’93, Trondheim, Norway 1993, In: J. Komorowski and Z. Ras (eds.): Lecture Notes in Artificial Intelligence, Vol.689. Springer-Verlag 1993, pp. 295–305.Google Scholar
  40. [40]
    Skowron A., “Extracting Laws from Decision Tables”, Computational Intelligence, 11(2) 1995, pp. 371–388.MathSciNetCrossRefGoogle Scholar
  41. [41]
    Skowron A., Stepaniuk J., “Decision Rules Based on Discernibility Matrices and Decision Matrices”, Conference Proceedings (RSSC’94) The Third International Workshop on Rough Sets and Soft Computing, San Jose State University, CA, November 10–12, 1994, pp. 602–609.Google Scholar
  42. [42]
    Skowron A., Polkowski L., “Adaptive Decision Algorithms”, Proc. of the Workshop on Intelligent Systems, Wigry, Poland, 6–10 June, 1994, Institute of Foundations of Computer Science PAS, Warsaw 1995, pp. 103–120.Google Scholar
  43. [43]
    Skowron A., “Data Filtration: A Rough Set Approach”, In: Rough Sets, Fuzzy Sets and Knowledge Discovery (ed.) W. Ziarko, Workshops in Computing, Springer-Verlag & British Computer Society 1994, pp. 108–118.Google Scholar
  44. [44]
    Skowron A., Grzymala-Busse J., “From Rough Set Theory to Evidence Theory”, In: Advances in the Dempster-Shafer Theory of Evidence, R.R.Yager, M.Fedrizzi, J.Kacprzyk (eds.), John Wiley & Sons, New York 1994 pp. 193–236.Google Scholar
  45. [45]
    Skowron A., Son N.H., “Quantization of Real Value Attributes”, Second Joint Annual Conference on Information Sciences, Wrightsville Beach, North Carolina, September 28-October 1, 1995.Google Scholar
  46. [46]
    Skowron A., Stepaniuk J., “Generalized Approximation Spaces”, Soft Computing, T.Y.Lin, A.M.Wildberger (eds.), Simulation Councils, San Diego 1995, pp. 18–21.Google Scholar
  47. [47]
    Skowron A., “Synthesis of Adaptive Decision Systems from Experimental Data”, In: Proc. of the Fifth Scandinavian Conference on Artificial Intelligence SCAI-95, Aamodt A., Komorowski J.(eds.), IOS Press, Amsterdam pp. 220–238.Google Scholar
  48. [48]
    Skowron A., Suraj Z., “A Rough Set Approach to the Real Time State Identification”, Bulletin EATCS, 50 (1993) pp. 264–275.MATHGoogle Scholar
  49. [49]
    Ślęzak D., “Approximate Reducts in Decision Tables”, In: Proc. Information Professing and Management of Uncertainty in Knowledge-Based Systems IPMU-96, to appear.Google Scholar
  50. [50]
    Tentush I., “On Minimal Absorbent Sets for some Types of Tolerance Relations”, Bull. Polish Acad. Sci. Tech., 43(1995), 79–88.MathSciNetMATHGoogle Scholar
  51. [51]
    Widrow B., Stearns S., “Adaptive Signal Processing”, Signal Processing Series, Prentice Hall, Englewood Cliffs, NJ 1985.MATHGoogle Scholar
  52. [52]
    Yager R.R., Fedrizzi M., Kacprzyk J., “Advances in the Dempster-Shafer Theory of Evidence”, Wiley, New York 1994.MATHGoogle Scholar
  53. [53]
    Ziarko W., “Variable Precision Rough Set Model, Journal of Computer and System Sciences”, 46(1993), pp. 39–59.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Andrzej Skowron
    • 1
  • Lech Polkowski
    • 2
  1. 1.Institute of MathematicsWarsaw UniversityWarsawPoland
  2. 2.Institute of MathematicsWarsaw University of TechnologyWarsawPoland

Personalised recommendations