Advertisement

Knowledge Discovery by Application of Rough Set Models

  • Jaroslaw Stepaniuk
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 56)

Abstract

The amount of electronic data available is growing very fast and this explosive growth in databases has generated a need for new techniques and tools that can intelligently and automatically extract implicit, previously unknown, hidden and potentially useful information and knowledge from these data. These tools and techniques are the subject of the field of Knowledge Discovery in Databases. In this Chapter we discuss selected rough set based solutions to two main knowledge discovery problems, namely the description problem and the classification (prediction) problem.

Keywords

Boolean Function Decision Table Approximation Space Uncertainty Function Discernibility Matrix 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agotnes T., Komorowski J., Loken T.: Taming Large Rule Models in Rough Set Approaches, 3rd European Conference of Principles and Practice of Knowledge Discovery in Databases, September 15–18, 1999, Prague, Czech Republic, Lecture Notes in Artificial Intelligence 1704, 1999, pp. 193–203.Google Scholar
  2. 2.
    Agrawal R., Mannila H., Srikant R., Toivonen H., Verkano A.: Fast Discovery of Association Rules, Fayyad U.M., Piatetsky-Shapiro G., Smyth P., Uthurusamy R. (Eds.): Advances in Knowledge Discovery and Data Mining, The AAAI Press/The MIT Press 1996, pp. 307–328.Google Scholar
  3. 3.
    An A., Chan C., Shan N., Cercone N., Ziarko W.: Applying Knowledge Discovery to Predict Water—Supply Consumption. IEEE Expert 12/4, 1997, pp. 72–78.CrossRefGoogle Scholar
  4. 4.
    Bazan J., Nguyen H.S., Nguyen T.T., Skowron A., Stepaniuk J.: Some Logic and Rough Set Applications for Classifying Objects. Institute of Computer Science, Warsaw University of Technology, ICS Research Report, 38/94, 1994.Google Scholar
  5. 5.
    Bazan J., Nguyen H.S., Nguyen T.T., Skowron A., Stepaniuk J.: Application of Modal Logics and Rough Sets for Classifying Objects. In: M. De Glas, Z. Pawlak (Eds.), Proceedings of the Second World Conference on Fundamentals of Artificial Intelligence (WOCFAI’95), Paris, July 3–7, Angkor, Paris, pp. 15–26.Google Scholar
  6. 6.
    Bazan J., Nguyen H.S., Nguyen T.T., Skowron A., Stepaniuk J.: Synthesis of Decision Rules for Object Classification, E. Orlowska (Ed.), Incomplete Information: Rough Set Analysis, Physica-Verlag, Heidelberg, 1998, pp. 23–57.Google Scholar
  7. 7.
    Bazan J.G.: A Comparison of Dynamic and Non—Dynamic Rough Set Methods for Extracting Laws from Decision Tables. L. Polkowski, A. Skowron, (Eds.), Rough Sets in Knowledge Discovery 1. Methodology and Applications. Physica-Verlag, Heidelberg, 1998, pp. 321–365.Google Scholar
  8. 8.
    Bodjanova S.: Approximation of Fuzzy Concepts in Decision Making. Fuzzy Sets and Systems 85, 1997, pp. 23–29.MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Bonikowski Z., Bryniarski E., Wybraniec-Skardowska U.: Extensions and Intensions in the Rough Set Theory. Information Sciences 107, 1998, pp. 149–167.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Brazdil P., Torgo L.: Knowledge Acquisition via Knowledge Integration, Current Trends in Knowledge Acqusition, IOS Press, 1990.Google Scholar
  11. 11.
    Brown F. M.: Boolean Reasoning. Kluwer Academic Publishers, Dordrecht, 1990.MATHGoogle Scholar
  12. 12.
    Bruha I.: Quality of Decision Rules: Definitions and Classification Schemes for Multiple Rules, G. Nakhaeizadeh, C. C. Taylor (Eds.), Machine Learning and Statistics, The Interface, John Wiley and Sons, 1997, pp. 107–131.Google Scholar
  13. 13.
    Bryniarski E., Wybraniec-Skardowska U.: Generalized Rough Sets in Contextual Spaces, T. Y. Lin, N. Cercone (Eds.), Rough Sets and Data Mining. Analysis of Imprecise Data, Kluwer Academic Publishers, Boston 1997, pp. 339–354.CrossRefGoogle Scholar
  14. 14.
    Budihardjo A., Grzymala-Busse J.W., Woolery L., Program LERS—LB 2.5 as a Tool for Knowledge Acquisition in Nursing. In: Proceedings of the Fourth International Conference on Industrial Engineering Applications of Artificial Intelligence Expert Systems, Koloa, Kauai, Hawaii, June 2–5, 1991, pp. 735–740.Google Scholar
  15. 15.
    Cattaneo G.: A Unified Algebraic Approach to Fuzzy Algebras and Rough Approximations. R. Trappl (Ed.), Proceedings of the 13th European Meeting on Cybernetics and Systems Research (CSR’96), April 9–12, 1996, The University of Vienna 1, pp. 352–357.Google Scholar
  16. 16.
    Cattaneo G.: Generalized Rough Sets. Preclusivity Fuzzy-Intuitionistic (BZ) Lattices. Studia Logica 58, 1997, pp. 47–77.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Cattaneo G.: Fuzzy Extension of Rough Sets Theory, Proceedings of the International Conference on Rough Sets and Current Trends in Computing, Warsaw, Poland, June 22–26, 1998, Lecture Notes in Artificial Intelligence 1424, pp. 275– 282.Google Scholar
  18. 18.
    Cattaneo G.: Abstract Approximation Spaces for Rough Theories, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 1. Methodology and Applications, Physica—Verlag, Heidelberg, 1998, pp. 59–98.Google Scholar
  19. 19.
    Carlin U.S., Komorowski J., Ohrn A.: Rough Set Analysis of Patients with Suspected Acute Appendicitis, Proceedings of IPMU’98, Paris, France, July 1998, pp. 1528–1533.Google Scholar
  20. 20.
    Chmielewski MR., Grzymala-Busse J.W.: Global Discretization of Attributes as Preprocessing for Machine Learning, T.Y. Lin, A.M. Wildberger (Eds.) Soft Computing, Simulation Councils Inc., San Diego, 1995, pp. 294–297.Google Scholar
  21. 21.
    Cios J., Pedrycz W., Świniarski R.W.: Data Mining in Knowledge Discovery, Kluwer Academic Publishers, Dordrecht, 1998.Google Scholar
  22. 22.
    Comer S.: An Algebraic Approach to the Approximation of Information. Fundamenta Informaticae 14, 1991, pp. 492–502.MathSciNetMATHGoogle Scholar
  23. 23.
    Czyżewski A.: Speaker—Independent Recognition of Digits — Experiments with Neural Networks, Fuzzy Logic Rough Sets. Journal of the Intelligent Automation and Soft Computing 2/2, 1996, pp. 133–146.Google Scholar
  24. 24.
    Czyżewski A., Królikowski R., Skórka P.: Automatic Detection of Speech Disorders. Proceedings of the Fourth European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, September 2–5, 1996, vol. 1, pp. 183–187.Google Scholar
  25. 25.
    Czyżewski A., Kostek B.: Rough Set-Based Filtration of Sound Applicable to Hearing Prostheses, Tsumoto S., Kobayashi, S., Yokomori, T., Tanaka, H. (Eds.), Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery (RSFD’96), Tokyo November 6–8, 1996, pp. 168–175.Google Scholar
  26. 26.
    Dasarathy B. V. (Ed.): Nearest Neighbor Pattern Classification Techniques. IEEE Computer Society Press 1991.Google Scholar
  27. 27.
    Dougherty J., Kohavi R., Sahami M.: Supervised Unsupervised Discretization of Continuous Features. Proceedings of the Twelfth International Conference on Machine Learning, Morgan Kaufmann, San Francisco, CA, 1995 pp. 194–202.Google Scholar
  28. 28.
    Drwal G., Mrózek A.: System RClass — Software Implementation of the Rough Classifier, Proceedings of the Seventh International Workshop on Intelligent Information Systems, Malbork, Poland, June 15–19, 1998, pp. 392–395.Google Scholar
  29. 29.
    Dubois D., Prade H.: Twofold Fuzzy Sets and Rough Sets — Some Issues in Knowledge Representation. Fuzzy Sets and Systems 23, 1987, pp. 3–18.MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    Dubois D., Prade H.: Similarity-Based Approximate Reasoning. J.M. Zurada, R.J. Marks II, and X.C.J. Robinson (Eds.), Proceedings of the IEEE Symposium, Orlando, FL, June 17—July 1st, 1997, IEEE Press, pp. 69–80.Google Scholar
  31. 31.
    Dubois D., Prade H.: Similarity Versus Preference in Fuzzy Set-Based Logics, E. Orlowska (Ed.), Incomplete Information: Rough Set Analysis, Physica Verlag, Heidelberg, 1998, pp. 440–460.Google Scholar
  32. 32.
    Düintsch I.: A Logic for Rough Sets. Theoretical Computer Science 179/1–2, 1997 pp. 427–436.MathSciNetCrossRefGoogle Scholar
  33. 33.
    Düntsch I., Gediga G.: Statistical Evaluation of Rough Set Dependency Analysis. International Journal of Human-Computer Studies 46, 1997, pp. 589–604.CrossRefGoogle Scholar
  34. 34.
    Düntsch I.: Rough Sets and Algebras of Relations, E. Orlowska (Ed.), Incomplete Information: Rough Set Analysis, Physica-Verlag, Heidelberg, 1998, pp. 95–108.Google Scholar
  35. 35.
    Dzeroski S.: Inductive Logic Programming and Knowledge Discovery in Databases, U. M. Fayyad, G. Piatetsky-Shapiro, P. Smyth, R. Uthurusamy (Eds.), Advances in Knowledge Discovery and Data Mining. The MIT Press. 1996. ppp. 117–152.Google Scholar
  36. 36.
    El-Mouadib F.A., Koronacki J., Żytkow J.M.: Taxonomy Formation by Approximate Equivalence Relations, Revisited, 3rd European Conference of Principles and Practice of Knowledge Discovery in Databases, September 1999, Prague, Czech Republic, Lecture Notes in Artificial Intelligence 1704, 1999, pp. 71–79.Google Scholar
  37. 37.
    Esposito F., Malerba D., Semeraro G., Pazzani M.: A Machine Learning Approach to Document Understanding, Proceedings of the Second International Workshop on Multistrategy Learning, West Virginia, 1993, pp. 276–292.Google Scholar
  38. 38.
    Fagin R., Halpern J.Y., Moses Y., Vardi M.: Reasoning about Knowledge, MIT Press, 1996.Google Scholar
  39. 39.
    Fayyad U.M., Irani K.B.: On the Handling of Continuous-Valued Attributes in Decision Tree Generation, Machine Learning 8, 1992, pp. 87–102.MATHGoogle Scholar
  40. 40.
    Fayyad U.M., Piatetsky-Shapiro G., Smyth P., Uthurusamy R. (Eds.): Advances in Knowledge Discovery and Data Mining, The AAAI Press/The MIT Press 1996.Google Scholar
  41. 41.
    Fibak J., Pawlak Z., Slowińński K., Słowiriski R.: Rough Sets Based Decision Algorithm for Treatment of Duodenal Ulcer by HSV. Bulletin of the Polish Academy of Sciences, Biological Sciences, 34/10–12, 1986, pp. 227–246.Google Scholar
  42. 42.
    Fedrizzi M., Kacprzyk J., Nurmi H.: How Different are Social Choice Functions, A Rough Set Approach. Quality & Quantity 30, 1996, pp. 87–99.Google Scholar
  43. 43.
    Funakoshi K., Ho T. B.: Information Retrieval by Rough Tolerance Relation, Tsumoto S., Kobayashi, S., Yokomori, T., Tanaka, H. (Eds.), Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery (RSFD’96), Tokyo November, 6–8 1996, pp. 31–35.Google Scholar
  44. 44.
    Funakoshi K., Ho T. B.: A Rough Set Approach to Information Retrieval, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 2. Applications, Case Studies and Software Systems, Physica-Verlag, Heidelberg, 1998, pp. 166–177.Google Scholar
  45. 45.
    Gemello R., Mana F.: An Integrated Characterization and Discrimination Scheme to Improve Learning Efficiency in Large Data Sets, Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, Detroit MI, 20–25 August 1989, pp. 719–724.Google Scholar
  46. 46.
    Greco S., Matarazzo B., Slowińński R.: Rough Approximation of a Preference Relation in a Pairwise Comparison Table, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 2. Applications, Case Studies and Software Systems, Physica-Verlag, Heidelberg, 1998, pp. 13–36.Google Scholar
  47. 47.
    Greco S., Matarazzo B., Slowińński R.: Fuzzy Similarity Relation as a Basis for Rough Approximations, Proceedings of the International Conference on Rough Sets and Current Trends in Computing, Warsaw, Poland, June 22–26, 1998, Lecture Notes in Artificial Intelligence 1424, pp. 283–289.Google Scholar
  48. 48.
    Greco S., Matarazzo B., Slowińński R.: On Joint Use of Indiscernibility, Similarity and Dominance in Rough Approximation of Decision Classes, 5th International Conference Integrating Technology and Human Decisions: Global Bridges Into The 21st Century, July 4–7, 1999, Athens, Greece.Google Scholar
  49. 49.
    Grzymala-Busse J.W.: Managing Uncertainty in Expert Systems, Kluwer Academic Publishers, Dordrecht, 1991.MATHCrossRefGoogle Scholar
  50. 50.
    Grzymala-Busse J.W.: A New Version of the Rule Induction System LERS. Fundamenta Informaticae 31, 1997, pp. 27–39.MATHGoogle Scholar
  51. 51.
    Grzymala-Busse J.W.: Applications of the Rule Induction System LERS. L. Polkowski, A. Skowron, (Eds.), Rough Sets in Knowledge Discovery 1. Methodology and Applications. Physica—Verlag, Heidelberg, 1998, pp. 366–375.Google Scholar
  52. 52.
    Grzymala-Busse J.W., Goodwin L.K.: Predicting Preterm Birth Risk Using Machine Learning from Data with Missing Values. S. Tsumoto (Ed.), Bulletin of International Rough Set Society 1/2, 1997, pp. 17–21.Google Scholar
  53. 53.
    Grzymala-Busse J.W., Gunn J.D.: Global Temperature Analysis based on the Rule Induction System LERS. In: Proceedings of the Fourth International Workshop on Intelligent Information Systems, Augustów, Poland, June 5–9, 1995, Institute od Computer Science, Polish Academy of Sciences, Warsaw, pp. 148–158.Google Scholar
  54. 54.
    Holte R.C.: Very Simple Classification Rules Perform Well on Most Commonly Used Datasets, Machine Learning 11, 1993, pp. 63–90.MATHCrossRefGoogle Scholar
  55. 55.
    Hu X., Cercone N.: Rough Sets Similarity-Based Learning from Databases, Proceedings of the First International Conference on Knowledge Discovery and Data Mining, Montreal, Canada, August 20–21 1995, pp. 162–167.Google Scholar
  56. 56.
    Huhns M.N., Singh M.P.(Eds.): Readings in Agents, Morgan Kaufmann, San Mateo, 1998.Google Scholar
  57. 57.
    Iwiński T.: Algebraic Approach to Rough Sets. Bulletin of the Polish Academy of Sciences Mathematics 35, 1987, pp. 673–683.MathSciNetMATHGoogle Scholar
  58. 58.
    Jelonek J., Krawiec K., Slowińński R., Szymaś J.: Rough Set Reduction of Features for Picture—Based Reasoning, T.Y. Lin, A.M. Wildberger (Eds.), Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, Knowledge Discovery, Simulation Councils, Inc., San Diego, 1995, pp. 89–92.Google Scholar
  59. 59.
    Johnson D.S.: Approximation Algorithms for Combinatorial Problems, Journal of Computer and System Sciences, 9, 1974, pp. 256–278.MathSciNetMATHCrossRefGoogle Scholar
  60. 60.
    Kandulski M., Marciniec J., Tukallo K.: Surgical Wound Infection — Conductive Factors and Their Mutual Dependencies, R. Slowinski (Ed.), Intelligent Decision Support — Handbook of Applications and Advances of the Rough Sets Theory. Kluwer Academic Publishers, Dordrecht, 1992, pp. 95–110.Google Scholar
  61. 61.
    Katzberg J. D., Ziarko W.: Variable Precision Extension of Rough Sets. Fundamenta Informaticae 27, 1996, pp. 155–168.MathSciNetMATHGoogle Scholar
  62. 62.
    Kent R.E.: Rough Concept Analysis: A Synthesis of Rough Sets and Formal Concept Analysis. Fundamenta Informaticae 27/2–3, 1996, pp. 169–181.MathSciNetMATHGoogle Scholar
  63. 63.
    Kim D., Kim C.: A Handwritten Numeral Character Classification Using Tolerant Rough Set, 1998, manuscript.Google Scholar
  64. 64.
    Kodratoff Y., Michalski R.: Machine Learning, An Artificial Intelligence Approach 3, Morgan Kaufmann, 1990.Google Scholar
  65. 65.
    Kohavi R., John G.H.: Wrappers for Feature Subset Selection, Artificial Intelligence Journal, 97, 1997, pp. 273–324.MATHCrossRefGoogle Scholar
  66. 66.
    Komorowski J., Pawlak Z., Polkowski L., Skowron A.: Rough Sets: A Tutorial, S.K. Pal, A. Skowron (Eds.), Rough-Fuzzy Hybridization: A New Trend in Decision Making, Springer Verlag, Singapore, 1999, pp. 3–98.Google Scholar
  67. 67.
    Konikowska B.: A logic for Reasoning about Similarity, E. Orlowska (Ed.), Incomplete Information: Rough Set Analysis, Physica-Verlag, Heidelberg, 1998, pp. 462–491.Google Scholar
  68. 68.
    Kostek B., Czyżewski A.: Automatic Classification of Musical Timbres based on Learning Algorithms Applicable to Cochlear Implants. In: Proceedings of IASTED International Conference — Artificial Intelligence, Expert Systems and Neural Networks, August 19–21, 1996, Honolulu, Hawaii, USA, pp. 98–101.Google Scholar
  69. 69.
    Krawiec K., Slowiiski R., Vanderpooten D.: Construction of Rough Classifiers Based on Application of a Similarity Relation. In: Tsumoto S., Kobayashi, S., Yokomori, T., Tanaka, H. (Eds.), Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery (RSFD’96), Tokyo November 6–8 1996, pp. 23–30.Google Scholar
  70. 70.
    Krawiec K., Slowiński R., Vanderpooten D.: Learning Decision Rules from Similarity Based Rough Approximations, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 2. Applications, Case Studies and Software Systems, Physica-Verlag, Heidelberg, 1998, pp. 37–54.Google Scholar
  71. 71.
    Krçtowski M., Polkowski L., Skowron A., Stepaniuk J.: Data Reduction Based on Rough Set Theory, Y. Kodratoff, G. Nakhaeizadeh, Ch. Taylor (Eds.), Proceedings of the International Workshop on Statistics, Machine Learning and Knowledge Discovery in Databases, Heraklion April 25–27 1995, pp. 210–215 see also: Institute of Computer Science, Warsaw University of Technology, ICS Research Report 13/95 1995.Google Scholar
  72. 72.
    Krętowski M., Stepaniuk J.: Selection of Objects and Attributes, a Tolerance Rough Set Approach, Proceedings of the Poster Session of Ninth International Symposium on Methodologies for Intelligent Systems, June 10–13, 1996, Zakopane, Poland, pp. 169–180 see also Institute of Computer Science, Warsaw University of Technology, ICS Research Report 54/95 1995.Google Scholar
  73. 73.
    Kryszkiewicz M.: Maintenance of Reducts in the Variable Precision Rough Set Model, T. Y. Lin, N. Cercone (Eds.), Rough Sets and Data Mining Analysis of Imprecise Data, Kluwer Academic Publishers, Dordrecht 1997, pp. 355–372.CrossRefGoogle Scholar
  74. 74.
    Langley P., Iba W.: Average-Case Analysis of a Nearest Neighbor Algorithm, Proceedings of the 13th International Joint Conference on Artificial Intelligence, Morgan Kaufmann, San Mateo, CA, 1993, pp. 889–894.Google Scholar
  75. 75.
    Lavrac N., Dzeroski S., Grobelnik M.: Learning Non-Recursive Definitions of Relations with LINUS, Proceedings of Fifth European Working Session on Learning, 1991, pp. 265–281.Google Scholar
  76. 76.
    Lavrac N., Dzeroski S.: Inductive Logic Programming, Ellis Horwood, Chichester, UK, 1994.MATHGoogle Scholar
  77. 77.
    Lavrac N., Gamberger D., Turney P.: A Relevancy Filter for Constructive Induction, IEEE Intelligent Systems and Their Applications, 13(2), March/April 1998, pp. 50–56.CrossRefGoogle Scholar
  78. 78.
    Lenarcik A., Piasta Z.: Probabilistic Approach to Decision Algorithm Generation in the case of Continuous Condition Attributes. Foundations of Computing and Decision Sciences 18/3–4, 1993, pp. 213–223.MathSciNetMATHGoogle Scholar
  79. 79.
    Lin T.Y.: Granular Computing on Binary Relations I Data Mining and Neighborhood Systems, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 1. Methodology and Applications, Physica—Verlag, Heidelberg, 1998, pp. 107–121.Google Scholar
  80. 80.
    Marcus S.: Tolerance Rough Sets, Cech Topologies, Learning Processes. Bulletin of the Polish Academy of Sciences, Technical Sciences 42/3, 1994, pp. 471–487.MATHGoogle Scholar
  81. 81.
    Marek W., Pawlak Z.: Rough Sets and Information Systems. Fundamenta Informaticae 17, 1984, pp. 105–115.MathSciNetGoogle Scholar
  82. 82.
    Martienne E., Quafafou M.: Learning Logical Descriptions for Document Understanding: a Rough Sets-Based Approach, Proceedings of the International Conference on Rough Sets and Current Trends in Computing, Warsaw, Poland, June 22–26, 1998, Lecture Notes in Artificial Intelligence 1424, Springer Verlag, pp. 202–209.Google Scholar
  83. 83.
    Martienne E., Quafafou M.: Vagueness and Data Reduction in Concept Learning, Proceedings of the 13th European Conference on Artificial Intelligence (ECAI-98), Brighton, UK, August 23–28, 1998, pp. 351–355.Google Scholar
  84. 84.
    Michalewicz Z.: Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin 1996.MATHGoogle Scholar
  85. 85.
    Michalski R.: A Theory and Methodology of Inductive Learning, R. S. Michalski, J.G. Carbonell, T.M. Mitchell (Eds.), Machine Learning, An Artificial Intelligence Approach, 1983, pp. 83–134.Google Scholar
  86. 86.
    Mitchell TM.: Machine Learning, McGraw-Hill, New York 1997.MATHGoogle Scholar
  87. 87.
    Michie D., Spiegelhalter D.J., Taylorc C., (Eds.): Machine learning, Neural and Statistical Classification. Ellis Horwood, New York, 1994.MATHGoogle Scholar
  88. 88.
    Michalski R. S., Larson J. B.: Selection of most Representative Training Examples and Incremental Generation of VL1 Hypotheses. Report 867 Department of Computer Science University of Illinois at Urbana-Champaign 1978.Google Scholar
  89. 89.
    Mrózek A.: Information Systems and Control Algorithms. Bulletin of the Polish Academy of Sciences Technical Sciences 33, 1985, pp. 195–212.MathSciNetMATHGoogle Scholar
  90. 90.
    Mrózek A., Płonka L.: Rough Sets in Image Analysis. Foundations of Computing Decision Sciences 18/3–4, 1993, pp. 259–273.MATHGoogle Scholar
  91. 91.
    Mrózek A., Plonka L.: Analiza Danych Metodą Zbiorów Przybliżonych. Zastosowania w Ekonomii, Medycyniei Sterowaniu, PLJ, Warszawa, 1999.Google Scholar
  92. 92.
    Muggleton S.: Inverse Entailment and Progol, New Generation Computing, 13, 1995, pp. 245–286.CrossRefGoogle Scholar
  93. 93.
    Nguyen H.S., Skowron A.: Quantization of Real Value Attributes, P.P. Wang (Ed.) Second Annual Joint Conference on Information Sciences, September 28—October 1, 1995, North Carolina, USA, pp. 34–37.Google Scholar
  94. 94.
    Nguyen S.H., Nguyen H.S.: Pattern Extraction from Data, Fundamenta Informaticae 34, 1998, pp. 129–144.MathSciNetMATHGoogle Scholar
  95. 95.
    Nguyen H.S., Nguyen S.H.: Discretization Methods in Data Mining, L. Polkowski, A. Skowron (Eds.): Rough Sets in Knowledge Discovery 1. Methodology and Applications. Physica-Verlag, Heidelberg 1998, pp. 451–482.Google Scholar
  96. 96.
    Nguyen S.H., Skowron A.: Searching for Relational Patterns in Data, Proceedings of the First European Symposium on Principles of Data Mining and Knowledge Discovery (PKDD’97) Trondheim, Norway, June 25–27 Lecture Notes in Artificial Intelligence 1263, 1997, pp. 265–276.Google Scholar
  97. 97.
    Nguyen S. H., Skowron A., Synak P.: Discovery of Data Patterns with Applications to Decomposition and Classification Problems, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 2. Applications, Case Studies and Software Systems, Physica-Verlag, Heidelberg, 1998, pp. 55–97.Google Scholar
  98. 98.
    Nieminen J.: Rough Tolerance Equality. Fundamenta Informaticae 11, 1988, pp. 289–296.MathSciNetMATHGoogle Scholar
  99. 99.
    Nowicki R., Slowiński R., Stefanowski J.: Rough Sets Analysis of Diagnostic Capacity of Vibroacoustic Symptoms. Journal of Computers Mathematics with Applications 24, 1992, pp. 109–123.MATHCrossRefGoogle Scholar
  100. 100.
    Novotny M., Pawlak Z.: On Problem Concerning Dependence Space. Fundamenta Informaticae 16/3–4, 1992, pp. 275–287.MathSciNetMATHGoogle Scholar
  101. 101.
    Ohrn A., Vinterbo S., Szymański P., Komorowski J.: Modelling Cardiac Patient Set Residuals Using Rough Sets. Proceedings of the AMIA Annual Fall Symposium (formerly SCAMC), Nashville, TN, USA, October 25–29, 1997, pp. 203–207.Google Scholar
  102. 102.
    Ohrn A., Komorowski J., Skowron A., Synak P.: The Design and Implementation of a Knowledge Discovery Toolkit Based on Rough Sets — The Rosetta System, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 1, Methodology and Applications, Physica-Verlag, Heidelberg, 1998, pp. 376–399.Google Scholar
  103. 103.
    Orlowska E.: A logic of Indiscernibility Relations A. Skowron (Ed.), Computation Theory, Lecture Notes in Computer Science 208, 1985, pp. 177–186.MathSciNetCrossRefGoogle Scholar
  104. 104.
    Orłowska E.: Information Algebras, Lecture Notes in Computer Science 936, 1995, pp. 55–65.CrossRefGoogle Scholar
  105. 105.
    Pagliani P.: From Concept Lattices to Approximation Spaces, Algebraic Structures of Some Spaces of Partial Objects. Fundamenta Informaticae 18/1, 1993, pp. 1–25.MathSciNetMATHGoogle Scholar
  106. 106.
    Pal S.K., Skowron A. (Eds.): Rough-Fuzzy Hybridization A New Trend in Decision Making, Springer-Verlag, 1999.MATHGoogle Scholar
  107. 107.
    Paszek P., Wakulicz-Deja A.: Optimization Diagnose in Progressive Encephalopathy Applying the Rough Set Theory, Proceedings of the Fourth European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, September 2–5, 1996, vol. 1, pp. 192–196.Google Scholar
  108. 108.
    Pawlak Z.: Rough Sets. International Journal of Computer and Information Science 11, 1982, pp. 341–356.MathSciNetMATHCrossRefGoogle Scholar
  109. 109.
    Pawlak Z.: Rough Relations, Bulletin of the Polish Academy of Sciences, Technical Sciences vol. 34 (9–10), 1986, pp. 587–590.MathSciNetMATHGoogle Scholar
  110. 110.
    Pawlak Z.: Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, 1991.MATHGoogle Scholar
  111. 111.
    Pawlak Z., Skowron A.: Rough Membership Functions, M. Fedrizzi, J. Kacprzyk, R. R. Yager (Eds.), Advances in the Dempster-Shafer Theory of Evidence, John Wiley and Sons, New York, 1994, pp. 251–271.Google Scholar
  112. 112.
    Pawlak Z., Slowiński K., Slowińński R.: Rough Classification of Patients After Highly Selected Vagotomy for Duodenal Ulcer, Journal of Man—Machine Studies 24, 1986, pp. 413–433.CrossRefGoogle Scholar
  113. 113.
    Peters J.F., Han L., Ramanna S.: Approximate Time Rough Software Cost Decision System: Multicriteria Decision-Making Approach, Proceedings of the 11th International Symposium on Foundations of Intelligent Systems, ISMIS’99, Warsaw, Poland, June 8–11, 1999, Lecture Notes in Artificial Intelligence 1609, SpringerVerlag, 1999, pp. 556–564.Google Scholar
  114. 114.
    Piasta Z., Lenarcik A., Tsumoto S.: Machine Discovery in Databases with Probabilistic Rough Classifiers. S. Tsumoto (Ed.): Bulletin of International Rough Set Society 1/2, 1997, pp. 51–57.Google Scholar
  115. 115.
    Polkowski L.: Mathematical Morphology of Rough Sets. Bulletin of the Polish Academy of Sciences Mathematics 41/3, 1993, pp. 241–273.MathSciNetMATHGoogle Scholar
  116. 116.
    Polkowski L., Skowron A.: Rough Mereology, Lecture Notes in Artificial Intelligence 869, Springer-Verlag, Berlin 1994, pp. 85–94.Google Scholar
  117. 117.
    Polkowski L., Skowron A.: Rough Mereology: A New Paradigm for Approximate Reasoning, International Journal of Approximate Reasoning, Vol. 15, No 4, 1996, pp. 333–365.MathSciNetMATHCrossRefGoogle Scholar
  118. 118.
    Polkowski L., Skowron A.: Towards Adaptive Calculus of Granules, Proceedings of FUZZ-IEEE’98 International Conference, Anchorage, Alaska, USA, May 5–9 1998, pp. 111–116.Google Scholar
  119. 119.
    Polkowski L., Skowron A. (Eds.): Rough Sets in Knowledge Discovery 1: Methodology and Applications. Physica-Verlag, Heidelberg, 1998.MATHGoogle Scholar
  120. 120.
    Polkowski L., Skowron A. (Eds.): Rough Sets in Knowledge Discovery 2: Applications Case Studies and Software Systems. Physica-Verlag, Heidelberg, 1998.MATHGoogle Scholar
  121. 121.
    Polkowski L., Skowron A., Komorowski J.: Towards a Rough Mereology-Based Logic for Approximate Solution Synthesis, Part 1. Studia Logica 58/1, 1997, pp. 143–184.MathSciNetMATHGoogle Scholar
  122. 122.
    Polkowski L., Skowron A., Żytkow J.M.: Tolerance Based Rough Sets, T.Y. Lin, A.M. Wildberger (Eds.), Soft Computing Simulation Councils, San Diego 1995, pp. 55–58.Google Scholar
  123. 123.
    Pomykala J. A.: Approximation Operations in Approximation Space, Bulletin of the Polish Academy of Sciences, Mathematics, 35, 1987, pp. 653–662.MathSciNetMATHGoogle Scholar
  124. 124.
    Pomykala J. A.: On Definability in the Nondeterministic Information System. Bulletin of the Polish Academy of Sciences, Mathematics, 36, 1988, pp. 193–210.MathSciNetMATHGoogle Scholar
  125. 125.
    Quinlan J.R.: Learning Logical Definitions from Relations, Machine Learning, 5, 1990, pp. 239–266.Google Scholar
  126. 126.
    Raś Z.W.: Cooperative Knowledge-Based Systems. Journal of the Intelligent Automation and Soft Computing 2/2, 1996, pp. 193–202.MathSciNetGoogle Scholar
  127. 127.
    Raś ZW.: Collaboration Control in Distributed Knowledge-Based Systems. Information Sciences 96/3–4, 1997, pp. 193–205.CrossRefGoogle Scholar
  128. 128.
    Raś Z.W., Skowron A. (Eds.): Proceedings of the Tenth International Symposium on Methodologies for Intelligent Systems, Foundations of Intelligent Systems (ISMIS’97), October 15–18, 1997, Charlotte, NC, USA, Lecture Notes in Artificial Intelligence 1325, Springer-Verlag, Berlin, pp. 1–630.Google Scholar
  129. 129.
    Rasiowa H., Skowron A.: Approximation Logic. In: Proceedings of Mathematical Methods of Specification and Synthesis of Software Systems Conference, Akademie Verlag 31, 1985, Berlin pp. 123–139.Google Scholar
  130. 130.
    Rauszer C.: Knowledge Representation Systems for Groups of Agents, J. Wolenski (Ed.), Philosophical Logic in Poland, Kluwer Academic Publishers, Dordrecht, 1994, pp. 217–238.Google Scholar
  131. 131.
    Schalkoff R.: Pattern Recognition: Statistical, Structural and Neural Approaches, Wiley, 1992.Google Scholar
  132. 132.
    Schreider J.A.: Equality, Resemblance and Order, Mir Publishers, Moscow, 1975. 133. Siromoney A.: A Rough Set Perspective of Inductive Logic Programming, L. De Raedt, S. Muggleton (Eds.), Proceedings of the IJCAI-97 Workshop on Frontiers of Inductive Logic Programming, Nagoya, Japan, August 1997, pp. 111–113.Google Scholar
  133. 134.
    Siromoney A., Inoue K.: A Framework for Rough Set Inductive Logic Programming — the gRS-ILP Model, Pacific Rim Knowledge Acquisition Workshop (PKAW98), Singapore, November 1998, pp. 201–217.Google Scholar
  134. 135.
    Siromoney A., Inoue K.: The gRS-ILP Model and Motifs in Strings. The Seventh International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and GranularSoft Computing (RSFDGrC’99), Ube, Yamaguchi, Japan November 9–11, Lecture Notes in Artificial Intelligence 1711, 1999.Google Scholar
  135. 136.
    Skowron A.: Data Filtration: A Rough Set Approach, W. Ziarko (Ed.), Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer-Verlag, Berlin 1994, pp. 108–118.CrossRefGoogle Scholar
  136. 137.
    Skowron A.: Extracting Laws from Decision Tables. Computational Intelligence 11/2, 1995, pp. 371–388.MathSciNetCrossRefGoogle Scholar
  137. 138.
    Skowron A., Grzymala-Busse J.: From Rough Set Theory to Evidence Theory. R.R. Yager, M. Fedrizzi, and J. Kacprzyk (Eds.), Advances in the Dempster Shafer Theory of Evidence, John Wiley and Sons, New York, 1994, pp. 193–236.Google Scholar
  138. 139.
    Skowron A., Nguyen H.S.: Boolean Resoning Scheme with Some Applications in Data Mining. 3rd European Conference of Principles and Practice of Knowledge Discovery in Databases, September 15–18, 1999, Prague, Czech Republic, Lecture Notes in Artificial Intelligence 1704, 1999, pp. 107–115.Google Scholar
  139. 140.
    Skowron A., Polkowski L.: Synthesis of Decision Systems from Data Tables, T. Y. Lin, N. Cercone (Eds.), Rough Sets and Data Mining Analysis of Imprecise Data, Kluwer Academic Publishers, Dordrecht, 1997, pp. 259–299.CrossRefGoogle Scholar
  140. 141.
    Skowron A., Polkowski L., Komorowski J.: Learning Tolerance Relations by Boolean Descriptors: Automatic Feature Extraction from Data Tables, Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery, November 6–8, 1996, Tokyo, Japan, pp. 11–17.Google Scholar
  141. 142.
    Skowron A., Polkowski L.: Rough Mereological Foundations for Design, Analysis, Synthesis and Control in Distributive Systems. Information Sciences 104/1–2, 1998, pp. 129–156.MathSciNetMATHCrossRefGoogle Scholar
  142. 143.
    Skowron A, Rauszer C.: The Discernibility Matrices and Functions in Information Systems, R. Slowiiski (Ed.), Intelligent Decision Support. Handbook of Applications and Advances of Rough Sets Theory, Kluwer Academic Publishers, Dordrecht, 1992, pp. 331–362.Google Scholar
  143. 144.
    Skowron A., Stepaniuk J.: Towards an Approximation Theory of Discrete Problems, Fundanenta Informaticae 15(2), 1991, pp. 187–208.MathSciNetMATHGoogle Scholar
  144. 145.
    Skowron A., Stepaniuk J.: Searching for Classifiers. M. De Glas, D. Gabbay (Eds.), Proceedings of the First World Conference on the Fundamentals of Artificial Intelligence (WOCFAI’91), July 1–5, 1991, Angkor, Paris pp. 447–460.Google Scholar
  145. 146.
    Skowron A., Stepaniuk J.: Intelligent Systems Based on Rough Set Approach. Foundations of Computing and Decision Sciences 18/3–4, 1993, pp. 343–360.MathSciNetGoogle Scholar
  146. 147.
    Skowron A., Stepaniuk J.: Approximations of Relations, W. Ziarko (Ed.), Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer Verlag, London Berlin 1994, pp. 161–166 see also: Institute of Computer Science, Warsaw University of Technology, ICS Research Report 20/94 1994.Google Scholar
  147. 148.
    Skowron A., Stepaniuk J.: Generalized Approximation Spaces, Proceedings of the Third International Workshop on Rough Sets and Soft Computing, San Jose, November 10–12, 1994, pp. 156–163.Google Scholar
  148. 149.
    Skowron A., Stepaniuk J.: Generalized Approximation Spaces, T.Y. Lin, A.M. Wildberger (Eds.), Soft Computing, Simulation Councils, San Diego 1995, pp. 18–21 see also: Institute of Computer Science, Warsaw University of Technology, ICS Research Report 41/94 1994.Google Scholar
  149. 150.
    Skowron A., Stepaniuk J.: Decision Rules Based on Discernibility Matrices and Decision Matrices, T.Y. Lin, A.M. Wildberger (Eds.), Soft Computing, Simulation Councils, San Diego 1995, pp. 6–9 see also Institute of Computer Science, Warsaw University of Technology, ICS Research Report 40/94 1994.Google Scholar
  150. 151.
    Skowron A., Stepaniuk J.: Tolerance Approximation Spaces, Fundamenta Informaticae, 27, 1996, pp. 245–253.MathSciNetMATHGoogle Scholar
  151. 152.
    Skowron A., Stepaniuk J.: Information Reduction Based on Constructive Neighborhood Systems, P.P. Wang (Ed.): Proceedings of the Fifth International Workshop on Rough Sets and Soft Computing (RSSC’97) at Third Annual Joint Conference on Information Sciences (JCIS’97). Duke University, Durham, NC, USA, Rough Set & Computer Science 3, March 1–5, 1997, pp. 158–160.Google Scholar
  152. 153.
    Skowron A., Stepaniuk J.: Constructive Information Granules, Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, August 24–29, 1997, Berlin, Germany, vol. 4 Artificial Intelligence and Computer Science, pp. 625–630.Google Scholar
  153. 154.
    Skowron A., Stepaniuk J.: Information Granules and Approximation Spaces, Proceedings of Seventh International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Paris, France, July 6–10 1998, pp. 354–361.Google Scholar
  154. 155.
    Skowron A., Stepaniuk J.: Towards Discovery of Information Granules, 3rd European Conference of Principles and Practice of Knowledge Discovery in Databases, September 15–18, 1999, Prague, Czech Republic, Lecture Notes in Artificial Intelligence 1704, Springer-Verlag, 1999, pp. 542–547.Google Scholar
  155. 156.
    Skowron A., Stepaniuk J.: Information Granules in Distributed Environment, New Directions in Rough Sets, Data Mining, and Granular-Soft Computing (RSFDGrC’99), Ube, Yamaguchi, Japan November 9–11, Lecture Notes in Artificial Intelligence 1711, Springer-Verlag, 1999, pp. 357–365.Google Scholar
  156. 157.
    Skowron A., Stepaniuk J.: Concept Approximation and Information Granules, International Journal of Intelligent Systems, submitted.Google Scholar
  157. 158.
    Skowron A., Suraj Z.: A Parallel Algorithm for Real—Time Decision Making, A Rough Set Approach. Journal of Intelligent Information Systems 7, 1996, pp. 5–28.CrossRefGoogle Scholar
  158. 159.
    Slowiński K.: Rough Classification of HSV Patients, Slowiński R. (Ed.), Intelligent Decision Support — Handbook of Applications and Advances of the Rough Sets Theory. Kluwer Academic Publishers, Dordrecht, 1992, pp. 77–93.Google Scholar
  159. 160.
    Slowińński K., Slowiriski R., Stefanowski J., Rough Sets Approach to Analysis of Data from Peritoneal Lavage in Acute Pancreatitis, Medical Informatics 13/3, 1988, pp. 143–159.CrossRefGoogle Scholar
  160. 161.
    Slowińński K., Stefanowski J.: Multistage Rough Set Analysis of Therapeutic Experience with Acute Pancreatitis, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 2. Applications, Case Studies and Software Systems, Physica-Verlag, Heidelberg, 1998, pp. 272–294.Google Scholar
  161. 162.
    Słowiriski R. (Ed.): Intelligent Decision Support — Handbook of Applications and Advances of the Rough Sets Theory. Kluwer Academic Publishers, Dordrecht, 1992.Google Scholar
  162. 163.
    Słowińński R.: A Generalization of the Indiscernibility Relation for Rough Sets Analysis of Quantitative Information. Revista di Matematica per le Scienze Economiche e Sociali 15/1, 1992, pp. 65–78.CrossRefGoogle Scholar
  163. 164.
    Slowińński R.: Strict and Weak Indiscernibility of Objects Described by Quantitative Attributes with Overlapping Norms, Foundations of Computing and Decision Sciences, Vol. 18, 1993, pp. 361–369.MathSciNetGoogle Scholar
  164. 165.
    Slowiński R., Stefanowski J.: Software Implementation of the Rough Set Theory, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 2. Applications, Case Studies and Software Systems, Physica-Verlag, Heidelberg, 1998, pp. 581–586.Google Scholar
  165. 166.
    Slowińński R., Vanderpooten D.: Similarity Relation as a Basis for Rough Approximations. Warsaw University of Technology, Institute of Computer Science Research Report 53, 1995.Google Scholar
  166. 167.
    Stanfill C., Waltz D.: Toward Memory-Based Reasoning, Communications of the ACM 29, 1986, pp. 1213–1228.CrossRefGoogle Scholar
  167. 168.
    Stefanowski J., Slowińński K.: Rough Set Theory and Rule Induction Techniques for Discovery of Attribute Dependencies in Medical Information Systems, Lecture Notes in Artificial Intelligence 1263, Springer-Verlag, 1997, pp. 36–46.Google Scholar
  168. 169.
    Stepaniuk J.: Elementary Approximation Theory. Bulletin of the Polish Academy of Sciences Tech. 38/1–12, 1990, pp. 121–128.MATHGoogle Scholar
  169. 170.
    Stepaniuk J.: Approximation Logic of Programs. Bulletin of the Polish Academy of Sciences Tech. 38/1–12, 1990, pp. 129–138.MATHGoogle Scholar
  170. 171.
    Stepaniuk J.: Applications of Finite Models Properties in Approximation and Algorithmic Logics. Fundamenta Informaticae 14/1, 1991, pp. 91–108.MathSciNetMATHGoogle Scholar
  171. 172.
    Stepaniuk J.: Methods of Approximate Reasoning for Discrete Problems. Ph.D. Dissertation, Warsaw University, 1992.Google Scholar
  172. 173.
    Stepaniuk J.: Decision Rules for Consistent Decision Tables. Proceedings of the Polish—English Meeting on Information Systems, Bialystok, Poland, September 22, 1993, pp. 76–86.Google Scholar
  173. 174.
    Stepaniuk J.: Decision Rules for Decision Tables. Bulletin of the Polish Academy of Sciences Tech. 42/3, 1994, pp. 457–469.MATHGoogle Scholar
  174. 175.
    Stepaniuk J.: Discernibility and Decision Matrices (in Polish). R. Kulikowski, L. Bogdan (Eds.), Wspomaganie Decyzji, Systemy Eksperckie, Institute of System Analysis PAS, Warsaw, Poland, 1995, pp. 440–443.Google Scholar
  175. 176.
    Stepaniuk J.: Properties and Applications of Rough Relations, Proceedings of the Fifth International Workshop on Intelligent Information Systems, Deblin, Poland, June 2–5, 1996, Institute od Computer Science, Polish Academy of Sciences, Warsaw, 1996, pp. 136–141 see also Institute of Computer Science, Warsaw University of Technology, ICS Research Report 26/96, 1996.Google Scholar
  176. 177.
    Stepaniuk J.: Similarity Based Rough Sets and Learning, Tsumoto S., Kobayashi, S., Yokomori, T., Tanaka, H. (Eds.), Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery (RSFD’96), Tokyo November 6–8 1996, pp. 18–22.Google Scholar
  177. 178.
    Stepaniuk J.: Rough Sets, First Order Logic and Attribute Construction. Proceedings of the Sixth International Conference, Information Processing and Management of Uncertainty in Knowledge—Based Systems (IPMU’96), July 1–5, 1996, Granada, Spain, 2, pp. 887–890.Google Scholar
  178. 179.
    Stepaniuk J.: Attribute Discovery and Rough Sets, Principles of Data Mining and Knowledge Discovery, First European Symposium, PKDD97, Trondheim, Norway, June 1997, Lecture Notes in Artificial Intelligence 1263, Springer Verlag, pp. 145–155.CrossRefGoogle Scholar
  179. 180.
    Stepaniuk J.: Rough Sets Similarity Based Learning. Proceedings of the Fifth European Congress on Intelligent Techniques and Soft Computing, September 8–12, Aachen, Germany, Verlag Mainz, 1997, pp. 1634–1638.Google Scholar
  180. 181.
    Stepaniuk J.: Conflict Analysis and Groups of Agents. Proceedings of the Poster Session at Tenth International Symposium on Methodologies for Intelligent Systems (ISMIS’97), October 15–18, 1997, Charlotte, USA, pp. 174–185.Google Scholar
  181. 182.
    Stepaniuk J.: Approximation Spaces, Reducts and Representatives, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 2. Applications, Case Studies and Software Systems, Physica-Verlag, Heidelberg, 1998, pp. 109–126.Google Scholar
  182. 183.
    Stepaniuk J.: Rough Relations and Logics, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 1. Methodology and Applications, PhysicaVerlag, Heidelberg 1998, pp. 248–260.Google Scholar
  183. 184.
    Stepaniuk J.: Approximation Spaces in Extensions of Rough Set Theory, Proceedings of the International Conference on Rough Sets and Current Trends in Computing, Warsaw, Poland, June 22–26, 1998, Lecture Notes in Artificial Intelligence 1424, pp. 290–297.Google Scholar
  184. 185.
    Stepaniuk J.: Optimizations of Rough Set Model, Fundamenta Informaticae Vol. 36 (2–3), October-November 1998, pp. 265–283.MathSciNetMATHGoogle Scholar
  185. 186.
    Stepaniuk J.: Rough Set Data Mining of Diabetes Data, Proceedings of the 11th International Symposium on Foundations of Intelligent Systems, Warsaw, Poland, June 8–11, 1999, Lecture Notes in Artificial Intelligence 1609, Springer-Verlag, pp. 457–465.Google Scholar
  186. 187.
    Stepaniuk J.: Rough Sets and Relational Learning, Proceedings of the Seventh European Congress on Intelligent Techniques and Soft Computing, September 13–16, Aachen, Germany, Verlag Mainz, 1999, CD-ROM, 6 pages.Google Scholar
  187. 188.
    Stepaniuk J., Krętowski M.: Decision System Based on Tolerance Rough Sets, Proceedings of the Fourth International Workshop on Intelligent Information Systems, Augustow, Poland, June 5–9, 1995, Institute od Computer Science, Polish Academy of Sciences, Warsaw 1995, pp. 62–73 see also Institute of Computer Science, Warsaw University of Technology, ICS Research Report 36/95 1995.Google Scholar
  188. 189.
    Stepaniuk J., Maj M.: Data Transformation and Rough Sets, PKDD98, Nantes, France, September, 1998, Lecture Notes in Artificial Intelligence 1510, SpringerVerlag, pp. 441–449.Google Scholar
  189. 190.
    Stepaniuk J., Tyszkiewicz J.: Probabilistic Properties of Approximation Problems. Bulletin of the Polish Academy of Sciences Tech. 39/3, 1991, pp. 535–555.MATHGoogle Scholar
  190. 191.
    Stepaniuk J., Urban M., Baszun-Stepaniuk E.: The Application of Rough Set Based Data Mining Technique in the Prognostication of the Diabetic Nephropathy Prevalence, Proceedings of the Seventh International Workshop on Intelligent Information Systems, Malbork, Poland, June 15–19, 1998, Institute od Computer Science, Polish Academy of Sciences, Warsaw 1998, pp. 388–391.Google Scholar
  191. 192.
    Ślęzak D.: Approximate Reducts in Decision Tables, Proceedings of the Six International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Granada, Spain, July 1–5, 1996, pp. 1159–1164.Google Scholar
  192. 193.
    Suraj Z.: Discovery of Concurrent Data Models from Experimental Tables, A Rough Set Approach. Fundamenta Informaticae 28/3–4, 1996, pp. 353–376.MathSciNetMATHGoogle Scholar
  193. 194.
    Winiarski R.: Rough Set Expert System for On-Line Prediction of Volleyball Game Progress for US Olympic Team. B.D. Czejdo, I.I. Est, B. Shirazi, B. Trousse (Eds.), Proceedings of the Third Biennial European Joint Conference on Engineering Systems Design Analysis, July 1–4, 1996, Montpellier, France, pp. 15–20.Google Scholar
  194. 195.
    Tentush I.: On Minimal Absorbent Sets for some Types of Tolerance Relations, Bulletin of the Polish Academy of Sciences, Technical Sciences 43/1, 1995, pp. 79–88.MathSciNetMATHGoogle Scholar
  195. 196.
    Torgo L.: Controlled Redundancy in Incremental Rule Learning, Lecture Notes in Artificial Intelligence 667, 1993, pp. 185–195.Google Scholar
  196. 197.
    Tsumoto S., Tanaka H.: PRIMEROSE, Probabilistic Rule Induction Method Based on Rough Set Resampling Methods. Computational Intelligence: An International Journal 11/2, 1995, pp. 389–405.Google Scholar
  197. 198.
    Tsumoto S., Tanaka H.: Machine Discovery of Functional Components of Proteins from Amino—Acid Sequences Based on Rough Sets Change of Representation. Journal of the Intelligent Automation and Soft Computing 2/2, 1996, pp. 169–180.MathSciNetGoogle Scholar
  198. 199.
    Tsumoto S.: Extraction of Experts Decision Process from Clinical Databases Using Rough Set Model, PKDD97, Trondheim, Norway, June 1997, Lecture Notes in Artificial Intelligence 1263, Springer Verlag, pp. 58–67.Google Scholar
  199. 200.
    Tsumoto S.: Formalization and Induction of Medical Expert System Rules Based on Rough Set Theory, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 2. Applications, Case Studies and Software Systems, Physica-Verlag, Heidelberg, 1998, pp. 307–323.Google Scholar
  200. 201.
    Tsumoto S., Ziarko W.: The Application of Rough Sets — Based Data Mining Technique to Differential Diagnosis of Meningoencephalitis, Proceedings of the 9th International Symposium, Foundations of Intelligent Systems, Zakopane, Poland, 9–13 June, 1996, Lecture Notes in Artificial Intelligence 1079, pp. 438–447.Google Scholar
  201. 202.
    Tversky A.: Features of Similarity. Psychological Review 84/4, 1997, pp. 327–352.Google Scholar
  202. 203.
    Yao Y. Y.: On Generalizing Pawlak Approximation Operators, Proceedings of the International Conference on Rough Sets and Current Trends in Computing, Warsaw, Poland, June 22–26, 1998, Lecture Notes in Artificial Intelligence 1424, pp. 298–307.Google Scholar
  203. 204.
    Yao Y. Y., Lin T. Y.: Generalization of Rough Sets Using Modal Logic. Intelligent Automation and Soft Computing 2, 1996, pp. 103–120.Google Scholar
  204. 205.
    Yao Y. Y., Wong S. K. M., Lin T. Y.: A Review of Rough Set Models, T. Y. Lin, N. Cercone (Eds.), Rough Sets and Data Mining Analysis of Imprecise Data, Kluwer Academic Publishers, 1997, pp. 47–75.Google Scholar
  205. 206.
    Yao Y. Y., Zhong N.: An Analysis of Quantitative Measures Associated with Rules, Proceedings of The Third Pacific-Asia Conference on Knowledge Discovery and Data Mining, Beijing, China, April 26–28, 1999, Lecture Notes in Artificial Intelligence 1574, pp. 479–488.Google Scholar
  206. 207.
    Vakarelov D.: A Modal Logic for Similarity Relations in Pawlak Knowledge Representation Systems. Fundamenta Informaticae 15, 1991, pp. 61–79.MathSciNetMATHGoogle Scholar
  207. 208.
    Vakarelov D.: Rough Polyadic Modal Logics, Journal of Applied Non-Classical Logics, vol. 1(1), 1991, pp. 9–36.MathSciNetMATHCrossRefGoogle Scholar
  208. 209.
    Vakarelov D.: Information Systems, Similarity Relations and Modal Logic, E. Orlowska (Ed.), Incomplete Information: Rough Set Analysis, Physica Verlag, Heidelberg, 1998, pp. 492–550.Google Scholar
  209. 210.
    Urban M., Baszun-Stepaniuk E., Stepaniuk J.: Application of the Rough Set Theory in the Prognostication of the Diabetic Nephropathy Prevalence. Preliminary Communication Endokrynologia, Diabetologia i Choroby Przemiany Materii Wieku Rozwojowego 1998, 4, 2, pp. 107–112.Google Scholar
  210. 211.
    Wakulicz-Deja A., Paszek P.: Diagnose Progressive Encephalopathy Applying the Rough Set Theory. International Journal of Medical Informatics 46, 1997, pp. 119–127.CrossRefGoogle Scholar
  211. 212.
    Wasilewska A.: Linguistically Definable Concepts and Dependencies. Journal of Symbolic Logic 54/2, 1989, pp. 671–672.Google Scholar
  212. 213.
    Weiss S.M., Kulikowski C.A.: Computer Systems that Learn: Classification and Prediction Methods from Statistics, Neural Networks, Machine Learning and Expert Systems, Morgan Kaufmann, San Mateo, CA, 1991.Google Scholar
  213. 214.
    Wilson D. A., Martinez T. R.: Improved Heterogeneous Distance Functions, Journal of Artificial Intelligence Research, Vol. 6, 1997, pp. 1–34.MathSciNetMATHGoogle Scholar
  214. 215.
    Wong S.K.M., Ziarko W., Ye LW.: Comparision of Rough Set and Statistical Methods in Inductive Learning. Journal of Man—Machine Studies 24, 1986, pp. 53–72.MATHCrossRefGoogle Scholar
  215. 216.
    Wong S.K.M.: A Rough-Set Model for Reasoning about Knowledge, L. Polkowski, A. Skowron (Eds.), Rough Sets in Knowledge Discovery 1. Methodology and Applications, Physica—Verlag, Heidelberg, 1998, pp. 276–285.Google Scholar
  216. 217.
    Woolery L., Grzymala-Busse J.W.: Machine learning for an Expert System to Predict Preterm Birth Risk. Journal of the American Medical Informatics Association 1, 1994, pp. 439–446.CrossRefGoogle Scholar
  217. 218.
    Wybraniec-Skardowska U.: On a Generalization of Approximation Space, Bulletin of the Polish Academy of Sciences, Mathematics, 37, 1989, pp. 51–61.MathSciNetMATHGoogle Scholar
  218. 219.
    Zadeh L. A.: Similarity Relations and Fuzzy Orderings. Information Sciences 3 1971, pp. 177–200.MathSciNetMATHCrossRefGoogle Scholar
  219. 220.
    Zadeh L.A.: Fuzzy Logic = Computing with Words, IEEE Trans. on Fuzzy Systems Vol. 4, 1996, pp. 103–111.CrossRefGoogle Scholar
  220. 221.
    Zadeh L.A.: Toward a Theory of Fuzzy Information Granulation and Its Certainty in Human Reasoning and Fuzzy Logic, Fuzzy Sets and Systems Vol. 90, 1997, pp. 111–127.MathSciNetMATHCrossRefGoogle Scholar
  221. 222.
    Zadeh L.A., Kacprzyk J. (Eds.): Computing with Words in Information/Intelligent Systems 1. Foundations, Physica-Verlag, Heidelberg, 1999.MATHGoogle Scholar
  222. 223.
    Zadeh L.A., Kacprzyk J. (Eds.): Computing with Words in Information/Intelligent Systems 2. Applications, Physica-Verlag, Heidelberg, 1999.MATHGoogle Scholar
  223. 224.
    Ziarko W.: The Discovery, Analysis and Representation of Data Dependencies in Databases, G. Piatetsky-Shapiro, W.J. Frawley (Eds.), Knowledge Discovery in Databases, AAAI Press/MIT Press, 1991, pp. 177–195.Google Scholar
  224. 225.
    Ziarko W.: Variable Precision Rough Sets Model, Journal of Computer and Systems Sciences, Vol. 46, No. 1, 1993, pp. 39–59.MathSciNetMATHCrossRefGoogle Scholar
  225. 226.
    Ziarko W., Shan N.: KDD—R: A Comprehensive System for Knowledge Discovery in Databases Using Rough Sets, Proceedings of the Third International Workshop on Rough Sets and Soft Computing, San Jose, November 10–12, 1994, pp. 164–173.CrossRefGoogle Scholar
  226. 227.
    Żakowski W.: On a Concept of Rough Sets. Demonstratio Mathematica XV, 1982, pp. 1129–1133.Google Scholar
  227. 228.
    Żytkow J.M., Zembowicz R.: Database Exploration in Search of Regularities, Journal of Intelligent Information Systems 2, 1993, pp. 39–81.CrossRefGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 2000

Authors and Affiliations

  • Jaroslaw Stepaniuk
    • 1
  1. 1.Institute of Computer Science BialystokUniversity of TechnologyBialystokPoland

Personalised recommendations