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Part of the book series: Massive Computing ((MACO,volume 6))

Abstract

The ability to acquire knowledge from empirical data or the environment is an important requirement in better understanding many natural and artificial organisms. This ability relies heavily on the quality of the raw information available about the target system. In reality, these raw information/data may contain uncertainty and fuzziness, that is, it may be imprecise or incomplete. A number of techniques, such as the Dempster-Shafer theory of belief functions and fuzzy set theory, have been developed to handle knowledge acquisition in environments that exhibit uncertainty and fuzziness. However, the advent of the rough set theory in the early 80’s provides a novel and promising way of dealing with vagueness and uncertainty. This chapter will address the issue systematically by covering a broad area including knowledge acquisition / extraction, uncertainty in general, and techniques for handling uncertainty. The basic notions of rough set theory as well as some recent applications are also included. Two simple case studies related to fault diagnosis in manufacturing systems a reused to illustrate the concepts presented in this chapter.

Triantaphyllou, E. and G. Felici (Eds.), Data Mining and Knowledge Discovery Approaches Based on Rule Induction Techniques, Massive Computing Series, Springer, Heidelberg, Germany, pp. 359–394, 2006.

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References

  • Barbara, D., Garcia-Molina, H., and Porter, D., “The management of probabilistic data”, IEEE Trans. on Knowledge and Data Engineering, Vol. 4, No. 5, pp. 487–502, 1992.

    Article  Google Scholar 

  • Chan, K. C. C. and Wong, A. K. C, “A statistical technique for extracting classificatory knowledge from database”, in G. Piatetsky-Shapiro, W. J. Frawley, eds, Knowledge Discovery in Database, 1991, Cambridge, MA, U.S.A.: AAAI/MIT, pp. 107–123.

    Google Scholar 

  • Chanas, S. and Kuchta, D., “Further remarks on the relation between rough sets and fuzzy sets”, Fuzzy Sets and Systems, 47, pp. 391–394, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  • Cheeseman, P., “Probabilistic vs. fuzzy reasoning”, in L. N. Kanal, J. F. Lemmer, eds, Uncertainty in Artificial Intelligence, 1986. Amsterdam: North Holland Press, pp. 85–102.

    Google Scholar 

  • Dempster, A. P., “Upper and lower probabilities induced by a multivariate mapping”, Annals of Mathematical Statistics, 38, pp. 325–339, 1967.

    MATH  MathSciNet  Google Scholar 

  • Dubois, D. and Prade, H. “Combination and propagation of uncertainty with belief functions”, in Proceedings of the 9th International Joint Conference on Artificial Intelligence, 1985, Los Angeles, CA, U.S.A., pp. 18–23.

    Google Scholar 

  • Dubois, D. and Prade, H., “Putting rough sets and fuzzy sets together”, in R. Slowinski, ed, Intelligent Decision Support-Handbook of Applications and Advances of the Rough Sets Theory, 1992. Dordrecht: Kluwer Academic Publishers. pp. 203–231.

    Google Scholar 

  • Dubois, D. and Prade, H., “Rough fuzzy sets and fuzzy rough sets”, International Journal of General Systems, 17, pp. 191–209, 1990.

    MATH  Google Scholar 

  • Elder-IV, J. F. and Pregibon, “DA statistical perspective on KDD”, in U. Fayyad, R. Utnurusamy, eds, The 1 st Int. Conf. on Knowledge Discovery and Data Mining, 1995. Montreal, Quebec, Canada, pp. 87–93.

    Google Scholar 

  • Fausett, L. V., Fundamentals of Neural Networks: Architectures, Algorithms, and Applications. Englewood Cliffs, NJ, U.S.A.: Prentice-Hall. 1994.

    MATH  Google Scholar 

  • Felici G. and Truemper K., “A MINSAT approach for learning in logic domains”, INFORMS Journal on Computing, 14, pp. 20–36, 2000.

    Article  MathSciNet  Google Scholar 

  • Fournier, D. and Crémilleux, “A quality index for decision tree pruning”, Knowledge-Based Systems, Vol. 15, No. 1–2, pp. 37–43, 2002.

    Article  Google Scholar 

  • Goldberg, D. E.. Genetic Algorithms in Search, Optimisation and Machine Learning, Reading, Mass., U.S.A.: Addison-Wesley. 1989.

    Google Scholar 

  • Gray, R. M., Entropy and Information Theory. New York, U.S.A.: Springer-Verlag. 1990.

    MATH  Google Scholar 

  • Grzymala-Busse, D. M. and Grzymala-Busse, J. W., “The usefulness of a machine learning approach to knowledge acquisition”, Computational Intelligence, Vol. 11, No. 2, pp. 268–279. 1995.

    Google Scholar 

  • Grzymala-Busse, J. W. and Wang Chien Pei, B., “Classification and rule induction based on rough sets”, in 1996 IEEE International Conference on Fuzzy Systems, 1996. Vol. 2, pp. 744–747. Piscataway, NJ, U.S.A..

    Google Scholar 

  • Grzymala-Busse, J. W., “LERS-A system for learning from examples based on rough sets”, in R. Slowinski, ed, Intelligent Decision Support-Handbook of Applications and Advances of the Rough Sets Theory, 1992. Dordrecht: Kluwer Academic Publishers. pp. 3–18.

    Google Scholar 

  • Grzymala-Busse, J. W., “On the unknown attribute values in learning from examples”, in Z. W. Ras, M. Zemankova, eds, Methodologies for Intelligent Systems, 1991a, New York, U.S.A.: Springer-Verlag. pp. 368–377.

    Google Scholar 

  • Grzymala-Busse, J. W., ed, Managing Uncertainty in Expert Systems, 1991b, Boston, MA, U.S.A: Kluwer Academic Publishers.

    MATH  Google Scholar 

  • H. Bandemer and S. Gottwald, eds, Fuzzy Sets, Fuzzy Logic, Fuzzy Methods with Applications. Chichester, New York, U.S.A.: Wiley J. 1995.

    MATH  Google Scholar 

  • Kaufmann, A. ed, Fuzzy Mathematical Models in Engineering and Management Science, New York, U.S.A.: North-Holland Press. 1988.

    MATH  Google Scholar 

  • Khoo L.P. and Zhai L.Y., “A rough set approach to the treatment of continuous-valued attributes in multi-concept classification for mechanical diagnosis”, Artificial Intelligence for Engineering Design, Analysis and Manufacturing (AIEDAM), Vol. 15, No. 3, pp.211–221. 2001b.

    Article  MATH  Google Scholar 

  • Khoo L.P. and Zhai L.Y., “Multi-concept classification of diagnostic knowledge to manufacturing systems: analysis of incomplete data with continuous-valued attributes”, International Journal of Production Research, Vol. 39, No. 17, pp.3941–3957. 2001c.

    Article  MATH  Google Scholar 

  • Khoo L.P. and Zhai L.Y., “RClass*: a prototype rough-set and genetic algorithms enhanced multi-concept classification system for manufacturing diagnosis”, in J. Wang, A. Kusiak eds, Computational Intelligence in Manufacturing Handbook, CRC Press LLC, Boca Raton, FL, U.S.A., pp. 19–1 to 19–20. 2001a.

    Google Scholar 

  • Khoo, L. P., Tor, S. B., and Zhai, L. Y., “A rough-set based approach for classification and rule induction”, International Journal of Advanced Manufacturing, 15, pp. 438–444. 1999.

    Article  Google Scholar 

  • Krusinska, E., Slowinski, R., and Stefanowski, J., “Discriminate versus rough sets approach to vague data analysis”, Journal of Applied Statistics and Data Analysis, Vol. 8, No. 2, pp.43–56. 1990.

    Google Scholar 

  • Lee, N. S., Grize, Y. L., and Dehnad, K., “Quantitative models for reasoning under uncertainty in knowledge-based expert systems”, International Journal of Intelligent Systems, 2, pp. 15–38. 1987.

    MATH  Google Scholar 

  • Lemmer, J. F., “Confidence factors, empiricism and the Dempster-Shafer theory of evidence”, in L. N. Kanal, J. F. Lemmer, eds, Uncertainty in Artificial Intelligence, pp. 117–125. New York, U.S.A.: North-Holland Press. 1986.

    Google Scholar 

  • Lin, T. Y. and Cercone, N. eds, Rough Sets and Data Mining-Analysis for Imprecise Data. Boston, Mass, U.S.A.: Kluwer Academic Publishers. 1997.

    Google Scholar 

  • Lin, T. Y. ed, Proceedings of the 3 rd International Workshop on Rough Sets and Soft Computing. San Jose, CA, U.S.A.. 1995.

    Google Scholar 

  • Lin, T. Y., “Fuzzy reasoning and rough sets”, in W. Ziarko, ed, Rough Sets, Fuzzy Sets and Knowledge Discovery-Proceedings of the Int. Workshop on Rough Sets and Knowledge Discovery, pp. 343–348. London: Spring-Verlag. 1994.

    Google Scholar 

  • Luba, T. and Lasocki, R., “On unknown attribute values in functional dependencies”, in Proceedings of the 2 nd Int. Workshop on Rough Sets and Soft Computing, pp. 490–497. San Jose, CA, U.S.A.. 1994.

    Google Scholar 

  • Michalski, R., Garbonell, J. G., and Mitchell, T. M., Machine Learning: An Artificial Intelligence Approach, Vol. 2. Los Altos, CA, U.S.A.: Morgan Kaufmann Publishers. 1983.

    Google Scholar 

  • Mingers, J., “An empirical comparison of selection measures for decision tree induction”, Machine Learning, 3, pp. 319–342. 1989.

    Google Scholar 

  • Mitchell, J. S., An Introduction to Machinery Analysis and Monitoring. Tulsa, Oklahoma, U.S.A.: PannWell Books Company. 1981.

    Google Scholar 

  • Morik, K., ed, Knowledge Representation and Organization in Machine Learning. New York, U.S.A.: Springer-Verlag. 1989.

    MATH  Google Scholar 

  • Mrozek, A., “Rough sets in computer implementation of rule-based control of industrial process”, in R. Slowinski, ed, Intelligent Decision Support-Handbook of Applications and Advances of the Rough Sets Theory, pp. 19–32. Dordrecht: Kluwer Academic Publishers. 1992.

    Google Scholar 

  • Nanda, S. and Majumdar, S., “Fuzzy rough sets”, Fuzzy Sets and Systems, 45, pp. 157–160. 1992.

    Article  MATH  MathSciNet  Google Scholar 

  • Newton, S. L., Yves, L. G., and Khosrow, D., “Quantitative models for reasoning under uncertainty in knowledge-based expert systems”, International Journal of Intelligent Systems, 2, pp. 15–38. 1987.

    MATH  Google Scholar 

  • Nowicki, R., Slowinscki, R., and Stefanoski, J., “Analysis of diagnostic symptoms in vibroacoustic diagnostics by means of rough sets theory”, in R. Slowinski, ed, Intelligent Decision Support-Handbook of Applications and Advances of the Rough Sets Theory, pp. 33–48. Dordrecht: Kluwer Academic Publishers. 1992.

    Google Scholar 

  • Pawlak, Z., “Hard and soft sets”, in W. Ziarko, ed, Rough Sets, Fuzzy Sets and Knowledge Discovery-Proceedings of the Int. Workshop on Rough Sets and Knowledge Discovery, pp. 130–135. London: Spring-Verlag. 1994a.

    Google Scholar 

  • Pawlak, Z., “Rough classification”, International Journal of Man-Machine Studies, 20, pp. 469–483. 1984.

    MATH  Google Scholar 

  • Pawlak, Z., “Rough set approach to multi-attribute decision analysis”, European Journal of Operational Research, Vol. 72, No. 3, pp. 443–459. 1994b.

    Article  MATH  Google Scholar 

  • Pawlak, Z., “Rough set: A new approach to vagueness”, in L. A. Zadeh, J. Kacprzyk, eds, Fuzzy Logic for the Management of Uncertainty, pp. 105–108. New York, U.S.A.: John Wiley and Sons. 1992.

    Google Scholar 

  • Pawlak, Z., “Rough sets and fuzzy sets”, Fuzzy Sets and Systems, 17, pp. 99–102. 1985.

    Article  MATH  MathSciNet  Google Scholar 

  • Pawlak, Z., “Rough sets”, in T. Y. Lin, N. Gercone, eds, Rough Sets and Data Mining-Analysis for Imprecise Data, pp. 3–7. Boston, Mass, U.S.A.: Kluwer Academic Publishers. 1997.

    Google Scholar 

  • Pawlak, Z., “Rough sets”, International Journal of Computer and Information Sciences, Vol. 11, No. 5, pp. 341–356. 1982.

    Article  MATH  MathSciNet  Google Scholar 

  • Pawlak, Z., “Why rough sets”, in 1996 IEEE International Conference on Fuzzy Systems: Vol. 2, pp. 738–743. Piscataway, NJ, U.S.A. 1996.

    Google Scholar 

  • Pawlak, Z., Grzymala-Busse, J., Slowinski, R., and Ziarko, W., “Rough sets”, Communications of the ACM, Vol. 38, No. 11, pp. 89–95. 1995.

    Article  Google Scholar 

  • Pawlak, Z., Rough Sets-Theoretical Aspects of Reasoning about Data. Dordrecht: Kluwer Academic Publishers. 1991.

    MATH  Google Scholar 

  • Pearl, J., Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo, CA., U.S.A.: Morgan Kaufmann Publishers. 1988.

    Google Scholar 

  • Pham, D. T. and Aksoy, M. S., “A new algorithm for inductive learning”, Journal of Systems Engineering, 5, pp. 115–122. 1995.

    Google Scholar 

  • Pham, D. T. and Dimov, S. S., “An efficient algorithm for automatic knowledge acquisition”, Pattern Recognition, Vol. 30, No. 7, pp. 1137–1143. 1997.

    Article  Google Scholar 

  • Quinlan, J. R., “Induction of decision trees”, Machine Learning, 1, pp.81–106. 1986b.

    Google Scholar 

  • Quinlan, J. R., “Learning logical definitions from relations”, Machine Learning, 5, pp. 239–266. 1990.

    Google Scholar 

  • Quinlan, J. R., “The effect of noise on concept learning”, in R. Michalski, J. Carbonell, T. Mitchell, eds, Machine Learning: An Artificial Intelligent Approach: Vol. 2, pp. 149–166. San Mateo, CA, U.S.A.: Morgan Kauffman Publishers. 1986a.

    Google Scholar 

  • Quinlan, J. R., “Unknown attribute values in induction”, in A. M. Segre, ed, Proceedings of the 6 th Int. Machine Learning Workshop, pp. 164–168. San Mateo, CA, U.S.A.: Morgan Kaufmann Publishers. 1989.

    Google Scholar 

  • Quinlan, J. R., C4.5: Programs for Machine Learning. San Mateo, CA, U.S.A.: Morgan Kaufmann Publishers. 1992.

    Google Scholar 

  • Rao, M. M., Probability Theory with Applications. New York, U.S.A.: Academic Press. 1984.

    MATH  Google Scholar 

  • Rojas-Guzman, C., “Comparison of belief networks and rule-based expert systems for fault diagnosis of chemical processes”, Engineering Application of Artificial Intelligence, Vol. 6, No. 3, pp. 191–202. 1993.

    Article  Google Scholar 

  • Shafer, G. and Logan, R., “Implementing Dempster’s rule for hierarchical evidence”, Artificial Intelligence, 33, pp. 248–271. 1987.

    Article  MathSciNet  Google Scholar 

  • Shafer, G., “Belief functions and parametric models”, Journal of Royal Statistical Society, 44, pp. 322–352. 1982.

    MATH  MathSciNet  Google Scholar 

  • Shafer, G., A Mathematical Theory of Evidence. Princeton, NJ, U.S.A.: Princeton Univ. Press. 1976.

    MATH  Google Scholar 

  • Shortliffe, H. and Buchanan, B. G., “A model of inexact reasoning in medicine”, Mathematical Biosciences, 23, pp. 351–379. 1975.

    Article  MathSciNet  Google Scholar 

  • Skowron, A. and Rauszer, C, “The discernibility matrices and functions in information systems”, in R. Slowinski, ed, Intelligent Decision Support-Handbook of Applications and Advances of the Rough Sets Theory, pp. 331–362. Dordrecht: Kluwer Academic Publishers. 1992.

    Google Scholar 

  • Slowinski, K., “Rough classification of HSV patients”, in R. Slowinski, ed, Intelligent Decision Support-Handbook of Applications and Advances of the Rough Sets Theory, pp. 77–94. Dordrecht: Kluwer Academic Publishers. 1992.

    Google Scholar 

  • Slowinski, R. and Stefanowski, J., “Rough classification in incomplete information systems”, Mathematical & Computer Modeling. Vol. 12, No. 10/11, pp. 1347–1357. 1989.

    Google Scholar 

  • Slowinski, R. and Stefanowski, J., “ROUGHDAS and ROUGH-CLASS software implementation of the rough sets approach”, in R. Slowinski, ed, Intelligent Decision Support-Handbook of Applications and Advances of the Rough Sets Theory, pp. 445–456. Dordrecht: Kluwer Academic Publishers. 1992.

    Google Scholar 

  • Slowinski, R. ed, Intelligent Decision Support — Handbook of Applications and Advances of the Rough Sets Theory. Dordrecht: Kluwer Academic Publishers. 1992.

    MATH  Google Scholar 

  • Tecuci, G. and Kodratoff, Y. eds, Machine Learning and Knowledge Acquisition: Integrated Approaches. London: Academic Press. 1995.

    Google Scholar 

  • Thiesson, B., “Accelerated qualification of Bayesian network with incomplete data”, in U. Fayyad, R. Uthurusamy, eds, The 1 st International Conference on Knowledge Discovery and Data Mining, pp. 306–311. Montreal, Quebec, Canada. 1995.

    Google Scholar 

  • Triantaphyllou, E., “The OCAT (One Clause At a Time) approach to data mining and knowledge discovery”, in E. Triantaphyllou, G. Felici, eds, Data Mining and Knowledge Discovery Approaches Based on Rule Induction Techniques. Kluwer Academic Publishers. 2003.

    Google Scholar 

  • Triantaphyllou, E., Liao, T. W., and Iyengar, S. S., “A focused issue on data mining and knowledge discovery in industrial engineering”, Computers and Industrial Engineering, Vol. 43, No. 4, pp. 657–659. 2002.

    Article  Google Scholar 

  • Uthurusamy, R., Fayyad, U., and Spangler, S., “Learning useful rules from inconclusive data”, in G. Piatetsky-Shapiro, W. J. Frawley, eds, Knowledge Discovery in Database, pp. 83–96. Cambridge, MA, U.S.A.: AAAI/MIT. 1991.

    Google Scholar 

  • Wong, S. K. M. and Ziarko, W., “INFER-an adaptive decision support system based on the probabilistic approximate classification”, in The 6 th International Workshop on Expert Systems and Their Applications, Vol. 1, pp. 713–726. Avignon, France. 1987.

    Google Scholar 

  • Wong, S. K. M., Ziarko, W., and Li, Y. R., “Comparison of rough-set and statistical methods in inductive learning”, International Journal of Man-Machine Studies, 24, pp. 53–72. 1986.

    Article  MATH  Google Scholar 

  • Wygralak, W., “Rough sets and fuzzy sets-some remarks on interrelations”, Fuzzy Sets and Systems, 29, pp. 241–243. 1989.

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh, L. A., “Fuzzy sets”, Information and Control, 8, pp. 338–353. 1965.

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh, L. A., “Is probability theory sufficient for dealing with uncertainty in AI: A negative view”, in L. N. Kanal, J. F. Lemmer, eds, Uncertainty in Artificial Intelligence, pp. 103–116. New York, U.S.A.: North Holland Press. 1986.

    Google Scholar 

  • Ziarko, W. ed, Rough Sets, Fuzzy Sets and Knowledge Discovery-Proceedings of the Int. Workshop on Rough Sets and Knowledge Discovery. London: Spring-Verlag. 1994b.

    Google Scholar 

  • Ziarko, W., “Rough sets and knowledge discovery: an overview”, in W. Ziarko, ed, Rough Sets, Fuzzy Sets and Knowledge Discovery-Proceedings of the Int. Workshop on Rough Sets and Knowledge Discovery, pp. 11–15. London: Spring-Verlag. 1994a.

    Google Scholar 

  • Zimmermann, H. J., Fuzzy Set Theory: And Its Applications (3rd ed). Boston, MA, U.S.A.: Kluwer Academic Publishers. 1996.

    MATH  Google Scholar 

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Zhai, LY., Khoo, LP., Fok, SC. (2006). Knowledge Acquisition and Uncertainty in Fault Diagnosis: A Rough Sets Perspective. In: Triantaphyllou, E., Felici, G. (eds) Data Mining and Knowledge Discovery Approaches Based on Rule Induction Techniques. Massive Computing, vol 6. Springer, Boston, MA . https://doi.org/10.1007/0-387-34296-6_11

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