Abstract
In the chapter an advanced fuzzy modeling method has been presented which can be useful in temporal data analysis. The method joints fuzzy and probabilistic approaches. The notions of the stochastic process with fuzzy states, and linguistic random variable have been defined to create a knowledge representation of the SISO and MISO dynamic systems. As the basic description of the stochastic process with fuzzy states observed at fixed moments, the joint probability distribution of n linguistic random variables has been assumed. The joint, conditional and marginal probability distributions of the stochastic process with fuzzy states valuate weights of particular rules of the knowledge rule base. Also, the probability distributions determine the probabilistic structure of the particular steps of the tested process. A mean fuzzy conclusion (prediction) can be calculated by the proposed inference procedure.
The implemented knowledge-based system, which creates the knowledge base with optimal number of elementary rules, has been also presented. The optimization method uses a fast algorithm to find fuzzy association rules as a process of automatic knowledge base extraction.
Two examples illustrate the presented methods of the knowledge base extraction from different numeric time series.
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References
Agrawal, R., Imielinski, T., Swami, A.: A Mining association rules between sets of items in large databases. In: ACM Sigmod Intern. Conf. on Management of Data, Washington D.C., pp. 207–216 (May 1993)
Box, G.E.P., Jenkins, G.M.: Time Series Analysis; Forecasting and Control. Holden-Day, San Francisco (1976)
Doob, J.L.: Stochastic Processes. Wiley, New York (1953)
Fayyad, U., Piatetsky-Shapiro, G., Smyth, P.: From data mining to knowledge discovery in databases. AI Magazine, 37–54 (1996)
Fisz, M.: Probability and Statistics Theory. PWN, Warsaw (1967) (in Polish)
Frawley, W., Piatetsky-Shapiro, G., Matheus, C.: Knowledge Discovery in Databases: An Overview. AI Magazine, 57–70 (1992)
Han, J., Pei, H., Yin, Y.: Mining Frequent Patterns without Candidate Generation. In: Proc. Conf. Management of Data, SIGMOD 2000, Dallas, TX. ACM Press, New York (2000)
Hellendoorn, H., Driankov, D. (eds.): Fuzzy Model identification, Selected Approaches. Springer, Berlin (1997)
Hüllermeier, E.: Fuzzy methods in machine learning and data mining: status and prospects. Fuzzy Sets and System 156(3), 387–406 (2005)
Łęski, J.: Neuro-Fuzzy Systems. WNT, Warsaw (2008) (in Polish)
Oh, S.-K., Pedrycz, W., Park, K.-J.: Identification of fuzzy systems by means of genetic optimization and data granulation. Journal of Intelligent & Fuzzy Systems 18, 31–41 (2007)
Papoulis, A.: Probability, Random Variables, and Stochastic Processes. WNT, Warsaw (1972) (Polish edition)
Rudnik, K.: Conception and implementation of the inference system with the probabilistic-fuzzy knowledge base. Dissertation, Opole University of Technology, Opole, Poland (2011) (in Polish)
Rudnik, K., Walaszek-Babiszewska, A.: Probabilistic-fuzzy knowledge-based system for managerial applications. Management and Production Engineering Review 3 (in press 2012)
Walaszek-Babiszewska, A.: Fuzzy probability for modelling of particle preparation processes. In: Proc. 4th Int. Conf. Intelligence Processing and Manufacturing of Materials (IPMM 2003), Sendai, Japan (2003)
Walaszek-Babiszewska, A.: IF-THEN Linguistic Fuzzy Model of a Discrete Stochastic System. In: Cader, A., Rutkowski, L., Tadeusiewicz, R., Żurada, J. (eds.) Artificial Intelligence and Soft Computing, pp. 169–174. Academic Publishing House EXIT, Warsaw (2006)
Walaszek-Babiszewska, A., Błaszczyk, K.: A modified Apriori algorithm to generate rules for inference system with probabilistic-fuzzy knowledge base. In: Proc. 7th Int. Workshop on Advanced Control and Diagnosis, November 19-20, CD-ROM, Zielona Góra, Poland (2009)
Walaszek-Babiszewska, A.: Fuzzy Modeling in Stochastic Environment; Theory, knowledge bases, examples. LAP LAMBERT Academic Publishing, Saarbrücken (2011)
Yager, R.R., Filev, D.: Essentials of Fuzzy Modeling and Control. John Wiley and Sons (1994)
Zadeh, L.A.: Probability Measures of Fuzzy Events. Journal of Mathematical Analysis and Applications 23(2), 421–427 (1969)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Part I. Information Sciences 8, 199–249 (1975); Part II. 8, 301–357, Part III. 9, 43–80
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Walaszek-Babiszewska, A., Rudnik, K. (2013). Stochastic-Fuzzy Knowledge-Based Approach to Temporal Data Modeling. In: Pedrycz, W., Chen, SM. (eds) Time Series Analysis, Modeling and Applications. Intelligent Systems Reference Library, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33439-9_5
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DOI: https://doi.org/10.1007/978-3-642-33439-9_5
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