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Probabilistic and Statistical Fuzzy Set Foundations of Competitive Exception Learning

Author

Listed:
  • van den Berg, J.H.
  • van den Bergh, W.-M.
  • Kaymak, U.

Abstract

Recently, a Competitive Exception Learning Algorithm (CELA) was introduced [1, 2]. This algorithm establishes an optimal mapping from a (continuous) M-dimensional input sample space to an N-dimensional (continuous) output sample space. CELA is aimed to discover regimes (i.e. local behavior in the input sample space) for which the conditional probability distribution in the output sample space systematically deviates from the average unconditional distribution. Previous papers on CELA dealt with the introduction of the algorithm by sketching its background and by describing the algorithmic sub-steps. The algorithm was tested successfully on both simulated and real world data, mainly in the field of financial markets. However, until now a precise and firm theoretical foundation of CELA is still lacking. The current paper resolves this imperfection. The contribution to be made here is twofold. First, we present, in section 2, a probability theory and statistics of fuzzy sets which in itself is interesting. Second, we re-formulate, in section 3, the CELA-algorithm within the probabilistic fuzzy framework introduced. We finalize with a discussion and outlook.

Suggested Citation

  • van den Berg, J.H. & van den Bergh, W.-M. & Kaymak, U., 2001. "Probabilistic and Statistical Fuzzy Set Foundations of Competitive Exception Learning," ERIM Report Series Research in Management ERS-2001-40-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:102
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    Citations

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    Cited by:

    1. Loquin, Kevin & Strauss, Olivier, 2008. "Histogram density estimators based upon a fuzzy partition," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1863-1868, September.
    2. van den Berg, J.H. & van den Bergh, W.-M. & Kaymak, U., 2003. "Financial Markets Analysis by Probabilistic Fuzzy Modelling," ERIM Report Series Research in Management ERS-2003-036-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. van den Berg, J.H. & Kaymak, U. & Almeida e Santos Nogueira, R.J., 2011. "Function Approximation Using Probabilistic Fuzzy Systems," ERIM Report Series Research in Management ERS-2011-026-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

    More about this item

    Keywords

    exception learning; fuzzy set; probability theory; statistics;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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