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Probabilistic and Statistical Fuzzy Set Foundations of Competitive Exception Learning

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Author Info
Berg, J. van den
Bergh, W.M. van den
Kaymak, U. (Erasmus Research Institute of Management (ERIM), RSM Erasmus University)

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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.

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Paper provided by 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. in its series Research Paper with number ERS-2001-40-LIS Revision_Date: 2009-07-29.

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Date of creation: 03 Jul 2001
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Handle: RePEc:dgr:eureri:200198

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Related research
Keywords: probability theory; statistics; fuzzy set; exception learning;

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  1. Berg, J. van den & Bergh, W.M. van den & Kaymak, U., 2003. "Financial Markets Analysis by Probabilistic Fuzzy Modelling," Research Paper ERS-2003-036-LIS Revision, 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 Uni. [Downloadable!]
  2. Bergh, W.M. van den & Steenbeek, O.W. & Berg, J. van den, 2002. "Relative Distress and Return Distribution Characteristics of Japanese Stocks, a Fuzzy-Probabilistic Approach," Research Paper ERS-2002-29-F&A Revision_, 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 Uni. [Downloadable!]
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