Competitive exception learning using fuzzy frequency distributions

A competitive exception learning algorithm for finding a non-linear mapping is proposed which puts the emphasis on the discovery of the important exceptions rather than the main rules. To do so,we first cluster the output space using a competitive fuzzy clustering algorithm and derive a fuzzy frequency distribution describing the general, average system's output behavior. Next, we look for a fuzzy partitioning of the input space in such away that the corresponding fuzzy output frequency distributions `deviate at most' from the average one as found in the first step. In this way, the most important `exceptional regions' in the input-output relation are determined. Using the joint input-output fuzzy frequency distributions, the complete input-output function as extracted from the data, can be expressed mathematically. In addition, the exceptions encountered can be collected and described as a set of fuzzy if-then-else-rules. Besides presenting a theoretical description of the new exception learning algorithm, we report on the outcomes of certain practical simulations

Financial Markets Analysis by Probabilistic Fuzzy Modelling

For successful trading in financial markets, it is important to develop financial models where one can identify different states of the market for modifying one???s actions. In this paper, we propose to use probabilistic fuzzy systems for this purpose. We concentrate on Takagi???Sugeno (TS) probabilistic fuzzy systems that combine interpretability of fuzzy systems with the statistical properties of probabilistic systems. We start by recapitulating the general architecture of TS probabilistic fuzzy rule-based systems and summarize the corresponding reasoning schemes. We mention how probabilities can be estimated from a given data set and how a probability distribution can be approximated by a fuzzy histogram. We apply our methodology for financial time series analysis and demonstrate how a probabilistic TS fuzzy system can be identified, assuming that a linguistic term set is given. We illustrate the interpretability of such a system by inspecting the rule bases of our models

Relative Distress and Return Distribution Characteristics of Japanese Stocks, a Fuzzy-Probabilistic Approach

In this article, we demonstrate that a direct relation exists between the context of Japanese firms indicating relative distress and conditional return distribution properties. We map cross-sectional vectors with company characteristics on vectors with return feature vectors, using a fuzzy identification technique called Competitive Exception Learning Algorithm (CELA)1. In this study we use company characteristics that follow from capital structure theory and we relate the recognized conditional return properties to this theory. Using the rules identified by this mapping procedure this approach enables us to make conditional predictions regarding the probability of a stock's or a group of stocks' return series for different return distribution classes (actually return indices). Using these findings, one may construct conditional indices that may serve as benchmarks. These would be particularly useful for tracking and portfolio management

Probabilistic and Statistical Fuzzy Set Foundations of Competitive Exception Learning

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-dime