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Cordon O.,European Center for Soft Computing
International Journal of Approximate Reasoning | Year: 2011

The need for trading off interpretability and accuracy is intrinsic to the use of fuzzy systems. The obtaining of accurate but also human-comprehensible fuzzy systems played a key role in Zadeh and Mamdani's seminal ideas and system identification methodologies. Nevertheless, before the advent of soft computing, accuracy progressively became the main concern of fuzzy model builders, making the resulting fuzzy systems get closer to black-box models such as neural networks. Fortunately, the fuzzy modeling scientific community has come back to its origins by considering design techniques dealing with the interpretability-accuracy tradeoff. In particular, the use of genetic fuzzy systems has been widely extended thanks to their inherent flexibility and their capability to jointly consider different optimization criteria. The current contribution constitutes a review on the most representative genetic fuzzy systems relying on Mamdani-type fuzzy rule-based systems to obtain interpretable linguistic fuzzy models with a good accuracy. © 2011 Elsevier Inc. All rights reserved. Source

Borgelt C.,European Center for Soft Computing
Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery | Year: 2012

Frequent item set mining is one of the best known and most popular data mining methods. Originally developed for market basket analysis, it is used nowadays for almost any task that requires discovering regularities between (nominal) variables. This paper provides an overview of the foundations of frequent item set mining, starting from a definition of the basic notions and the core task. It continues by discussing how the search space is structured to avoid redundant search, how it is pruned with the a priori property, and how the output is reduced by confining it to closed or maximal item sets or generators. In addition, it reviews some of the most important algorithmic techniques and data structures that were developed to make the search for frequent item sets as efficient as possible.© 2012 Wiley Periodicals, Inc. Source

Trillas E.,European Center for Soft Computing
International Journal of Intelligent Systems | Year: 2012

In the setting of a general type of fuzzy algebras, this paper deals with a new theoretic view on the commonsense reasoning, consisting of a kind of Popper's search for conjectures and refutations. It is supposed that the reasoning is done in natural language, but only with nonambiguous precise and imprecise terms, respectively, represented by crisp and fuzzy sets. © 2012 Wiley Periodicals, Inc. Source

Ramos-Guajardo A.B.,European Center for Soft Computing
Computational Statistics and Data Analysis | Year: 2012

The problem of testing equality of variances often arises when distributions of random variables are compared or linear models between them are considered. The usual tests for variances given normality of the underlying populations are highly non-robust to non-normality and are strongly dependent on the kurtosis. Some alternative formulations of Levene's test statistic for testing the homoscedasticity have been shown to be powerful and robust under non-normality. On the basis of Levene's classical procedure, a test for the equality of variances of k fuzzy-valued random elements is developed. Accordingly, consistent asymptotic and bootstrap tests are established and their empirical behaviour is analyzed by means of extensive simulation studies. In addition, the proposed test is compared with a Bartlett-type test. A case-study illustrating the applicability of the procedure is presented. © 2011 Elsevier B.V. All rights reserved. Source

Trutschnig W.,European Center for Soft Computing
Fuzzy Sets and Systems | Year: 2012

It is shown that pointwise convergence of a sequence ( An) n∈N of copulas to a copula A is equivalent (1) to the convergence of the corresponding endographs and (2) to the convergence of the corresponding upper (or lower) α-levels for all but at most countably many α in [0,1] (all with respect to the Hausdorff metric). Examples are given that show that the countably many exceptions in (2) cannot be omitted. It is furthermore shown that the main results also hold on the bigger class of quasi-copulas. © 2011 Elsevier B.V. All rights reserved. Source

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