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Fuzzy clustering: Insights and new approach.

Frank Klawonn — 2004

Mathware and Soft Computing

Fuzzy clustering extends crisp clustering in the sense that objects can belong to various clusters with different membership degrees at the same time, whereas crisp or deterministic clustering assigns each object to a unique cluster. The standard approach to fuzzy clustering introduces the so-called fuzzifier which controls how much clusters may overlap. In this paper we illustrate, how this fuzzifier can help to reduce the number of undesired local minima of the objective function that is associated...

Significance tests to identify regulated proteins based on a large number of small samples

Frank Klawonn — 2012

Kybernetika

Modern biology is interested in better understanding mechanisms within cells. For this purpose, products of cells like metabolites, peptides, proteins or mRNA are measured and compared under different conditions, for instance healthy cells vs. infected cells. Such experiments usually yield regulation or expression values – the abundance or absence of a cell product in one condition compared to another one – for a large number of cell products, but with only a few replicates. In order to distinguish...

A Lukasiewicz logic based Prolog.

Frank KlawonnRudolf Kruse — 1994

Mathware and Soft Computing

Prolog is a programming language based on a restricted subset of classical first order predicate logic. In order to overcome some problems of classical logic to handle imperfect human knowledge, we provide a formal framework for a Lukasiewicz logic based Prolog system. The use of Lukasiewicz logic with its connection to Ulam games enables us to deal with partial inconsistencies by interpreting the truth values as relative distance to contradiction. We also present the software tool LULOG which is...

Learning fuzzy systems. An objective function-approach.

Frank HöppnerFrank Klawonn — 2004

Mathware and Soft Computing

One of the most important aspects of fuzzy systems is that they are easily understandable and interpretable. This property, however, does not come for free but poses some essential constraints on the parameters of a fuzzy system (like the linguistic terms), which are sometimes overlooked when learning fuzzy system autornatically from data. In this paper, an objective function-based approach to learn fuzzy systems is developed, taking these constraints explicitly into account. Starting from fuzzy...

Relative cost curves: An alternative to AUC and an extension to 3-class problems

Olga MontvidaFrank Klawonn — 2014

Kybernetika

Performance evaluation of classifiers is a crucial step for selecting the best classifier or the best set of parameters for a classifier. Receiver Operating Characteristic (ROC) curves and Area Under the ROC Curve (AUC) are widely used to analyse performance of a classifier. However, the approach does not take into account that misclassification for different classes might have more or less serious consequences. On the other hand, it is often difficult to specify exactly the consequences or costs...

Fuzzy max-min classifiers decide locally on the basis of two attributes.

Birka von SchmidtFrank Klawonn — 1999

Mathware and Soft Computing

Fuzzy classification systems differ from fuzzy controllers in the form of their outputs. For classification problems a decision between a finite number of discrete classes has to be made, whereas in fuzzy control the output domain is usually continuous, i.e. a real interval. In this paper we consider fuzzy classification systems using the max-min inference scheme and classifying an unknown datum on the basis of maximum matching, i.e. assigning it to the class appearing in the consequent of the rule...

Similarity in fuzzy reasoning.

Frank KlawonnJuan Luis Castro — 1995

Mathware and Soft Computing

Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that this indistinguishability cannot be overcome in approximate reasoning. For our investigations we generalize from the unit interval as the basis...

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