Milan Petrík

On n-contractive fuzzy logics

It is well known that MTL satisfies the finite embeddability property. Thus MTL is complete w. r. t. the class of all finite MTL-chains. In order to reach a deeper understanding of the structure of this class, we consider the extensions of MTL by adding the generalized contraction since each finite MTL-chain satisfies a form of this generalized contraction. Simultaneously, we also consider extensions of MTL by the generalized excluded middle laws introduced in [9] and the axiom of weak cancellation defined in [31]. The algebraic counterpart of these logics is studied characterizing the subdirectly irreducible, the semisimple, and the simple algebras. Finally, some important algebraic and logical properties of the considered logics are discussed: local finiteness, finite embeddability property, finite model property, decidability, and standard completeness.

Examining cross-database global training to evaluate five different methods for ventricular beat classification.

The detection of ventricular beats in the holter recording is a task of great importance since it can direct clinicians toward the parts of the electrocardiogram record that might be crucial for determining the final diagnosis. Although there already exists a fair amount of research work dealing with ventricular beat detection in holter recordings, the vast majority uses a local training approach, which is highly disputable from the point of view of any practical-real-life-application. In this paper, we compare five well-known methods: a classical decision tree approach and its variant with fuzzy rules, a self-organizing map clustering method with template matching for classification, a back-propagation neural network and a support vector machine classifier, all examined using the same global cross-database approach for training and testing. For this task two databases were used-the MIT-BIH database and the AHA database. Both databases are required for testing any newly developed algorithms for holter beat classification that is going to be deployed in the EU market. According to cross-database global training, when the classifier is trained with the beats from the records of one database then the records from the other database are used for testing. The results of all the methods are compared and evaluated using the measures of sensitivity and specificity. The support vector machine classifier is the best classifier from the five we tested, achieving an average sensitivity of 87.20% and an average specificity of 91.57%, which outperforms nearly all the published algorithms when applied in the context of a similar global training approach.

Comparison of seven approaches for holter ECG clustering and classification

In this work we present a comparative study, testing selected methods for clustering and classification of Holter electrocardiogram (ECG). More specifically we focus on the task of discriminating between normal N beats and premature ventricular V beats. Some of the tested methods represent the state of the art in pattern analysis, while others are novel algorithms developed by us. All the algorithms were tested on the same datasets, namely the MIT-BIH and the AHA databases. The results for all the employed methods are compared and evaluated using the measures of sensitivity and specificity.

Fuzzy Control – Expectations, Current State, and Perspectives

We summarize the history of fuzzy sets. We try to find the reasons why fuzzy control has been so successful in applications. This is mainly explained by the fact that fuzzy logic created an alternative to exact computation and it better fits to the human way of reasoning. We point out some aspects in which current fuzzy systems are not completely satisfactory and directions in which they should develop in the future.

Quine–McCluskey method for many-valued logical functions

In this paper we deal with a generalization of the Quine–McCluskey method. We show that the generalized method can find a normal form for any finite-valued logical function. Moreover, this normal form is simpler than that found by the intuitive method using the table of values. The method has been successfully implemented and tested on examples.

Generalization of Rule-Based Decision Tree to Fuzzy Intervals for ECG-Beat Clustering

In this paper, we compare two approaches to clustering and diagnosis of the ECG heart beats. In the first approach, the rule-based decision tree method is presented; in this method the decision rules are based on classical intervals. The second approach is based on fuzzification of the intervals; this accords with the situation when the knowledge described by books and cardiologists is vague or unclear. We discuss the way how the results of the fuzzy and the classical approaches can be compared. We choose the sensitivity and specificity as they are a well established measures in the field of the clinical medicine. We define a generalization of the sensitivity and specificity for fuzzy clusters in order to prove correctness of our presented fuzzy approach.