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Rough support vector machine for classification with interval and incomplete data

Nowicki Robert K., Grzanek Konrad, Hayashi Yoichi

Journal of Artificial Intelligence and Soft Computing Research

2020

Vol. 10, No. 1

47--56

The paper presents the idea of connecting the concepts of the Vapnik’s support vector machine with Pawlak’s rough sets in one classification scheme. The hybrid system will be applied to classifying data in the form of intervals and with missing values [1]. Both situations will be treated as a cause of dividing input space into equivalence classes. Then, the SVM procedure will lead to a classification of input data into rough sets of the desired classes, i.e. to their positive, boundary or negative regions. Such a form of answer is also called a three–way decision. The proposed solution will be tested using several popular benchmarks.

Breakthrough in Interval Data Fitting II. From Ranges to Means and Standard Deviations

Gutowski M.W.

Prace Naukowe Politechniki Warszawskiej. Elektronika

2009

z. 169

73-78

Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all. Worse yet, if this happens, then we are left in the state of complete ignorance concerning the unknown parameters of interest. This is in sharp contrast with widespread statistical methods of data analysis. In this paper I show the connections between those two approaches: how to process experimental data rigorously, using interval methods, and present the final results either as intervals (guaranteed, rigorous results) or in a more familiar probabilistic form: as a mean value and its standard deviation.

Breakthrough in Interval Data Fitting I. The Role of Hausdorff Distance

Gutowski M.W.

Prace Naukowe Politechniki Warszawskiej. Elektronika

2009

z. 169

63-72

This is the first of two papers describing the process of fitting experimental data under interval uncertainty. Probably the most often encountered application of global optimization methods is finding the so called best fitted values of various parameters, as well as their uncertainties, based on experimental data. Here I present the methodology, designed from the very beginning as an interval-oriented tool, meant to replace to the large extent the famous Least Squares (LSQ) and other slightly less popular methods. Contrary to its classical counterparts, the presented method does not require any poorly justified prior assumptions, like smallness of experimental uncertainties or their normal (Gaussian) distribution. Using interval approach, we are able to fit rigorously and reliably not only the simple functional dependencies, with no extra effort when both variables are uncertain, but also the cases when the constitutive equation exists in implicit rather than explicit functional form. The magic word and a key to success of interval approach appears the Hausdorff distance.

Identification of "input-output" dynamic model of the electrical circuits on the basis of interval data

Dyvak M., Stakchiv P., Calishchuc I.

Przegląd Elektrotechniczny

2005

R. 81, nr 2

60-62

The problem of identification of "input-output" dynamic model of electrical circuit on the basis of interval data is considered. The method of interval parameter's identification of dynamic system is proposed. The results of proposed method used for modeling of electrical circuit ol transformer are shown.

W pracy przedstawiono problem identyfikacji dynamicznego modelu obwodu elektrycznego na podstawie danych interwałowych. Zaproponowano metodę identyfikacji interwałowych parametrów systemu dynamicznego. Zaprezentowano wyniki zastosowania przedstawionej metody do modelowania obwodu elektrycznego transformatora.