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A realistic tolerant solution of a system of interval linear equations with the use of multidimensional interval arithmetic

Piegat Andrzej, Pluciński Marcin

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 2

229--247

EN

The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in the form of improper intervals have been obtained (which cannot be implemented in practice). The research conducted by the authors has shown that for many problems it is impossible to arrive at ideal solutions that would be fully robust to data uncertainty. However, partially robust solutions can be obtained, and those with the highest robustness can be selected and put into practice. The paper shows that the degree of robustness to the uncertainty of the entire system can be calculated on the basis of the degrees of robustness of individual equations, which greatly simplifies calculations. The presented method is illustrated with a series of examples (also benchmark ones) that facilitate its understanding. It is an extension of the authors’ previously published method for first-order ILEs.

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A decomposition approach to type 2 interval arithmetic

Piegat Andrzej, Dobryakova Larisa

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 1

185--201

EN

The classic interval has precise borders A = [a, ā] . Therefore, it can be called a type 1 interval. Because of great practical importance of such interval data, several versions of type 1 interval arithmetic have been created. However, sometimes precise borders a and ā of intervals cannot be determined in practice. If the borders are uncertain, then we have to do with type 2 intervals. A type 2 interval can be denoted as AT2 = [aL, aR], [āL, āR]. The paper presents multidimensional decomposition RDM type 2 interval arithmetic (D-RDM-T2-I arithmetic), where RDM means relative-distance measure. The decomposition approach considerably simplifies calculations and is transparent for users. Apart from this arithmetic, examples of its applications are also presented. To the authors’ best knowledge, no papers on this arithmetic exist. D-RDM-T2-I arithmetic is necessary to create type 2 fuzzy arithmetic based on horizontal µ-cuts, which the authors aim to do.

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Significance of condition attributes in child well-being analysis

Adamus Ewa, Klęsk Przemysław, Kołodziejczyk Joanna, Korzeń Marcin, Piegat Andrzej, Pluciński Marcin

Studia i Materiały Informatyki Stosowanej

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2011

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nr 4

11--16

EN

In this study the significance of attributes in child well-being is presented. The main goal was to find features most specific for child-well being evaluation in Poland. The dataset was obtained from a survey based on a special questionnaire. To select important attributes three filter for individual attribute rank were used ?2, information gain and relief attribute evaluator and one filter-subset selector based on rough set theory. In the article the dataset is described in details. All the attributes are named, divided by category and for each a domain is given. Then methods of attribute selection applied in experiments are presented. Finally results on selecting attributes relevant for child well-being are discussed.