2014

DOI: 10.14313/jamris_4-2014/38

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On Perturbation Measure of Sets – Properties

Maciej Krawczak¹,

Grażyna Szkatuła²

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Asymmetric Matching Between Binary Vectors1

Introduction1

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Cited by 4 publications

(2 citation statements)

References 6 publications

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“…The cardinality of the set A;\ Ai can be normalized to a value ranged from O to 1 and can be defined a measure of perturbation. The measure of perturbation type 2 of one set by another set was proposed in the paper by Krawczak and Szkatula [7] in the following manner:…”

Section: Asymmetric Matching Between Binary Vectorsmentioning

confidence: 99%

“…Krawczak and Szkatula [61) . The measure of perturbation type 2 of one set by another set was proposed in the paper by Krawczak and Szkatula [7] and the mathematical properties of this measure were studied.…”

Section: Introductionmentioning

confidence: 99%

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On Perturbation Measure for Binary Vectors

¹

,

²

2015

Artificial Intelligence and Soft Computing

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The paper is about remoteness of objects described by the nominal-valued attributes. Nominal values of the attributes are replaced by respective binary vectors. A new measure of remoteness between sets, based on binary attributes' values, is introduced. The new measure is called a measure of perturbation of one binary vector by another binary vector and can be treated as a binary version of developed by the authors sets' perturbation measure. Values of the newly developed measure range between 0 and 1, and the perturbation measure of one binary vector by another is not the same as the perturbation of the second binary vector by the first one-it means that the measure is not symmetric in general.

“…The cardinality of the set A;\ Ai can be normalized to a value ranged from O to 1 and can be defined a measure of perturbation. The measure of perturbation type 2 of one set by another set was proposed in the paper by Krawczak and Szkatula [7] in the following manner:…”

Section: Asymmetric Matching Between Binary Vectorsmentioning

confidence: 99%

“…Krawczak and Szkatula [61) . The measure of perturbation type 2 of one set by another set was proposed in the paper by Krawczak and Szkatula [7] and the mathematical properties of this measure were studied.…”

Section: Introductionmentioning

confidence: 99%

On Perturbation Measure for Binary Vectors

¹

,

²

2015

Artificial Intelligence and Soft Computing

Self Cite

View full text Add to dashboard Cite

The paper is about remoteness of objects described by the nominal-valued attributes. Nominal values of the attributes are replaced by respective binary vectors. A new measure of remoteness between sets, based on binary attributes' values, is introduced. The new measure is called a measure of perturbation of one binary vector by another binary vector and can be treated as a binary version of developed by the authors sets' perturbation measure. Values of the newly developed measure range between 0 and 1, and the perturbation measure of one binary vector by another is not the same as the perturbation of the second binary vector by the first one-it means that the measure is not symmetric in general.

On Bilateral Matching between Multisets

¹

,

²

2015

Advances in Intelligent Systems and Computing

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No abstract

Bidirectional comparison of multi-attribute qualitative objects

¹

,

²

2018

Information Sciences

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In the paper, the multi-attribute objects with repeating qualitative values of attributes are considered. Each object is represented by a collection of multisets drawn from sets of values of the attributes. Formalism of the theory of multisets allows taking into account simultaneously all the combinations of attribute values and various versions of the objects. The effective procedure for comparing such obj ects as well as groups of such objects is developed. The considered measure of perturbation of one obj ect by another is proposed as the difference of the multisets representing the objects. The measure describes remoteness between the objects, and, in general, is asymmetrical , and therefore cannot be treated as the distance. Next, we introduce the new measure of perturbation of one group of objects by another group of objects and then generate the description of each group of objects in the form of the classification rules to distinguish the considered groups. A practical illustration of the proposed approach is carried out for the task of grouping of text documents described by multisets.

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