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Proximity of Multi-attribute Objects in Multiset Metric Spaces

  • Alexey B. Petrovsky
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 874)

Abstract

The paper considers new classes of metric spaces of finite, bounded, measurable multisets. We discuss the possibilities to use new types of metrics, pseudometrics, quasimetrics, symmetrics for estimating proximity of objects with many numerical and/or verbal attributes that are represented as multisets. New indexes of similarity and dissimilarity of multi-attribute objects are used in new methods of group multiple criteria decision making.

Keywords

Multiset Space of multisets Metric Pseudometric Quasimetric Symmetric Multi-attribute objects Similarity and dissimilarity of objects Group multiple criteria decision making Group verbal decision analysis 

Notes

Acknowledgments

This work was supported by the Russian Foundation for Basic Research (projects 16-29-12864, 17-07-00512, 17-29-07021, 18-07-00132, 18-07-00280).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Federal Research Center “Informatics and Control”, Russian Academy of SciencesMoscowRussia
  2. 2.Belgorod State National Research UniversityBelgorodRussia
  3. 3.V.G. Shukhov Belgorod State Technological UniversityBelgorodRussia
  4. 4.Volgograd State Technical UniversityVolgogradRussia

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