ISSN 2071-8594

Russian academy of sciences

Editor-in-Chief

Gennady Osipov

A. B. Petrovsky Shortening Dimensionality of Attribute Space: Method SOCRATE

Abstract.

A new method SOCRATES (ShOrtening Criteria and ATtributES) to reduce the dimensionality of attribute space is described. In the method, a lot of initial numerical and/or verbal characteristics of objects are aggregated into a single integral index or several composite indicators with small scales of qualitative estimates. Multi-attribute objects are represented as multisets of object properties. Aggregating indicators includes various methods for a transformation of attributes and their scales. Reducing the number of attributes and shortening their scales allows us to simplify the solution of applied problems, in particular, problems of multiple criteria choice, and explain the obtained results.

Keywords:

multi-attribute objects, multisets, attribute space, dimensionality reduction, aggregation of attributes, composite indicator, multiple criteria choice.

PP. 63-77.

DOI 10.14357/20718594200205

References

1. Ayvazyan S.A., Bukhshtaber V.M., Enyukov I.S., Meshalkin L.D. Prikladnaya statistika. Klassifikatsiya i snizheniye razmernosti [Applied statistics. Classification and reduction of dimension]. M.: Finansy i statistika, 1989.
2. Glotov V.A., Pavel’yev V.V. Vektornaya stratifikatsiya [Vector stratification]. M.: Nauka, 1984.
3. Larichev O.I. Nauka i iskusstvo prinyatiya resheniy [Science and art of decision making]. M.: Nauka, 1979.
4. Larichev O.I. Verbal’niy analiz resheniy [Verbal decision analysis]. M.: Nauka, 2006.
5. Larichev O.I., Moshkovich E.M. Kachestvennye metody
prinyatiya resheniy. Verbal’niy analiz resheniy [Qualitative decision-making methods. Verbal decision analysis]. M.: Nauka, Fizmatlit, 1996.
6. Petrovsky A.B. Mul’timnozhestva kak model’ predstavleniya mnogopriznakovykh ob”yektov v prinyatii resheniy i raspoznavanii obrazov [Multisets as a model for representing multi-attribute objects in decision-making and pattern recognition] // Iskusstvenniy intellect [Artificial Intelligence], 2002. No. 2. P. 236-243.
7. Petrovsky A.B. Teoriya prinyatiya resheniy [Decision theory]. M.: Izdatel’skiy tsentr “Akademiya”, 2009.
8. Petrovsky A.B. Pokazateli skhodstva i razlichiya mnogopriznakovykh ob”yektov v metricheskikh pro-stranstvakh mnozhestv i mul’timnozhestv [Similarity and differences indices of multi-attribute objects in metric spaces of sets and multisets] // Iskusstvenniy intellekt i prinyatie resheniy [Artificial Intelligence and Decision Making], 2017. No. 4. P. 78-94.
9. Petrovsky A.B. Teoriya izmerimykh mnozhestv i mul’timnozhestv [Theory of measurable sets and multisets]. M.: Nauka, 2018.
10. Petrovsky A.B. Gruppovoy verbal’niy analiz resheniy [Group verbal decision analysis]. M.: Nauka, 2019.
11. Petrovsky A.B., Lobanov V.N. Multi-criteria choice in the attribute space of large dimension: multi-method technol-ogy PAKS-M // Scientific and Technical Information Pro-cessing, 2015. V. 42. No 5. P. 76-86.
12. Petrovsky A.B., Royzenzon G.V. Mnogokriterial’niy vybor s umen’sheniyem razmernosti prostranstva
priznakov: mnogoetapnaya tekhnologiya PAKS [Multi-criteria choice with reducing dimension of attribute space: the multi-stage technology PAKS] // Iskusstvenniy intellekt i prinyatie resheniy [Artificial Intelligence and Decision Making], 2012. No. 4. P. 88-103.
13. Petrovsky A.B., Royzenson G.V. Multi-stage technique ‘PAKS’ for multiple criteria decision aiding // Internation-al Journal of Information Technology and Decision Making, 2013. V. 12. No 5. P. 1055-1071.
14. Hartigan J.A. Clustering algoritms. New York: Wiley, 1975.
15. Kahneman D., Slovik P., Tverski A. Decision-making in uncertainty: heuristics and biases. Cambridge: Cambridge University Press, 1982.
16. Samet H. Foundation of multidimensional and metric data structures. Boston: Elsevier, 2006.