Abstract
A new approach is considered to the group classification of objects that are described by many qualitative and/or quantitative attributes and can exist in many versions. New techniques are described for the aggregation of multi-attribute objects and the properties of the generated classes. Clustering and sorting methods are based on the theory of multiset metric spaces.
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References
Arlazarov, V.L., Loginov, A.S., and Slavin, O.A., Characteristics of Programs for Optical Recognition of Text, Programmirovaniye, 2002, no. 3, pp. 45–63.
Deza, M.M. and Laurent, M., Geometry of Cuts and Metrics. Algorithms and Combinatorics, vol. 15, Berlin: Springer-Verlag, 1997.
Komarova, N.A. and Petrovsky, A.B., Method for Consistent Group Classification of Multi-attribute Objects. Podderzhka Prinyatiya Resheniy (Decision-Making Aid), Proc. of the Institute for System Analysis, Russ. Acad. Sci., vol. 35, pp. 19–32, Moscow: LKI, 2008.
Knut, D.E., The Art of Computer Programming, vol. 2, Seminumerical Algorithms, Reading, MA: Addison-Wesley, 1997.
Larichev, O.I., Verbal’niy Analiz Resheniy (Verbal Decision Analysis), Moscow: Nauka, 2006.
Larichev, O.I., Prokhorov, A.S., Petrovsky, A.B., Sternin, M.Yu., and Shepelev, G.I., Experience of Planning Fundamental Research on a Competitive Basis, Vestn. Akad. Nauk SSSR, 1989, no. 7, pp. 51–61.
Petrovsky, A.B., Prostranstva mnozhestv i multimnozhestv (Spaces of Sets and Multisets), Moscow: Editorial URSS, 2003.
Petrovsky, A.B., Cluster Analysis of Objects with Contradictory Properties, Proc. of the 10 National Conference on Artificial Intelligence with International Participation (AIC-2006), vol. 3, pp. 755–764, Moscow: Fizmatlit, 2006.
Petrovsky, A.B., Tikhonov, I.P., Balyshev, A.V., and Komarova, N.A., Drawing up Consistent Group Rules for Competitive Selection of Research Projects, Proc. of the Third International Conference “Systems Analysis and Information Technologies, pp. 337–348, Moscow: PoliPrintService, 2009.
Anderberg, M.R., Cluster Analysis for Applications, New York: Academic Press, 1973.
Blizard, W., Multiset Theory, Notre Dame Journal of Formal Logic, 1989, vol. 30, no. 1, pp. 36–66.
Doumpos, M. and Zopounidis, C., Multicriteria Decision Aid Classification Methods, Dordrecht: Kluwer Academic Publishers, 2002.
Furems, E., Knowledge-Based Multi-attribute Classification Problems Structuring., Ruan, D., Montero, I., Lu, J., Martinez, L., D’Hondt, P., and Kerre, E., Eds., Computational Intelligence in Decision and Control, pp. 465–470, Singapore: World Scientific Publisher, 2008.
Greco, S., Matarazzo, B., and Slowinski, R., Rough Sets Methodology for Sorting Problems in Presence of Multiple Attributes and Criteria, European Journal of Operational Research, 2002, vol. 138, no. 2, pp. 247–259.
Hartigan, J.A., Clustering Algoritms, New York: Wiley, 1975.
Hwang, C.L. and Lin, M.J., Group Decision Making under Multiple Criteria, Berlin: Springer-Verlag, 1987.
Koksalan, M. and Ulu, C., An Interactive Approach for Placing Alternatives in Preference Classes, European Journal of Operational Research, 2003, vol. 144, no. 2, pp. 429–439.
Larichev, O.I. and Olson, D.L., Multiple Criteria Analysis in Strategic Siting Problems, Boston: Kluwer Academic Publishers, 2001.
Miyamoto, S., Cluster Analysis as a Tool of Interpretation of Complex Systems, Working Paper WP-87-41, Laxenburg, Austria: IIASA, 1987.
Petrovsky, A.B., Structuring Techniques in Multiset Spaces, Fandel, G., and Gal, T. Eds., Multiple Criteria Decision Making, pp. 174–184, Berlin: Springer-Verlag, 1997.
Petrovsky, A.B., Multi-attribute Sorting of Qualitative Objects in Multiset Spaces, Koksalan, M., and Zionts, S., Eds., Multiple Criteria Decision Making in the New Millenium, pp. 124–131, Berlin: Springer-Verlag, 2001.
Petrovsky, A.B., Multi-attribute Classification of Credit Cardholders: Multiset Approach, International Journal of Management and Decision Making, 2006, vol. 7, no. 2/3, pp. 166–179.
Roubens, M., Ordinal Multi-attribute Sorting and Ordering in the Presence of Interacting Points of View., Bouyssou, D., Jacquet-Lagreze, E., Peray, P., Slowinski, R., Vanderpooten, D., and Vincke, P., Eds., Aiding Decisions with Multiple Criteria: Essays in Honor of Bernard Roy, pp. 229–246, Dordrecht: Kluwer Academic Publishers, 2001.
Roy, B., Multicriteria Methodology for Decision Aiding, Dordrecht: Kluwer Academic Publishers, 1996.
Roy, B. and Bouyssou, D., Aide Multicritère à la Décision; Méthodes et Cas, Paris: Economica, 1993.
Saaty, T., Multicriteria Decision Making: The Analytic Hierarchy Process, Pittsburgh: RWS Publications, 1990.
Vincke, P., Multicriteria Decision Aid, Chichester: Wiley, 1992.
Yager, R.R., On the Theory of Bags, International Journal of General Systems, 1986, vol. 13, pp. 23–37.
Zadeh, L.A., From Computing with Numbers to Computing with Words — From Manipulation of Measurements to Manipulation of Perceptions, IEEE Trans. Circuits and Systems, 1999, vol. 45, no. 1, pp. 105–119.
Additional information
Original Russian Text © A.B. Petrovsky, 2009, published in Iskusstvennyi Intellekt i Prinyatie Reshenii, 2009, No. 3, pp. 3–14.
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Petrovsky, A.B. Methods for the group classification of multi-attribute objects (part 1). Sci. Tech.Inf. Proc. 37, 346–356 (2010). https://doi.org/10.3103/S0147688210050102
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DOI: https://doi.org/10.3103/S0147688210050102