Object structure


On Interaction between Groups of Objects – Multiset Approach


Raport Badawczy = Research Report ; RB/63/2013


Krawczak, Maciej. Autor ; Szkatuła, Grażyna Maria. Autor


Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

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16 pages ; 21 cm ; Bibliography p. 16

Subject and Keywords:

Multisets ; Nominal attributes ; Atrybuty nominalne ; Symbolic data analysis ; Measure of proximity ; Analiza danych symbolicznych ; Miary bliskości ; Groups of objects ; Grupy obiektów ; Multizbiory


Properties of objects can be specified by a set of attributes which values can be symbolic. Defining a good measure of proximity (or remoteness) between objects is crucial importance in applied research like data mining or machine learning. Much attention has been devoted to continuous attributes while little attention to nominal attributes which seems to be much more difficult to handle. The proposed approach is based on the theory of multisets. In the paper we defined a group of objects with nominal description as a AT-tuple of multisets (i.e., an ordered collection of multisets). There are introduced the following definitions: perturbation of multisets’ for each attribute and a measure of groups’ perturbations. The measure of perturba­tion is assumed to return a value from [0, 1], where 1 is interpreted as the most level of pertur­bation, while 0 is the lowest level of perturbation. In general these two measures are different, asymmetrical, so they should not be considered as the distance between the groups.


Raport Badawczy = Research Report

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Creative Commons Attribution BY 4.0 license

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Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -

Digitizing institution:

Systems Research Institute of the Polish Academy of Sciences

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Library of Systems Research Institute PAS

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.



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