Object structure


On Asymmetric Matching between Sets


Raport Badawczy = Research Report ; RB/62/2013


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:

Sets of nominal values ; Tversky index ; Symbolic data analysis ; Measure of proximity ; Zbiory wartości nominalnych ; Indeks tverskego ; Analiza danych symbolicznych ; Miary bliskości


Defining a good measure of proximity or similarity (or remoteness or dissimilarity) be­tween objects is crucial importance in theories of knowledge. Usually each object is represented as a point in some coordinate space so the metric distance between points reflects similarities be­tween the respective objects. In general, the space is assumed to be Euclidean. A metric distance is a function which assigns a nonnegative number, called their distance to every pair of objects. The assumption of symmetry underlies essentially all theoretical treatments of similarity. Tversky (1977) provides empirical evidence of asymmetric similarities and argues that similarity should not be treated as a symmetric relation. Tversky considered objects as sets of features instead of geo­metric points in a metric space. In this paper we propose the measure of remoteness between sets of nominal values based on Tversky’s similarity measures. Instead of considering distance between two sets, we introduce a definition of measure of perturbation of one set by another set, the con­sideration is based on set-theoretic operations. The measure describes changes of the first set after adding the second set. The measure of sets’ perturbation returns a value from [0, 1], where I is in­terpreted as highest level of perturbation, while 0 denotes the lowest level of perturbation. It is in­teresting that this measure is not symmetric.


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

Original in:

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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