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On Asymmetric Matching between Sets
Subtitle:Raport Badawczy = Research Report ; RB/35/2014
Creator:Krawczak, Maciej ; Szkatuła, Grażyna
Publisher:Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences
Place of publishing: Date issued/created: Description:[1],1-18 stron ; 21 cm ; Bibliografia s. 17-18
Subject and Keywords:Jaccard coefficient ; Sets’ perturbation ; Perturbacja zbiorów ; Tversky index ; Symbolic data analysis ; Indeks tverskego ; Analiza danych symbolicznych ; Sets' matching ; Dopasowanie zbiorów
Abstract:This paper proposes the new measure of remoteness between sets of nominal values. Instead of considering distance between two sets, the measures of perturbation of one set by another are introduced. The consideration is based on set-theoretic operations and the proposed measure describes changes of the second set after adding the first set to it, or vice versa. The measure of sets' perturbation returns a value from (0, 1], and it must be emphasized that this measure is not symmetric in general. The difference between 1 and the sum of these two measures of perturbation of a pair of sets can be understood as Jaecard's extended similarity measure. In this paper several mathematical properties of the measure of sets' perturbation are studied, and interpretation of proximity is explained by the comparison of selected measures.
Relation:Raport Badawczy = Research Report
Resource type: Detailed Resource Type: Source: Language: Language of abstract: Rights:Licencja Creative Commons Uznanie autorstwa 4.0
Terms of use:Zasób chroniony prawem autorskim. [CC BY 4.0 Międzynarodowe] Korzystanie dozwolone zgodnie z licencją Creative Commons Uznanie autorstwa 4.0, której pełne postanowienia dostępne są pod adresem: ; -
Digitizing institution:Instytut Badań Systemowych Polskiej Akademii Nauk
Original in:Biblioteka Instytutu Badań Systemowych PAN
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