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Tools for comparison of fuzzy sets

  1. NázovTools for comparison of fuzzy sets
    Aut.údajeVladimír Kobza
    Autor Kobza Vladimír 1988- (100%) UMBFP10 - Katedra matematiky
    Zdroj.dok. Acta Universitatis Matthiae Belii : series Mathematics, Vol. 30. Pp. 36-77. - Banská Bystrica : Vydavateľstvo Univerzity Mateja Bela - Belianum, 2022
    Kľúč.slová fuzzy množiny - fuzzy sets   miera divergencie   odlišnosti   entropia  
    Form.deskr.príspevky v zborníku - proceedings papers
    Jazyk dok.angličtina
    KrajinaSlovenská republika
    AnotáciaThe basic study of fuzzy sets theory was introduced by Lotfi Zadeh in 1965. Many authors investigated possibilities how two fuzzy sets can be compared and the most common kind of measures used in the mathematical literature are dissimilarity measures. The previous approach to the dissimilarities is too restrictive, while there exist many pairs of fuzzy sets, which are incomparable to each other with respect to inclusion ⊆. Therefore we need some new concept for measuring a difference between fuzzy sets so that it could be applied for arbitrary fuzzy sets. In order to overcome this problem the divergence measures as another kind of measures useful to compare two fuzzy sets have been introduced recently. The last condition in previous dissimilarity measures max{D(A,B),D(B,C)} ≤ D(A,B) has been replaced by the new one max{D(A∪C,B∪C),D(A∩C,B∩C)} ≤ D(A,B), where the fuzzy sets operations - union and intersection are defined by a triangular conorm S and its dual triangular norm T, respectively. In this paper we focus on the special class of so-called local divergences and their possible generalizations.
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    Kategória publikačnej činnosti AED
    Číslo archívnej kópie52846
    Katal.org.BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici
    Báza dátxpca - PUBLIKAČNÁ ČINNOSŤ
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