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Tools for comparison of fuzzy sets

  1. TitleTools for comparison of fuzzy sets
    Author infoVladimír Kobza
    Author Kobza Vladimír 1988- (100%) UMBFP10 - Katedra matematiky
    Source document Acta Universitatis Matthiae Belii : series Mathematics, Vol. 30. Pp. 36-77. - Banská Bystrica : Vydavateľstvo Univerzity Mateja Bela - Belianum, 2022
    Keywords fuzzy množiny - fuzzy sets   miera divergencie   odlišnosti   entropia  
    Form. Descr.príspevky v zborníku - proceedings papers
    LanguageEnglish
    CountrySlovak Republic
    AnnotationThe 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 The last condition in previous dissimilarity measures max{D(A,B),D(B,C)} ≤ D(A,B) has been replaced by the new one max{D(A∪C,B∪C),D(A∩C,B∩C)} ≤ D(A,B), where the fuzzy sets operations - union and intersection are defined by a triangular conorm S and its dual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.
    URLLink na plný text
    Public work category AED
    No. of Archival Copy52846
    Catal.org.BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici
    Databasexpca - PUBLIKAČNÁ ČINNOSŤ
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