Tools for comparison of fuzzy sets

Kobza, Vladimír, 1988- Tools for comparison of fuzzy sets / Vladimír Kobza. -- The 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 The last condition in previous dissimilarity measures max{D(A,B),D(B,C)} ≤ D(A,B) has been replaced by the new one max{D(A∪C,B∪C),D(A∩C,B∩C)} ≤ D(A,B), where the fuzzy sets operations - union and intersection are defined by a triangular conorm S and its dual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.

In Acta Universitatis Matthiae Belii : series Mathematics. -- Banská Bystrica : Vydavateľstvo Univerzity Mateja Bela - Belianum, 2022. -- 77 p.. -- ISSN 1338-7111. -- Pp. 36-77

1. fuzzy množiny 2. miera divergencie 3. odlišnosti 4. entropia 5. príspevky v zborníku

I. Acta Universitatis Matthiae Belii : series Mathematics. -- Pp. 36-77
BB301