Andrea Stupnanová

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We study the following problem: If ξ1, ξ2, . . . are fuzzy numbers with modal values M1, M2, . . . , then what is the strongest t-norm for which lim n→∞ Nes ( mn − ≤ ξ1 + · · · + ξn n ≤ mn + ) = 1, for any > 0, where mn = M1 + · · · + Mn n , the arithmetic mean ξ1 + · · · + ξn n is defined via sup-t-norm convolution and Nes denotes necessity.
OWA operators can be seen as symmetrized weighted arithmetic means, as Choquet integrals with respect to symmetric measures, or as comonotone additive functionals. Following these three different looks on OWA’s, we discuss several already known generalizations of OWA operators, including GOWA, IOWA, OMA operators, as well as we propose new types of such(More)
A hierarchical family of integrals based on a fixed copula is introduced and discussed. The extremal members of this family correspond to the inner and outer extension of integrals of basic functions, the copula under consideration being the corresponding multiplication. The limits of the members of the family are just copulabased universal integrals as(More)
Three different types of universal integral based on level dependent capacities are introduced and discussed. Two extremal types are based on Caratheodory’s idea of inner and outer measures, while the third type is introduced for copula-based universal integrals only. Keywords—Choquet integral, Copula, Fuzzy measure, Level dependent capacities, Sugeno(More)
The stability of discrete universal integrals based on copulas is discussed and examined, both with respect to the norms L1 (Lipschitz stability) and L∞ (Chebyshev stability). Each of these integrals is shown to be 1-Lipschitz. Exactly the discrete universal integrals based on a copula which is stochastically increasing in its first coordinate turn out to(More)