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Pseudo-integral of the interval-valued functions based on the pseudo-operations has been introduced. Some basic properties, as well as, some limit properties of the pseudo-integral of interval-valued functions have been investigated.
We shall consider generated pseudo-operations of the following form: x⊕ y = g(−1) (g(x) + g(y)) , x ̄ y = g(−1) (g(x)g(y)) , where g is a positive strictly monotone generating function and g(−1) is its pseudo-inverse. Using this type of pseudo-operations, the Riemann-Stieltjes type integral will be introduced and investigated.
In this paper the classical Portmanteau theorem which provides equivalent conditions of weak convergence of sequence of probability measures is extended on the space of the sequence of probability measures induced by random sets.
In this paper, the portmanteau theorem which provides the equivalent conditions of the weak convergence of a sequence of probability measures is extended on the sequence of distorted probabilities.
In this paper, the definitions of central g-moments of the order n, n ϵN for random variables and g-expectation for a random variable are given. With the suitable choice of the generator g, and choosing different values for n, it is possible to calculate central g-moments of the order n even for a random variable f for which neither expectation nor… (More)
In this paper asymmetric and symmetric separable aggregation functions are discussed. Some properties of separable aggregation functions as comonotone ©-additivity, symmetry, etc., are investigated.
The aim of this paper is to study sustainability of the pseudo-linear superposition principle, that is, of the nonlinear superposition principle (NLSP) observed in the pseudo-analysis' framework and to discuss some possible extensions.
A natural generalization of (classical) measures are monotone set valued functions, the so called non-additive measures. Further generalization of measures are intervalvalued measures and interval-valued non-additive measures. Since interval-valued ⊕-measures, as a special case of intervalvalued non-additive measures, have been extensively applied in the… (More)