minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. also related inequalities to minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. several examples are given to illustrate the validity of theorems. some results on chebyshev and minkowski type inequalities are obtained.

Let a function f 2 L p ?1; 1], 0 < p 1 have 1 r < 1 changes of monotonicity. For all suuciently large n, we construct algebraic polynomials p n of degree n which are comonotone with f, and such that kf ? p n k Lp?1; 1] C(r)! ' 2 (f; n ?1) p , where ! ' 2 (f; n ?1) p denotes the Ditzian-Totik second modulus of smoothness in L p metric.

We estimate the degree of comonotone polynomial approximation of continuous functions f , on [−1,1], that change monotonicity s ≥ 1 times in the interval, when the degree of unconstrained polynomial approximation En(f ) ≤ n−α , n ≥ 1. We ask whether the degree of comonotone approximation is necessarily ≤ c(α, s)n−α , n ≥ 1, and if not, what can be said. It turns out that for each s ≥ 1, there i...

Considering the space of all non–negative measurable functions F(X,A) linked to a fixed measurable space (X,A), the Lebesgue integral can be seen as an additive, continuous from below functional L on F(X,A), related to a measure m : A → [0,∞] given by m(A) = L(1A). We introduce several other integrals which can be seen as special functionals on F(X,A). For example, the Choquet integral [7] is a...

The paper extends author’s previous works on a probability/possibility transformation based on a maximum specificity principle to the case of the sum of two identical unimodal symmetric random variables. This transformation requires the knowledge of the dependency relationship between the two added variables. In fact, the comonotone case is closely related to the Zadeh’s extension principle. It...

This paper studies efficient risk-sharing rules for the concave dominance order. For a univariate risk, it follows from a comonotone dominance principle, due to Landsberger and Meilijson [27], that efficiency is characterized by a comonotonicity condition. The goal of the paper is to generalize the comonotone dominance principle as well as the equivalence between efficiency and comonotonicity t...