Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with 13 some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic submeasures and more general semi-copula-based probabilistic submeasures. Some algebraic properties of classes of such submeasures are also studied. 15 © 2012 Else...

Classification algorithms based on different forms of support vector machines (SVMs) for dealing with interval-valued training data are proposed in the paper. L2-norm and L∞-norm SVMs are used for constructing the algorithms. The main idea allowing us to represent the complex optimization problems as a set of simple linear or quadratic programming problems is to approximate the Gaussian kernel ...

In this paper, we propose a generalized concept of openness and closedness with respect to arbitrary fuzzy relations, along with appropriate opening and closure operators. We will show that this framework includes the existing concept defined for fuzzy preorderings as well as the triangular norm-based approach to fuzzy mathematical morphology.

This short note provides an improvement on a recent result of Vecchio on a norm bound for the inverse of a lower triangular Toeplitz matrix with nonnegative entries. A sharper asymptotic bound is obtained as well as a version for matrices of finite order. The results are shown to be nearly best possible under the given constraints. 1. Introduction. This paper provides an improvement on a recent...

For any interpolatory ternary subdivision scheme with two-ring stencils for a regular triangular or quadrilateral mesh, in this paper we show that the critical Hölder smoothness exponent of its basis function cannot exceed log3 11(≈ 2.18266), where the critical Hölder smoothness exponent of a function f : R2 7→ R is defined to be ν∞(f) := sup{ν : f ∈ Lip ν}. On the other hand, for both regular ...

The space of upper triangular matrices with Hilbert{Schmidt norm can be viewed as a nite dimensional analogue of the Hardy space H2 of the unit disk when one introduces the adequate notion of \point" evaluation. A bitangential interpolation problem in this setting is studied. The description of all solution in terms of Beurling{Lax representation is given.

Let A and B be bounded linear operators acting on a Hilbert space H. It is shown that the triangular inequality serves as the ultimate estimate of the upper norm bound for the sum of two operators in the sense that sup{‖U∗AU + V ∗BV ‖ : U and V are unitaries} = min{‖A+ μI‖+ ‖B − μI‖ : μ ∈ C}. Consequences of the result related to spectral sets, the von Neumann inequality, and normal dilations a...

For any interpolatory ternary subdivision scheme with two-ring stencils for a regular triangular or quadrilateral mesh, we show that the critical Hölder smoothness exponent of its basis function cannot exceed log3 11(≈ 2.18266), where the critical Hölder smoothness exponent of a function f : R2 → R is defined to be ν∞(f) := sup{ν : f ∈ Lip ν}. On the other hand, for both regular triangular and ...

In this paper, a multigrid algorithm is developed for the third-order accurate solution of Cauchy–Riemann equations discretized in the cell-vertex finite-volume fashion: the solution values stored at vertices and the residuals defined on triangular elements. On triangular grids, this results in a highly overdetermined problem, and therefore we consider its solution that minimizes the residuals ...