Recently, Jeĺınek derived that the number of self-dual interval orders of reduced size n is twice the number of row-Fishburn matrices of size n by using generating functions. In this paper, we present a bijective proof of this relation by establishing a bijection between two variations of upper-triangular matrices of nonnegative integers. Using the bijection, we provide a combinatorial proof of...

The behaviour of a discrete event dynamic system is often conveniently described using a matrix algebra with operations max and plus Such a system moves forward in regular steps of length equal to the eigenvalue of the system matrix if it is set to operation at time instants corresponding to one of its eigenvectors However due to imprecise measurements it is often unappropriate to use exact mat...

Stability analysis of linear circuits and systems under interval parameter uncertainties can be equated to estimating the eigenvalues of interval matrices. In this paper, the problem of determining outer bounds on the ranges of the real eigenvalues is considered. A method for computing such bounds is suggested. It consist of setting up and solving a system of n nonlinear equations, n being the ...

Pairwise comparison matrices are increasingly used in settings where some pairs missing. However, there exist few inconsistency indices for similar incomplete data sets and no reasonable measure has an associated threshold. This paper generalises the famous rule of thumb acceptable level inconsistency, proposed by Saaty, to pairwise matrices. The extension is based on choosing missing elements ...

Several verifiable sufficient conditions for regularity and singularity of interval matrices are given. As an application, a verifiable sufficient condition is derived for an interval matrix to have all eigenvalues real.

The computation of an enclosure for the solution of a sparse set of linear equations Ax = b with a thin matrix A and an interval right hand side b is considered. Gaussian elimination works well when the matrix is an M-matrix, but fails when the matrix is a general matrix. This paper illustrates how, for sparse matrices, an ordering intended to reduce the height of the elimination tree (and thus...

As the main result of this paper it is proved that an interval matrix [Ac −∆, Ac +∆] is strongly regular if and only if the matrix inequality M(I − |I − RAc| − |R|∆) ≥ I has a solution, where M and R are real square matrices and M is nonnegative. Several consequences of this result are drawn.