Abstract: This paper studies the multiple attribute group decision making problems, in which the decision makers (DMs) have multiplicative preference information on alternatives. We first make the decision information uniform by using a transformation formula and introduce some linear deviation elements, and then establish a constrained optimization model. Based the model, an approach is develo...

A non-linear digital filter is presented in this paper: this filter aims at extending the concept of scalar rank-ordering in the case of multichannel images. The filter is based on two steps: 1) a transformation from a p-dimensional steps to a onedimensional space by means of a space filling curve; 2) a scalar median filtering step. Results which demonstrate the advantages and the good restorat...

We reexamine and continue the work of J. Vosmanskyý [23] on the concept of continuous ranking of zeros of certain special functions from the point of view of the transformation theory of second order linear differential equations. This leads to results on higher monotonicity of such zeros with respect to the rank and to the evaluation of some definite integrals. The applications are to Airy, Be...

in his paper mentioned in the title, which appears in the same issue of this journal, mehdi radjabalipour derives the cyclic decomposition of an algebraic linear transformation. a more general structure theory for linear transformations appears in irving kaplansky's lovely 1954 book on infinite abelian groups. we present a translation of kaplansky's results for abelian groups into the...

The rounding-error analysis of Gaussian elimination shows that the method is stable only when the elements of the matrix do not grow excessively in the course of the reduction. Usually such growth is prevented by interchanging rows and columns of the matrix so that the pivot element is acceptably large. In this paper firstly we introduce the Boosting LU factorization method based on a rank one ...

In this paper, we establish new bounds for restricted isometry constants (RIC) in low-rank matrix recovery. Let A be a linear transformation from Rm×n into Rp, and r the rank of recovered matrix X ∈ Rm×n. Our main result is that if the condition on RIC satisfies δ2r+k + 2( r k ) δmax{r+ 3 2 k,2k} < 1 for a given positive integer k ≤ m − r, then r-rank matrix can be exactly recovered via nuclear...

We study the behavior of crystals that undergo martensitic transformations. On cooling, the high-temperature phase (austenite) transforms to the martensite phase changing its crystalline symmetry. The lower crystalline symmetry of the martensite gives rise to several variants of martensite. Each variant has an associated transformation strain. These variants accommodate themselves (according to...