An orthogonal basis for computing a consistent approximation to a pairwise comparisons matrix

An Algorithm for the Optimal Consistent Approximation to a Pairwise Comparisons Matrix by Orthogonal Projections

The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comaprisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric. Orthogonal basis is introduced in the vector space. The orthogonal projection of the transformed matrix onto the space formed by the images of consistent matrices is ...

On inconsistency of a pairwise comparison matrix

A Framework for Linear Transform Approximation Using Orthogonal Basis Projection

This paper aims to develop a novel framework to systematically trade-off computational complexity with output distortion in linear multimedia transforms, in an optimal manner. The problem is important in real-time systems where the computational resources available are time-dependent. We solve the real-time adaptation problem by developing an approximate transform framework. There are three key...

On the Optimal Consistent Approximation to Pairwise Comparison Matrices

Consistency retrieval from a biased relative preference table is an imperative task in decision theory This paper considers the least squares approximation of a pairwise comparison matrix by consistent matrices It is observed that the highly nonlinear manifold of consistent matrices can be changed into a linear subspace by the component wise logarithmic transformation A rst order optimality con...

‏‎a 10-bit 50-ms/s parallel successive-approximation analog-to-digital converter‎‏

‏‎applications such as high definition viedeo reproduction, portable computers, wireless, and multimedia demand, and ever-increasing need for ligh-frequency high-resolution and low-power analog-to-digital converters. flash, two-step flash, and pipeline convertors are fast but consume large amount of power and require large area. to overcome these problems, successive approximation converter blo...