相关论文: Efficient vectors for block perturbed consistent m…

In prioritization schemes, based on pairwise comparisons, such as the Analytical Hierarchy Process, it is necessary to extract a cardinal ranking vector from a reciprocal matrix that is unlikely to be consistent. It is natural to choose…

In decision making a weight vector is often obtained from a reciprocal matrix A that gives pairwise comparisons among n alternatives. The weight vector should be chosen from among efficient vectors for A. Since the reciprocal matrix is…

Efficient vectors are the natural set from which to choose a cardinal ranking vector for a pairwise comparison matrix. Such vectors are the key to certain business project selection models. Many ways to construct specific efficient vectors…

For a given reciprocal matrix A, we give a union of matrix intervals in which any consistent matrix obtained from an efficient vector for A lies, and, conversely, any consistent matrix in this union comes from an efficient vector for A. The…

We focus upon the relationship between Hamiltonian cycle products and efficient vectors for a reciprocal matrix $A$, to more deeply understand the latter. This facilitates a new description of the set of efficient vectors (as a union of…

Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the…

The Analytic Hierarchy Process (AHP) is a much discussed method in ranking business alternatives based on empirical and judgemental information. We focus here upon the key component of deducing efficient vectors for a reciprocal matrix of…

Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and…

Efficiency is a core concept of multi-objective optimization problems and multi-attribute decision making. In the case of pairwise comparison matrices a weight vector is called efficient if the approximations of the elements of the pairwise…

In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…

Pairwise comparison matrices and the weight vectors obtained from them are important concepts in multi-criteria decision making. A weight vector calculated from a pairwise comparison matrix is called Pareto efficient if the approximation of…

In models using pair-wise (ratio) comparisons among alternatives, a cardinal ranking vector should be deduced from a reciprocal matrix. The right Perron eigenvector (RP) was traditionally used, though several other options have emerged. We…

Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper…

Improperly efficient solutions in the sense of Geoffrion in linear fractional vector optimization problems with unbounded constraint sets are studied in this paper. We give two sets of conditions which assure that all the efficient…

We present an efficient algorithm for the application of sequences of planar rotations to a matrix. Applying such sequences efficiently is important in many numerical linear algebra algorithms for eigenvalues. Our algorithm is novel in…

We present two criteria for checking approximate proper efficiency in vector optimization problems with the ordering cone being a nonnegative orthant. Although the criteria can be established by Benson's approach [H.P. Benson, \textit{An…

This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is…

Interpreting the decisions of complex computer vision models is crucial to establish trust and accountability, especially in safety-critical domains. An established approach to interpretability is generating visual attribution maps that…

Strict linear feasibility or linear separation is usually tackled using efficient approximation/stochastic algorithms (that may even run in sub-linear times in expectation). However, today state of the art for solving…