Constructive Consistent Approximations in Pairwise Comparisons

Abstract

In this paper we investigate groups which admit the existence of weighted consistent approximations for pairwise comparisons matrices. These approximations are defined by extending the classical matrix projection for R + to abstract weighted projections on the non-linear sets of transitive group-valued matrices. It is of interest that all of them are represented by general explicit formulae dependent on an abstract logarithmic function. This general approach is applied to the groups Z p and F 2 m m which are of fundamental importance in cryptography. Finally, we use our unified mathematical model of pairwise comparisons for continuous one-parameter unitary groups, which play a fundamental role in physics.

REDUCE – A Python Module for Reducing Inconsistency in Pairwise Comparison Matrices

“…The appearance of the free pairwise comparison inconsistency reduction library with tools presented in this paper, and the fact that these applications are able to effectively count the most important matrix inconsistency indices, may enable small and medium-sized enterprises to take advantage of the capabilities of multi-criteria decision-making methods -until now they have had to use either cumbersome and time-consuming spreadsheets or paid software such as Expert Choice [43] to do so. Implementing decision-making methods is also an important part of the transition to Industry 4.0 [44], which, from the perspective of today's applications, has already had tangible effects in industrial applications as well [45,46]. From a scientific point of view, the reduction of inconsistency in the elements of a pairwise comparison matrix is an important element of research in fuzzy logic [14], preference programming [15], or constructive consistent approximations [45].…”

“…Implementing decision-making methods is also an important part of the transition to Industry 4.0 [44], which, from the perspective of today's applications, has already had tangible effects in industrial applications as well [45,46]. From a scientific point of view, the reduction of inconsistency in the elements of a pairwise comparison matrix is an important element of research in fuzzy logic [14], preference programming [15], or constructive consistent approximations [45].…”