arXiv subjects

Y. Yayli

Publications and source records attributed to Y. Yayli.

3 recordsLinked to original sources

arXiv2021

Pairwise Comparisons Matrix Decomposition into Approximation and Orthogonal Component Using Lie Theory

This paper examines the use of Lie group and Lie Algebra theory to construct the geometry of pairwise comparisons matrices. The Hadamard product (also known as coordinatewise, coordinate-wise, elementwise, or element-wise product) is analyzed in the context of inconsistency and inaccuracy by the decomposition method. The two designed components are the approximation and orthogonal components. The decomposition constitutes the theoretical foundation for the multiplicative pairwise comparisons. Keywords: approximate reasoning, subjectivity, inconsistency, consistency-driven, pairwise comparison, matrix Lie group, Lie algebra, approximation, orthogonality, decomposition.

math.GM↗

arXiv2020

On the use of group theory to generalize elements of pairwise comparisons matrix: a cautionary note

This paper examines the constricted use of group theory in the studies of pairwise comparisons. The presented approach is based on the application of the famous Levi Theorems of 1942 and 1943 for orderable groups. The theoretical foundation for multiplicative (ratio) pairwise comparisons has been provided. Counterexamples have been provided to support the theory. In our opinion, the scientific community must be made aware of the limitations of using the group theory in pairwise comparisons. Groups, which are not torsion free, cannot be used for ratios by Levi's theorems.

math.HO↗

arXiv2012

Slant helices in three dimensional lie groups

In this paper, we define slant helices in three dimensional Lie Groups with a bi-invariant metric and obtain a characterization of slant helices. Moreover, we give some relations between slant helices and their involutes, spherical images.

math.DG↗