Axiomatizations of inconsistency indices for triads
- EconomicsAnn. Oper. Res.
The logically independent properties of triads are chosen and it is proved that they characterize, that is, uniquely determine the inconsistency ranking induced by most inconsistency indices that coincide on this restricted domain.
Inconsistency thresholds for incomplete pairwise comparison matrices
- Computer ScienceOmega
Extension of Saaty's inconsistency index to incomplete comparisons: Approximated thresholds
- Computer ScienceArXiv
The inconsistency of random matrices turns out to be the function of matrix size and the number of missing elements, with a nearly linear dependence in the case of the latter variable.
NEW PREFERENCE VIOLATION INDICES FOR THE CONDITION OF ORDER PRESERVATION
- Computer Science
The aim of this paper is to fill this gap and propose new preference violation indices for measuring violation of the condition of the order preservation, and it is shown that the proposed indices satisfy uniqueness, invariance under permutation, invariant under inversion of preferences and continuity axioms.
Efficiency of the principal eigenvector of some triple perturbed consistent matrices
- MathematicsEur. J. Oper. Res.
DYNAMIC THRESHOLDS OF GEOMETRIC CONSISTENCY INDEX ASSOCIATED WITH PAIRWISE COMPARISON MATRIX
- Computer ScienceTechnological and Economic Development of Economy
The induced dynamic thresholds of GCI are induced by combining hypothesis testing and random index, which vary with the order of the PCM, significance level and assessment level of decision maker, to explain different results obtained by approximate thresholds ofGCI and CR.
Efficient vectors for simple perturbed consistent matrices
- MathematicsInt. J. Approx. Reason.
Monotonicity in sharing the revenues from broadcasting sports leagues
- EconomicsEur. J. Oper. Res.
Strategic Manipulation in Group Decisions with Pairwise Comparisons: A Game Theoretical Perspective
- EconomicsEuropean Journal of Operational Research
SHOWING 1-10 OF 83 REFERENCES
Notes on discrepancy in the pairwise comparisons method
- Computer ScienceArXiv
Inefficient weights from pairwise comparison matrices with arbitrarily small inconsistency
- Computer Science, Economics
A class of pairwise comparison matrices with arbitrarily small inconsistency is provided such that the eigenvector method yields an internally inefficient weight vector.
The mathematical equivalence of the "spanning tree" and row geometric mean preference vectors and its implications for preference analysis
- Computer ScienceEur. J. Oper. Res.
A Scaling Method for Priorities in Hierarchical Structures
- Computer Science
Inferring Efficient Weights from Pairwise Comparison Matrices
- Computer Science, MathematicsMath. Methods Oper. Res.
A characterization of the set of efficient solutions is given, which enables us to assert that the least-logarithmic-squares solution is always efficient, whereas the (widely used) eigenvector solution is not, in some cases, efficient, thus its use in practice may be questionable.
On a proposal of Jensen for the analysis of ordinal pairwise preferences using Saaty's eigenvector scaling method
Abstract In 1977, Saaty proposed a scaling method for priorities based on the normalized, positive eigenvector corresponding to the largest eigenvalue of a matrix of paired comparisons. Originally…
The limit of inconsistency reduction in pairwise comparisons
- Computer ScienceInt. J. Appl. Math. Comput. Sci.
It is demonstrated that the vector of geometric means and the right principal eigenvector are linearly independent for the pairwise comparisons matrix size greater than three, although both vectors are identical for a consistent PC matrix of any size.
A common framework for deriving preference values from pairwise comparison matrices
- Computer ScienceComput. Oper. Res.
On some useful properties of the Perron eigenvalue of a positive reciprocal matrix in the context of the analytic hierarchy process
Axiomatic properties of inconsistency indices for pairwise comparisons
- Economics, Computer ScienceJ. Oper. Res. Soc.
Five axioms aimed at characterizing inconsistency indices are presented and it is proved that some of the indices proposed in the literature satisfy these axiomatic, whereas others do not, and therefore, in this view, they may fail to correctly evaluate inconsistency.