The limit of inconsistency reduction in pairwise comparisons
نویسندگان
چکیده
منابع مشابه
On the Convergence of the Pairwise Comparisons Inconsistency Reduction Process
This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction transforms an inconsistent pairwise comparisons (PC) matrix into a consistent PC matrix which is generated by the geometric means of rows of a given inconsistent PC matrix. The distance-based inconsistency indicator was de...
متن کاملOn distance-based inconsistency reduction algorithms for pairwise comparisons
One of the major challenges for collective intelligence is inconsistency, which is unavoidable whenever subjective assessments are involved. Pairwise comparisons allow one to represent such subjective assessments and to process them by analyzing, quantifying and identifying the inconsistencies. We propose using smaller scales for pairwise comparisons and provide mathematical and practical justi...
متن کاملOn Inconsistency Indices and Inconsistency Axioms in Pairwise Comparisons
Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several inconsistency indices were proposed as an alternative to Saaty’s inconsistency index and inconsistency ratio for reciprocal pairwise comparisons matrices. This paper aim...
متن کاملAxiomatization of inconsistency indicators for pairwise comparisons
This study proposes axioms for inconsistency indicators in pairwise comparisons. The new observation (by Szybowski), that “no PC submatrix may have a worse inconsistency indicator than the given PC matrix” is an essential simplification of the axiomatization. The goal of formulating axioms for all future definitions of new inconsistency indicators is difficult and as illusive as the inconsisten...
متن کاملA Geometric Framework for the Inconsistency in Pairwise Comparisons
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group G, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided. Basic criteria for finding a nearest consistent pairwise comparisons matrix (extended to the class of group G) are proposed. A geometric interpretation of pairwis...
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ژورنال
عنوان ژورنال: International Journal of Applied Mathematics and Computer Science
سال: 2016
ISSN: 2083-8492
DOI: 10.1515/amcs-2016-0050