The Cycle Inconsistency Index in Pairwise Comparisons Matrices
نویسندگان
چکیده
منابع مشابه
On 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...
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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...
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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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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...
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A formal proof of convergence of a class of algorithms for reducing inconsistency of pairwise comparisons (PC) method is presented. The design of such algorithms is proposed. The convergence of the algorithms justifies making an inference that iterated modifications of the pc matrix made by human experts should also converge. This is instrumental for credibility of practical applications of the...
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ژورنال
عنوان ژورنال: Procedia Computer Science
سال: 2016
ISSN: 1877-0509
DOI: 10.1016/j.procs.2016.08.266