Abstract
Consistency of pairwise comparisons is one particular aspect that is studied thoroughly in the recent decades. However, since the introduction of the concept of the condition of the order preservation in 2008, there is no inconsistency measure based on the aforementioned condition. Therefore, 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. Further, an axiomatic system for the proposed measures is discussed, and it is shown that the proposed indices satisfy uniqueness, invariance under permutation, invariance under inversion of preferences and continuity axioms.
Highlights
Over last decades, pairwise comparisons became one of the most popular tools in multiple criteria decision making
A number of studies focused on the problem of inconsistency of pairwise comparisons, properties of inconsistency indices and their relationships, as well as on proposition of axiomatic systems for inconsistency indices, see e.g. Alonso and Lamata [1], Bozoki and Rapcsak [10], Bozoki et al [11], Brunelli et al [17], Brunelli [14, 15], Brunelli and Fedrizzi [16], Csato [23,24,25], Golden and Wang
Let A = [aij] be a pairwise comparison matrix considered consistent according to relation (2.2), and let w = (w1, . . . , wn) be a priority vector associated to A via the eigenvalue method or the geometric mean method
Summary
Pairwise comparisons became one of the most popular tools in multiple criteria decision making. The condition of the order preservation (COP) in the context of (multiplicative) pairwise comparisons was introduced in 2008 by Bana e Costa and Vansnick [2]. If an object A is directly preferred over B, the weight of A should be greater than the weight of the object B This condition is called the Preservation of Order Preference condition (POP). The aim of the paper is to fill this research gap by proposing new preference violation indices based on the condition of the order preservation.
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