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arXiv · 2408.13297

An Overview and Comparison of Axiomatization Structures Regarding Inconsistency Indices' Properties in Pairwise Comparisons Methods

Sangeeta Pant·Anuj Kumar·Jiří Mazurek
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Abstract

Mathematical analysis of the analytic hierarchy process (AHP) led to the development of a mathematical function, usually called the inconsistency index, which has the center role in measuring the inconsistency of the judgements in AHP. Inconsistency index is a mathematical function which maps every pairwise comparison matrix (PCM) into a real number. An inconsistency index can be considered more trustworthy when it satisfies a set of suitable properties. Therefore, the research community has been trying to postulate a set of desirable rules (axioms, properties) for inconsistency indices. Subsequently, many axiomatic frameworks for these functions have been suggested independently, however, the literature on the topic is fragmented and missing a broader framework. Therefore, the objective of this article is twofold. Firstly, we provide a comprehensive review of the advancements in the axiomatization of inconsistency indices' properties during the last decade. Secondly, we provide a comparison and discussion of the aforementioned axiomatic structures along with directions of the future research.

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Sangeeta Pant, Anuj Kumar, Jiří Mazurek. 2024-08-23. An Overview and Comparison of Axiomatization Structures Regarding Inconsistency Indices' Properties in Pairwise Comparisons Methods. https://arxiv.org/abs/2408.13297

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