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

• URL: http://arxiv.org/abs/2408.13297v1
• Date: Fri, 23 Aug 2024 16:20:09 GMT
• Title: An Overview and Comparison of Axiomatization Structures Regarding Inconsistency Indices' Properties in Pairwise Comparisons Methods
• Authors: Sangeeta Pant, Anuj Kumar, Jiří Mazurek,
• Abstract summary: Inconsistency index is a function which maps every pairwise comparison matrix (PCM) into a real number. Inconsistency index can be considered more trustworthy when it satisfies a set of suitable properties.
• Score: 3.670919236694521
• License: http://creativecommons.org/licenses/by/4.0/
• 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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