Sangeeta Pant
Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University), Lavale, Pune, Maharashtra, India.

Anuj Kumar
School of Computer Science Engineering & Applications, D Y Patil International University (DYPIU), Akrudi, Pune, 411044, Maharashtra, India.

Jiří Mazurek
Department of Informatics and Mathematics, Silesian University in Opava, Na Rybnicku 626/1, Opava, 74601, Czech Republic.

DOI https://doi.org/10.33889/IJMEMS.2025.10.1.015

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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, various axiomatic frameworks for these functions have been proposed independently. However, the existing literature remains fragmented and lacks a unifying framework. Therefore, the objective of this article is twofold. Over the past decade (2014-2024), significant progress has been made in the axiomatization of inconsistency indices' properties. In this article, we first provide a comprehensive review of these advancements. We then critically evaluate and compare the aforementioned axiomatic structures, discussing future research directions.

Keywords- Analytic hierarchy process, Inconsistency indices, Axioms, Pairwise comparisons.

Citation

Pant, S., Kumar, A., & Mazurek, J. (2025). An Overview and Comparison of Axiomatization Structures Regarding Inconsistency Indices’ Properties in Pairwise Comparisons Methods: A Decade of Advancements. International Journal of Mathematical, Engineering and Management Sciences, 10(1), 265-284. https://doi.org/10.33889/IJMEMS.2025.10.1.015.