An Overview and Comparison of Axiomatization Structures Regarding Inconsistency Indices' Properties in Pairwise Comparisons Methods
<|reference_start|>An Overview and Comparison of Axiomatization Structures Regarding Inconsistency Indices' Properties in Pairwise Comparisons Methods: 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.<|reference_end|>
@article{pant2024an,
    title={An Overview and Comparison of Axiomatization Structures Regarding
  Inconsistency Indices' Properties in Pairwise Comparisons Methods},
    author={Sangeeta Pant, Anuj Kumar, Jiv{r}'i Mazurek},
    journal={arXiv preprint arXiv:2408.13297},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.13297},
    primaryClass={cs.LO cs.AI}
}