# A gradient method for inconsistency reduction of pairwise comparisons matrices

arXiv: https://arxiv.org/abs/2108.04034 · HTML: https://mlsanity.com/paper/2108.04034/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2021.

## Built on by (most cited first, 1 of 1)

- [Almost optimal manipulation of a pair of alternatives](https://mlsanity.com/paper/2304.03060/) (2023)

## Abstract (arXiv)

We investigate an application of a mathematically robust minimization method -- the gradient method -- to the consistencization problem of a pairwise comparisons (PC) matrix. Our approach sheds new light on the notion of a priority vector and leads naturally to the definition of instant priority vectors. We describe a sample family of inconsistency indicators based on various ways of taking an average value, which extends the inconsistency indicator based on the "sup"- norm. We apply this family of inconsistency indicators both for additive and multiplicative PC matrices to show that the choice of various inconsistency indicators lead to non-equivalent consistencization procedures.