# Lexicographic optimization-based approaches to learning a representative model for multi-criteria sorting with non-monotonic criteria

arXiv: https://arxiv.org/abs/2409.01612 · HTML: https://mlsanity.com/paper/2409.01612/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 64 references that are in the map.
- First posted on arXiv 3 Sep 2024.

## Builds on (most cited first, 5 of 5)

- [Data-driven preference learning methods for value-driven multiple criteria sorting with interacting criteria](https://mlsanity.com/paper/1905.08506/) (2019)
- [A preference learning framework for multiple criteria sorting with diverse additive value models and valued assignment examples](https://mlsanity.com/paper/1910.05485/) (2019)
- [UTA-poly and UTA-splines: additive value functions with polynomial marginals](https://mlsanity.com/paper/1603.02626/) (2016)
- [Recommending Multiple Criteria Decision Analysis Methods with A New Taxonomy-based Decision Support System](https://mlsanity.com/paper/2106.07378/) (2021)
- [Inducing a probability distribution in Stochastic Multicriteria Acceptability Analysis](https://mlsanity.com/paper/2304.06650/) (2023)

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

- [An incremental preference elicitation-based approach to learning potentially non-monotonic preferences in multi-criteria sorting](https://mlsanity.com/paper/2409.02760/) (2024)

## Abstract (arXiv)

Deriving a representative model using value function-based methods from the perspective of preference disaggregation has emerged as a prominent and growing topic in multi-criteria sorting (MCS) problems. A noteworthy observation is that many existing approaches to learning a representative model for MCS problems traditionally assume the monotonicity of criteria, which may not always align with the complexities found in real-world MCS scenarios. Consequently, this paper proposes some approaches to learning a representative model for MCS problems with non-monotonic criteria through the integration of the threshold-based value-driven sorting procedure. To do so, we first define some transformation functions to map the marginal values and category thresholds into a UTA-like functional space. Subsequently, we construct constraint sets to model non-monotonic criteria in MCS problems and develop optimization models to check and rectify the inconsistency of the decision maker's assignment example preference information. By simultaneously considering the complexity and discriminative power of the models, two distinct lexicographic optimization-based approaches are developed to derive a representative model for MCS problems with non-monotonic criteria. Eventually, we offer an illustrative example and conduct comprehensive simulation experiments to elaborate the feasibility and validity of the proposed approaches.