arXiv subjects

Marc Pirlot

Publications and source records attributed to Marc Pirlot.

8 recordsLinked to original sources

arXiv2026

Identifying two piecewise linear additive value functions from anonymous preference information

Eliciting a preference model involves asking a person, named decision-maker, a series of questions. We assume that these preferences can be represented by an additive value function. In this work, we query simultaneously two decision-makers in the aim to elicit their respective value functions. For each query we receive two answers, without noise, but without knowing which answer corresponds to which decision-maker.We propose an elicitation procedure that identifies the two preference models when the marginal value functions are piecewise linear with known breaking points.

cs.AI↗

arXiv2025

On compromising freedom of choice and subjective

This paper proposes a new framework for evaluating capability sets by incorporating individual preferences over the diversity of accessible options. Building on the Capability Approach, we introduce a compromise method that balances between the notions of negative and positive freedom, effectively capturing the intrinsic and instrumental values of diverse choices within capability sets.

cs.CY↗

arXiv2024

ELECTRE TRI-nB, pseudo-disjunctive: axiomatic and combinatorial results

ELECTRE TRI-nB is a method designed to sort alternatives evaluated on several attributes into ordered categories. It is an extension of ELECTRE TRI-B, using several limiting profiles, instead of just one, to delimit each category. ELECTRE TRI-nB comes in two flavours: pseudo-conjunctive and pseudo-disjunctive. In a previous paper we have characterized the ordered partitions that can be obtained with ELECTRE TRI-nB, pseudo-conjunctive, using a simple axiom called linearity. The present paper is dedicated to the axiomatic analysis of ELECTRE TRI-nB, pseudo-disjunctive. It also provides some combinatorial results.

cs.DM↗

arXiv2024

About maximal antichains in a product of two chains:A catch-all note

We establish one-to-one correspondences between maximal antichains in products of two finite linear orders and other mathematical objects, such as certain alignments of two strings, walks on a grid, lattice paths, words of two or three letters. Leaning on these correspondences, we gather what is known about the number of maximal antichains in products of two finite linear orders and we establish some new results.

math.CO↗

arXiv2021

Axiomatic characterization of the $\chi^{2}$ dissimilarity measure

We axiomatically characterize the $\chi^{2}$ dissimilarity measure. To this end, we solve a new generalization of a functional equation discussed in Aczel (Lectures on functional equations and their applications, Academic Press, 1966).

math.ST↗

arXiv2020

A theoretical look at ELECTRE TRI-nB and related sorting models

Electre Tri is a set of methods designed to sort alternatives evaluated on several criteria into ordered categories. In these methods, alternatives are assigned to categories by comparing them with reference profiles that represent either the boundary or central elements of the category. The original Electre Tri-B method uses one limiting profile for separating a category from the category below. A more recent method, Electre Tri-nB, allows one to use several limiting profiles for the same purpose. We investigate the properties of Electre Tri-nB using a conjoint measurement framework. When the number of limiting profiles used to define each category is not restricted, Electre Tri-nB is easy to characterize axiomatically and is found to be equivalent to several other methods proposed in the literature. We extend this result in various directions.

econ.TH↗

arXiv2019

The size of the largest antichains in products of linear orders

We present new exact and asymptotic results about the size of the largest antichain in the product of $n$ linear orders.

math.CO↗

arXiv2016

UTA-poly and UTA-splines: additive value functions with polynomial marginals

Additive utility function models are widely used in multiple criteria decision analysis. In such models, a numerical value is associated to each alternative involved in the decision problem. It is computed by aggregating the scores of the alternative on the different criteria of the decision problem. The score of an alternative is determined by a marginal value function that evolves monotonically as a function of the performance of the alternative on this criterion. Determining the shape of the marginals is not easy for a decision maker. It is easier for him/her to make statements such as "alternative $a$ is preferred to $b$". In order to help the decision maker, UTA disaggregation procedures use linear programming to approximate the marginals by piecewise linear functions based only on such statements. In this paper, we propose to infer polynomials and splines instead of piecewise linear functions for the marginals. In this aim, we use semidefinite programming instead of linear programming. We illustrate this new elicitation method and present some experimental results.

math.OC↗