Related papers: Axiomatization of the Choquet integral for 2-dimen…
We propose an axiomatization of the Choquet integral model for the general case of a heterogeneous product set $X = X_1 \times \ldots \times X_n$. In MCDA elements of $X$ are interpreted as alternatives, characterized by criteria taking…
The Choquet integral is a powerful aggregation operator which lists many well-known models as its special cases. We look at these special cases and provide their axiomatic analysis. In cases where an axiomatization has been previously given…
In this paper we deal with the problem of axiomatizing the preference relations modelled through Choquet integral with respect to a $k$-additive capacity, i.e. whose M\"obius transform vanishes for subsets of more than $k$ elements. Thus,…
We axiomatize the Choquet rank-dependent utility model within a Savage framework with an exogenous source of pure risk. This model is a decision model under ambiguity, serving as a conceptual generalization of the Choquet expected utility…
This paper addresses the question of which models fit with information concerning the preferences of the decision maker over each attribute, and his preferences about aggregation of criteria (interacting criteria). We show that the…
Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
Preference Inference involves inferring additional user preferences from elicited or observed preferences, based on assumptions regarding the form of the user's preference relation. In this paper we consider a situation in which…
In this paper we propose a new multiple criteria decision aiding method to deal with sorting problems in which alternatives are evaluated on criteria structured in a hierarchical way and presenting interactions. The underlying preference…
We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices.…
Several non-linear functions and machine learning methods have been developed for flexible specification of the systematic utility in discrete choice models. However, they lack interpretability, do not ensure monotonicity conditions, and…
A total set of $n$ states $|i\rangle$ and the corresponding projectors $\Pi(i)=|i\rangle \langle i|$ are considered, in a quantum system with $d$-dimensional Hilbert space $H(d)$. A partially known density matrix $\rho$ with given…
Understanding consumer preferences is essential to product design and predicting market response to these new products. Choice-based conjoint analysis is widely used to model user preferences using their choices in surveys. However,…
In a quantum system with d-dimensional Hilbert space, the Q-function of a Hermitian positive semidefinite operator ?, is defined in terms of the d2 coherent states in this system. The Choquet integral CQ of the Q-function, is introduced…
In multi-criteria decision aiding, the Choquet integral has been used as an aggregation operator to deal with interacting criteria, having as a requirement a prior assumption of common scale for all the criteria. This restriction on the…
This paper studies the strategic manipulation of set-valued social choice functions according to Kelly's preference extension, which prescribes that one set of alternatives is preferred to another if and only if all elements of the former…
We consider the problem of rationalizing choice data by a preference satisfying an arbitrary collection of invariance axioms. Examples of such axioms include quasilinearity, homotheticity, independence-type axioms for mixture spaces,…
People care about decision outcomes and how decisions get made, both when making decisions and reflecting on decisions. But formalizing the full range of normative concerns that drive decisions is an open challenge. We introduce Axiomatic…
We propose a class of semimetrics for preference relations any one of which is an alternative to the classical Kemeny-Snell-Bogart metric. (We take a fairly general viewpoint about what constitutes a preference relation, allowing for any…
Bi-capacities arise as a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wide variety of decision behaviours, encompassing models such…