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## Publications

Publications (141)

Capacity is an important tool in decision-making under risk and uncertainty and multi-criteria decision-making. When learning a capacity-based model, it is important to be able to generate uniformly a capacity. Due to the monotonicity constraints of a capacity, this task reveals to be very difficult. The classical Random Node Generator (RNG) algori...

Explanation methods can be formal or heuristic-based. Many explanation methods have been developed. Formal methods provide principles to derive sufficient reasons (prime implicants) or necessary reasons (counterfactuals, causes). These approaches are appealing but require to discretize the input and output spaces. Heuristic-based approaches such as...

The Simple Ranking Method using Reference Profiles (or SRMP) is a Multi-Criteria Decision Aiding technique based on the outranking paradigm, which allows to rank decision alternatives according to the preferences of a decision maker (DM). Inferring the preference parameters of such a model can lead to a cognitive fatigue of the DM, who is often ask...

Multi-Criteria Decision Aiding arises in many industrial applications where the user needs an explanation of the recommendation. We consider, in particular, an explanation taking the form of a contribution level assigned to each variable. Decision models are often hierarchical, and the influence is computed by the Winter value, which is an extensio...

Capacities on a finite set are sets functions vanishing on the empty set and being monotonic w.r.t. inclusion. Since the set of capacities is an order polytope, the problem of randomly generating capacities amounts to generating all linear extensions of the Boolean lattice. This problem is known to be intractable even as soon as $n>5$, therefore ap...

Generalized additive independence (GAI) models permit to represent interacting variables in decision making. A fundamental problem is that the expression of a GAI model is not unique as it has several equivalent different decompositions involving multivariate terms. Considering for simplicity 2-additive GAI models (i.e., with multivariate terms of...

The Choquet integral w.r.t. a capacity is a versatile tool commonly used in decision making. Its practical identification requires, however, to solve an optimization problem with exponentially many variables and constraints. The introduction of k-additive capacities, through the use of the Möbius transform, permits to reduce the number of variables...

In this paper, we elaborate on two important developments in the realm of multi-criteria decision aid, which have attracted increasing attention in the recent past: first, the idea of leveraging methods from preference learning for the data-driven (instead of human-centric) construction of decision models, and second, the use of hierarchical instea...

Multi-Criteria Decision Aiding arises in many industrial applications where the user needs an explanation of the recommendation. We consider in particular an explanation taking the form of a contribution level assigned to each variable. Decision models are often hierarchical, and the influence is computed by the Winter value, which is an extension...

Artificial Neural Networks (ANNs) allow to exploit the information contained in data in order to build highly-performant pre-dictive models, at the cost of interpretability and transparency. In this work, we describe the Neur-HCI framework, a class of ANNs which learns highly constrained and naturally interpretable models called Hierarchical Choque...

The Choquet integral, a main ingredient in Multi-Criteria Decision Aid systems, is meant to capture interactions among criteria while enforcing the interpretability of the full aggregated model. The scalability of the approach when the number of criteria increases is achieved using the so-called Hierarchical Choquet integrals (HCI), gradually aggre...

Multifunction radars (MFR) are met with complex capability requirements, involving various kinds of targets and saturating scenarios. In order to achieve these goals, radar systems use Active Electronically Scanned Array (AESA) to switch between their functions. This complexity makes it difficult to assess their performance both taking into account...

We are interested in the explanation of the solution to a hierarchical multi-criteria decision aiding problem. We extend a previous approach in which the explanation amounts to identifying the most influential criteria in a decision. This is based on an influence index which extends the Shapley value on trees. The contribution of this paper is twof...

Due to the nature of autonomous Unmanned Aerial Vehicles (UAV) missions, it is important that the decisions of a UAV stay consistent with the priorities of an operator, while at the same time allowing them to be easily audited and explained. We therefore propose a multi-layer decision engine that follows the logic of an operator and integrates its...

We introduce a way of reasoning about preferences represented as pairwise comparative statements, based on a very simple yet appealing principle: cancelling out common values across statements. We formalize and streamline this procedure with argument schemes. As a result, any conclusion drawn by means of this approach comes along with a justificati...

It is often the case in the applications of Multi-Criteria Decision Making that the values of alternatives are unknown on some attributes. An interesting situation arises when the attributes having missing values are actually not relevant and shall thus be removed from the model. Given a model that has been elicited on the complete set of attribute...

We consider general MCDA models with discrete attributes. These models are shown to be equivalent to a multichoice game and we put some emphasis on discrete Generalized Independence Models (GAI), especially those which are 2-additive, that is, limited to terms of at most two attributes. The chapter studies the interpretation of these models. For ge...

Models in Multicriteria Decision Analysis (MCDA) can be analyzed by means of an importance index and an interaction index for every group of criteria. We consider first discrete models in MCDA, without further restriction, which amounts to considering multichoice games, that is, cooperative games with several levels of participation. We propose and...

We address the problem of how to define an importance index in multicriteria decision problems, when a numerical representation of preferences is given. We make no restrictive assumption on the model, which could have discrete or continuous attributes, and in particular, it is not assumed that the model is monotonically increasing or decreasing wit...

An axiomatization of the Choquet integral is proposed in the context of multiple criteria decision making without any commensurability assumption. The most essential axiom—named Commensurability Through Interaction—states that the importance of an attribute i takes only one or two values when a second attribute k varies. When the importance takes t...

The capability to explain the result of aggregation models to decision makers is key to reinforcing user trust. In practice, Multi-Criteria Decision Aiding models are often organized in a hierarchical way, based on a tree of criteria. We present an explanation approach usable with any hierarchical multi-criteria model, based on an influence index o...

We consider decision situations in which a set of points of view (voters, criteria) are to sort a set of candidates to ordered categories (Good/Bad). Candidates are judged good, when approved by a sufficient set of points of view; this corresponds to NonCompensatory Sorting. To be accountable, such approval sorting should provide guarantees about t...

Models in Multicriteria Decision Analysis (MCDA) can be analyzed by means of an importance index and an interaction index for every group of criteria. We consider first discrete models in MCDA, without further restriction, which amounts to considering multichoice games, that is, cooperative games with several levels of participation. We propose and...

In many Multi-Criteria Decision problems, one can construct with the decision maker several reference levels on the attributes such that some decision strategies are conditional on the comparison with these reference levels. The classical models (such as the Choquet integral) cannot represent these preferences. We are then interested in two models....

The literature on Multiple Criteria Decision Analysis (MCDA) proposes several methods in order to sort alternatives evaluated on several attributes into ordered classes. Non Compensatory Sorting models (NCS) assign alternatives to classes based on the way they compare to multicriteria profiles separating the consecutive classes. Previous works have...

We consider MultiCriteria Decision Analysis (MCDA) models where the underlying attributes are discrete. Without any additional feature, such general models are equivalent to multichoice games in cooperative game theory. Our aim is to define an importance index for attributes. In specific models based on capacities, fuzzy measures, the Shapley value...

We are interested in the aggregation of preference information provided by several decision makers regarding the relative importance of criteria. When a large number of decision makers are involved, they have specific areas of expertise and express their preferences on possibly different subsets of criteria. The standard aggregation methods do not...

We address the problem of multicriteria ordinalsorting through the lens of accountability, i.e. theability of a human decision-maker to own a recommendationmade by the system. We put forward anumber of model features that would favor the capabilityto support the recommendation with a convincingexplanation. To account for that, we designa recommende...

We consider MultiCriteria Decision Analysis models which are defined over discrete attributes, taking a finite number of values. We do not assume that the model is monotonically increasing with respect to the attributes values. Our aim is to define an importance index for such general models, encompassing Generalized-Additive Independence models as...

We consider MultiCriteria Decision Analysis models which are defined over discrete attributes, taking a finite number of values. We do not assume that the model is monotonically increasing with respect to the attributes values. Our aim is to define an importance index for such general models, considering that they are equivalent to $k$-ary games (m...

Multicriteria decision analysis aims at supporting a person facing a decision
problem involving conflicting criteria. We consider an additive utility model
which provides robust conclusions based on preferences elicited from the
decision maker. The recommendations based on these robust conclusions are even
more convincing if they are complemented b...

In systems engineering, practitioners shall explore numerous architectural alternatives until choosing the most adequate variant. The decision-making process is most of the time a manual, time-consuming, and error-prone activity. The exploration and justification of architectural solutions is ad-hoc and mainly consists in a series of tries and erro...

We are interested in aggregation function based on two weights vectors: the criteria weights p and the rank weights w. The main drawback of the existing proposals based on p and w (in particular the Weighted OWA (WOWA) and the Semi-Uninorm OWA (SUOWA) operators) is that their expression is rather complex and the contribution of the weights p and w...

The GAI (Generalized Additive Independence) model proposed by Fishburn is a generalization of the additive utility model, which need not satisfy mutual preferential independence. Its great generality makes however its application and study difficult. We consider a significant subclass of GAI models, namely the discrete 2-additive GAI models, and pr...

The Choquet integral and the Owen extension (or multilinear extension) are
the most popular tools in multicriteria decision making to take into account
the interaction between criteria. It is known that the interaction transform
and the Banzhaf interaction transform arise as the average total variation of
the Choquet integral and multilinear extens...

This chapter aims at a unified presentation of various methods of MCDA based on fuzzy measures (capacity) and fuzzy integrals, essentially the Choquet and Sugeno integral. A first section sets the position of the problem of multicriteria decision making, and describes the various possible scales of measurement (cardinal unipolar and bipolar, and or...

This paper proposes a comparison between a GAI model and the Choquet integral w.r.t. a k-ary capacity. We show that these two models are much closer than one would expect. Based on this comparison, we show a new result on the GAI models: any 2-additive GAI model can be rewritten in such a way that all utility terms in the GAI decomposition are non-...

In the context of decision under uncertainty, standard gambles are classically used to elicit a utility function on a set X of consequences. The utility of an element x in X is derived from the probability p for which a gamble giving the best outcome in X with probability p and the worst outcome in X otherwise, is indifferent to getting x for sure....

In the context of multi-criteria decision making, we propose a new approach to construct an ordered weighted average (OWA) operator in a general case, a convex OWA operator and a trapezoidal OWA operator. Our methodology, based on an interactive decision process, extends the MACBETH methodology and takes as input some preferences on a specific set...

To provide convincing recommendations, which can be fully understood and accepted by a decision-maker, a decisionaider must often engage in an interaction and take the decision maker's responses into account. This feedback can lead to revising the model used to represent the preferences of the decision-maker. Our objective in this paper is to equip...

Preference models often represent a (global) degree of utility of an alternative in terms of an aggregation of
several local utility degrees, each of which pertains to a speciﬁc criterion. Methods for preference learning, i.e., for learning preference models from observed preference data, have mainly focused on ﬁtting the aggregation function while...

Designing the way a complex system should evolve to better match
customers’ requirements provides an interesting class of applications
for muticriteria techniques. The models required to support the improvement
design of a complex system must include both preference
models and system behavioral models. A MAUT model captures decisions
related to des...

We consider a multi-criteria evaluation function U defined over a Cartesian product of attributes. We assume that U is written as the combination of an aggregation function and one value function over each attribute. The aggregation function is assumed to be a Choquet integral w.r.t. an unknown bi-capacity. The problem we wish to address in this pa...

In crisis management contexts such as search-and-rescue – where an autonomous platform must look for victims to rescue after a disaster – , and in many other applications, one encounters the following sequential decision-making problem: at given times, a choice must be done between options but there is a dilemma because they satisfy different crite...

There are different methods for estimating the reliability of a source depending on the nature of the available data about that source. This chapter presents a new method to evaluate the reliability of a source by way of a combination of the evaluations of different dimensions (or attributes) that characterize the reliability. The basic notions of...

A Dung-style argumentation framework aims at representing conflicts among elements called arguments. The basic ingredients of this framework is a set of arguments and a Boolean abstract (i.e., its origin is not known) binary defeat relation. Preference-based argumentation frameworks are instantiations of Dungʼs framework in which the defeat relatio...

This paper is devoted to the use of the GAI (Generalized Additive) model in a Multi-Criteria Decision Making context. We first discuss on some new conditions (concerning the sign and monotonicity) to add on the terms appearing in a GAI model. Secondly, we propose some algorithms to propose the learning examples to change or remove, together with an...

The current approaches to construct a multi-criteria model based on a Choquet integral are split into two separate steps: construct first the utility functions and then the aggregation function. Unfortunately, the decision maker may feel some difficulties in addressing these tricky steps. In this paper, we propose a preference learning algorithm th...

An important aspect of decision making is that a decision is not made at a time assuming that the decision maker (DM) has all relevant information at hand at the same time. On the contrary making a decision results from a process during which (non) relevant and possibly conflicting information come at different instant. Multi-criteria decision maki...

Preference-based argumentation frameworks are instantiation of Dung's framework in which the defeat relation (in the sense of Dung) is computed from an attack relation and a preference relation over the set of arguments. Value-based argumentation framework is a preference-based argumentation framework where the preference relation over arguments is...

This paper presents a new method to update the probability of occurrence of a dreaded event, according to environmental influencers and reports of evidence on the presence or absence of such occurrence. It is particularly useful in military contexts at the tactical level for the risk assessment of a task. Indeed, the computation done during the pla...

Providing convincing explanations to accompany recommendations is a key issue in decision-aiding. In the context of decisions involving multiple criteria, the problem is made very difficult because the decision model itself may involve a complex process. In this paper, we investigate the following issue: when the preferential information provided b...

We propose an axiomatization of global utility functions that can be factorized as a composition of a Choquet integral with local utility functions, without assuming any commensurability condition. This was an open problem in the literature. The main axiom, called commensurability through interaction (CTI), allows to construct commensurate sequence...

In the context of multiple criteria decision analysis, we present the necessary and sufficient conditions to represent a cardinal preferential information by the Choquet integral w.r.t. a 2-additive capacity. These conditions are based on some complex cycles called cyclones.

The ability to provide explanations along with recommended decisions to the user is a key feature of decision-aiding tools. We address the question of providing minimal and complete explanations, a problem relevant in critical situations where the stakes are very high. More specifically, we are after explanations with minimal cost supporting the fa...

MACBETH 2-additive is the generalization of the Choquet integral to the MACBETH approach, a MultiCriteria Decision Aid method. In the elicitation of a 2-additive capacity step, the inconsistencies of the preferential information, given by the Decision Maker on the set of binary alternatives, is tested by using the MOPI conditions. Since a 2-additiv...

The notion of interaction among a set of players has been defined on the Boolean lattice and Cartesian products of lattices. The aim of this paper is to extend this concept to combinatorial structures with forbidden coalitions. The set of feasible coalitions is supposed to fulfil some general conditions. This general representation encompasses conv...

Designing the way a complex system should evolve to better match the customers’ requirements provides an interesting class of applications for muticriteria techniques. The required models to support the improvement design of a complex system must include both preference models and system behavioral models. A MAUT model captures the decisions relate...

We consider a multi-criteria evaluation function U defined over a Cartesian product of attributes. We assume that U is written as the combination of an aggregation function and one value function over each attribute. The aggregation function is assumed to be a Choquet integral w.r.t. an unknown capac-ity. The problem we wish to address in this pape...

We propose an algorithm to solve inconsistencies when the preferences of a decision-maker, given by a strict and an indifference relations on a set of binary actions, are not representable by a 2-additive Cho-quet integral. According to the characterization of this type of information, these inconsistencies arise from the violation of the MOPI prop...

Dung’s argumentation is based on a Boolean binary defeat relation. Recently, this framework has been extended in order to
consider the strength of the defeat relation, i.e., to quantify the degree to which an argument defeats another one. In the
extended framework, the defeat relation with varied strength is abstract, i.e., its origin is not known....

This paper proposes a new model, the EMDP (Evidential Markov Decision Process). It is a MDP (Markov Decision Process) for belief functions in which rewards are defined for each state transition, like in a classical MDP, whereas the transitions are modeled as in an EMC (Evidential Markov Chain), i.e. they are sets transitions instead of states trans...

The automatic generation of an explanation of the prescription made by a multi-attribute decision model is crucial in many applications, such as recommender systems. This task is complex since the quantitative models are not designed to be easily explainable. The major limitation of the previous research is that there is no formal justification of...

In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent
an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide
also a characterization of this type of preferential information by a belief function which c...

Dung’s argumentation developed in Artificial Intelligence is based on a binary attack relation. An important particular case
arises when there is a Boolean preference relation between the arguments. We propose to extend this argumentation framework
to a fuzzy preference relation. This implies that an argument can attack another one to a certain deg...

Preference modeling consists in constructing a preference relation from initial preferences given by a decision maker. We
are interested in the preference relation obtained from the use of the Choquet integral. We give some properties related to
the completeness of the necessary preference relation and its comparison with the traditional approach w...

We present a new interactive algorithm allowing to solve the inconsistencies problem, when the preferences of a decision maker
cannot be representable by a numerical function. This algorithm is based on technics of linear programming and the type of
preferences we use are cardinal information.

Recently, Dung's argumentation has been extended in order to consider the strength of the defeat relation, i.e., to quantify the degree to which an argument defeats another one. We construct an argumentation framework with varied-strength defeats from a preference-based argumentation framework with an intensity degree in the preference relation. We...

The capabilities of modern multifunction/mission Radar can be only fully realized by using new sensor control strategies and the most obvious sensor management imperative is the development of optimal realtime waveform scheduling algorithms. For this purpose, Thales is studying Intelligent Radar Time Resources management for Multi-mission extended...

Grabisch and Labreuche have recently proposed an extension of the Choquet integral adapted to situations where the values to be aggregated lie on a bipolar scale. The resulting continuous piecewise linear aggregation function has the ability to represent decisional behaviors that depend on the ldquopositiverdquo or ldquonegativerdquo satisfaction o...

In the context of decision under uncertainty, we characterize the 2-additive Choquet integral on the set of fic- titious acts called binary alternatives or binary actions. This characterization is based on a fundamental property called MOPI which permits us to relate belief functions and the 2- additive Choquet integral. Keywords— Capacity, M¨ obiu...

Preference modeling consists in constructing a preference relation from initial preferences given by a decision maker. We are interested in the preference relation obtained from the use of the Choquet integral. The necessity preference is constructed as the intersection of all preference relations cor- responding to a Choquet integral which are com...

The Choquet integral w.r.t. a capacity can be seen in the finite case as a
parsimonious linear interpolator between vertices of $[0,1]^n$. We take this
basic fact as a starting point to define the Choquet integral in a very general
way, using the geometric realization of lattices and their natural
triangulation, as in the work of Koshevoy. A second...

The aim of this paper is to define an importance index for bi-capacities in the context of MCDA. We adopt an axiomatic approach. As for capacities the axioms are given in the context of cooperative game theory. The importance index is then derived from the parallel between MCDA and game theory.

In this paper, a new protocol to address multilateral multi-issue negotiation in a cooperative context is presented. Complex dependencies between multiple issues are considered by modelling the preferences of the agents with a multi-criteria decision aid tool, also enabling to extract relevant information on a proposal assessment. This information...

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 conditions induced by these information plus some intuitive conditions lead to a unique possible aggregation operator:...