The Experts below are selected from a list of 49617 Experts worldwide ranked by ideXlab platform
Didier Dubois - One of the best experts on this subject based on the ideXlab platform.
-
New axiomatisations of discrete quantitative and qualitative possibilistic integrals
Fuzzy Sets and Systems, 2018Co-Authors: Didier Dubois, Agnés RicoAbstract:Necessity (resp. possibility) measures are very simple min-decomposable (resp. max-decomposable) representations of epistemic Uncertainty due to incomplete knowledge. They can be used in both quantitative and qualitative settings. In the present work, we revisit Choquet and Sugeno integrals as criteria for Decision under Uncertainty and propose new axioms when Uncertainty is representable in possibility theory. First, a characterization of Choquet integral with respect to a possibility or a necessity measure is proposed. We respectively add an optimism or a pessimism axiom to the axioms of the Choquet integral with respect to a general capacity. This new axiom enforces the maxitivity or the minitivity of the capacity without requiring the same property for the functional. It essentially assumes that the Decision-maker preferences only reflect the plausibility ordering between states of nature. The obtained pessimistic (resp. optimistic) criterion is an average maximin (resp. maximax) criterion of Wald across cuts of a possibility distribution on the state space. The additional axiom can be also used in the axiomatic approach to Sugeno integral and generalized forms thereof to justify possibility and necessity measures. The axiomatization of these criteria for Decision under Uncertainty in the setting of preference relations among acts is also discussed. We show that the new axiom justifying possibilistic Choquet integrals can be expressed in this setting. In the case of Sugeno integral, we correct a characterization proof for an existing set of axioms on acts, and study an alternative set of axioms based on the idea of non-compensation.
-
Extracting Decision Rules from Qualitative Data via Sugeno Utility Functionals
2018Co-Authors: Quentin Brabant, Didier Dubois, Henri Prade, Miguel Couceiro, Agnés RicoAbstract:Sugeno integrals are qualitative aggregation functions. They are used in multiple criteria Decision making and Decision under Uncertainty, for computing global evaluations of items, based on local evaluations. The combination of a Sugeno integral with unary order preserving functions on each criterion is called a Sugeno utility functionals (SUF). A noteworthy property of SUF is that they represent multi-threshold Decision rules, while Sugeno integrals represent single-threshold ones. However, not all sets of multi-threshold rules can be represented by a single SUF. In this paper, we consider functions defined as the minimum or the maximum of several SUF. These max-SUF and min-SUF can represent all functions that can be described by a set of multi-threshold rules, i.e., all order-preserving functions on finite scales. We study their potential advantages as a compact representation of a big set of rules, as well as an intermediary step for extracting rules from empirical datasets.
-
Axiomatisation of discrete fuzzy integrals with respect to possibility and necessity measures
2016Co-Authors: Didier Dubois, Agnés RicoAbstract:Necessity (resp. possibility) measures are very simple representations of epistemic Uncertainty due to incomplete knowledge. In the present work, a characterization of discrete Choquet integrals with respect to a possibility or a necessity measure is proposed, understood as a criterion for Decision under Uncertainty. This kind of criterion has the merit of being very simple to define and compute. To get our characterization, it is shown that it is enough to respectively add an optimism or a pessimism axiom to the axioms of the Choquet integral with respect to a general capacity. This additional axiom enforces the maxitivity or the minitivity of the capacity and essentially assumes that the Decision-maker preferences only reflect the plausibility ordering between states of nature. The obtained pessimistic (resp. optimistic) criterion is an average of the maximin (resp. maximax) criterion of Wald across cuts of a possibility distribution on the state space. The additional axiom can be also used in the axiomatic approach to Sugeno integral and generalized forms thereof. The possibility of axiomatising of these criteria for Decision under Uncertainty in the setting of preference relations among acts is also discussed.
-
Decision-making with Sugeno integrals
Order, 2016Co-Authors: Miguel Couceiro, Didier Dubois, Henri Prade, Tamas WaldhauserAbstract:This paper clarifies the connection between multiple criteria Decision-making and Decision under Uncertainty in a qualitative setting relying on a finite value scale. While their mathematical formulations are very similar, the underlying assumptions differ and the latter problem turns out to be a special case of the former. Sugeno integrals are very general aggregation operations that can represent preference relations between uncertain acts or between multifactorial alternatives where attributes share the same totally ordered domain. This paper proposes a generalized form of the Sugeno integral that can cope with attributes which have distinct domains via the use of qualitative utility functions. It is shown that in the case of Decision under Uncertainty, this model corresponds to state-dependent preferences on act consequences. Axiomatizations of the corresponding preference functionals are proposed in the cases where Uncertainty is represented by possibility measures, by necessity measures, and by general order-preserving set-functions, respectively. This is achieved by weakening previously proposed axiom systems for Sugeno integrals.
-
Decision-making with Sugeno integrals: DMU vs. MCDM
2012Co-Authors: Miguel Couceiro, Didier Dubois, Henri Prade, Tamas WaldhauserAbstract:This paper clarifies the connection between multiple criteria Decision-making and Decision under Uncertainty in a qualitative setting relying on a finite value scale. While their mathematical formulations are very similar, the underlying assumptions differ and the latter problem turns out to be a special case of the former. Sugeno integrals are very general aggregation operations that can represent preference relations between uncertain acts or between multifactorial alternatives where attributes share the same totally ordered domain. This paper proposes a generalized form of the Sugeno integral that can cope with attributes which have distinct domains via the use of qualitative utility functions. In the case of Decision under Uncertainty,this model corresponds to state-dependent preferences on act consequences. Axiomatizations of the corresponding preference functionals are proposed in the cases where Uncertainty is represented by possibility measures, by necessity measures, and by general monotonic set-functions, respectively. This is achieved by weakening previously proposed axiom systems for Sugeno integrals.
Henri Prade - One of the best experts on this subject based on the ideXlab platform.
-
Extracting Decision Rules from Qualitative Data via Sugeno Utility Functionals
2018Co-Authors: Quentin Brabant, Didier Dubois, Henri Prade, Miguel Couceiro, Agnés RicoAbstract:Sugeno integrals are qualitative aggregation functions. They are used in multiple criteria Decision making and Decision under Uncertainty, for computing global evaluations of items, based on local evaluations. The combination of a Sugeno integral with unary order preserving functions on each criterion is called a Sugeno utility functionals (SUF). A noteworthy property of SUF is that they represent multi-threshold Decision rules, while Sugeno integrals represent single-threshold ones. However, not all sets of multi-threshold rules can be represented by a single SUF. In this paper, we consider functions defined as the minimum or the maximum of several SUF. These max-SUF and min-SUF can represent all functions that can be described by a set of multi-threshold rules, i.e., all order-preserving functions on finite scales. We study their potential advantages as a compact representation of a big set of rules, as well as an intermediary step for extracting rules from empirical datasets.
-
Decision-making with Sugeno integrals
Order, 2016Co-Authors: Miguel Couceiro, Didier Dubois, Henri Prade, Tamas WaldhauserAbstract:This paper clarifies the connection between multiple criteria Decision-making and Decision under Uncertainty in a qualitative setting relying on a finite value scale. While their mathematical formulations are very similar, the underlying assumptions differ and the latter problem turns out to be a special case of the former. Sugeno integrals are very general aggregation operations that can represent preference relations between uncertain acts or between multifactorial alternatives where attributes share the same totally ordered domain. This paper proposes a generalized form of the Sugeno integral that can cope with attributes which have distinct domains via the use of qualitative utility functions. It is shown that in the case of Decision under Uncertainty, this model corresponds to state-dependent preferences on act consequences. Axiomatizations of the corresponding preference functionals are proposed in the cases where Uncertainty is represented by possibility measures, by necessity measures, and by general order-preserving set-functions, respectively. This is achieved by weakening previously proposed axiom systems for Sugeno integrals.
-
Decision-making with Sugeno integrals: DMU vs. MCDM
2012Co-Authors: Miguel Couceiro, Didier Dubois, Henri Prade, Tamas WaldhauserAbstract:This paper clarifies the connection between multiple criteria Decision-making and Decision under Uncertainty in a qualitative setting relying on a finite value scale. While their mathematical formulations are very similar, the underlying assumptions differ and the latter problem turns out to be a special case of the former. Sugeno integrals are very general aggregation operations that can represent preference relations between uncertain acts or between multifactorial alternatives where attributes share the same totally ordered domain. This paper proposes a generalized form of the Sugeno integral that can cope with attributes which have distinct domains via the use of qualitative utility functions. In the case of Decision under Uncertainty,this model corresponds to state-dependent preferences on act consequences. Axiomatizations of the corresponding preference functionals are proposed in the cases where Uncertainty is represented by possibility measures, by necessity measures, and by general monotonic set-functions, respectively. This is achieved by weakening previously proposed axiom systems for Sugeno integrals.
-
ECSQARU - Answer Set Programming for Computing Decisions under Uncertainty
Lecture Notes in Computer Science, 2011Co-Authors: Roberto Confalonieri, Henri PradeAbstract:Possibility theory offers a qualitative framework for modeling Decision under Uncertainty. In this setting, pessimistic and optimistic Decision criteria have been formally justified. The computation by means of possibilistic logic inference of optimal Decisions according to such criteria has been proposed. This paper presents an Answer Set Programming (ASP)-based methodology for modeling Decision problems and computing optimal Decisions in the sense of the possibilistic criteria. This is achieved by applying both a classic and a possibilistic ASP-based methodology in order to handle both a knowledge base pervaded with Uncertainty and a prioritized preference base.
-
explaining qualitative Decision under Uncertainty by argumentation
National Conference on Artificial Intelligence, 2006Co-Authors: Leila Amgoud, Henri PradeAbstract:Decision making under Uncertainty is usually based on the comparative evaluation of different alternatives by means of a Decision criterion. In a qualitative setting, pessimistic and optimistic criteria have been proposed. In that setting, the whole Decision process is compacted into a criterion formula on the basis of which alternatives are compared. It is thus impossible for an end user to understand why an alternative is good, or better than another. Besides, argumentation is a powerful tool for explaining inferences, Decisions, etc. This paper articulates optimistic and pessimistic Decision criteria in terms of an argumentation process that consists of constructing arguments in favor/against Decisions, evaluating the strengths of those arguments, and comparing pairs of alternatives on the basis of their supporting/attacking arguments.
Regis Sabbadin - One of the best experts on this subject based on the ideXlab platform.
-
GMDPtoolbox: A Matlab library for designing spatial management policies. Application to the long-term collective management of an airborne disease
PLoS ONE, 2017Co-Authors: Marie-josee Cros, Nathalie Peyrard, Jean-noel Aubertot, Regis SabbadinAbstract:Designing management policies in ecology and agroecology is complex. Several components must be managed together while they strongly interact spatially. Decision choices must be made under Uncertainty on the results of the actions and on the system dynamics. Furthermore, the objectives pursued when managing ecological systems or agroecosystems are usually long term objectives, such as biodiversity conservation or sustainable crop production. The framework of Graph-Based Markov Decision Processes (GMDP) is well adapted to the qualitative modeling of such problems of sequential Decision under Uncertainty. Spatial interactions are easily modeled and integrated control policies (combining several action levers) can be designed through optimization. The provided policies are adaptive, meaning that management actions are decided at each time step (for instance yearly) and the chosen actions depend on the current system state. This framework has already been successfully applied to forest management and invasive species management. However, up to now, no ªeasy-to-useº implementation of this framework was available. We present GMDPtoolbox, a Matlab toolbox which can be used both for the design of new management policies and for comparing policies by simulation. We provide an illustration of the use of the toolbox on a realistic crop disease management problem: the design of long term management policy of blackleg of canola using an optimal combination of three possible cultural levers. This example shows how GMDPtoolbox can be used as a tool to support expert thinking.
-
GMDPtoolbox: a Matlab library for solving Graph-based Markov Decision Processes
2016Co-Authors: Marie-josee Cros, Nathalie Peyrard, Regis SabbadinAbstract:Systems management in ecology or agriculture is complex because several entities in interaction must be managed together with a long term objective. Finding an optimal (or at least a good) policy to govern these large systems is still a challenge in practice. Graphbased Markov Decision Processes (GMDPs) form a suitable tool for modelling and solving such structured problems of sequential Decision under Uncertainty. In this article we introduce GMDPtoolbox: a Matlab library dedicated to the GMDP framework. The toolbox allows to easily represent a problem as a GMDP, to solve it (e.g. finding a “good” local policy) and finally to analyze a policy or compare its performance with human-built policies, like expert ones.
-
Solving F(3)MDPs: Collaborative Multiagent Markov Decision Processes with Factored Transitions, Rewards and Stochastic Policies
2015Co-Authors: Julia Radoszycki, Nathalie Peyrard, Regis SabbadinAbstract:Multiagent Markov Decision Processes provide a rich framework to model problems of multiagent sequential Decision under Uncertainty, as in robotics. However, when the state space is also factored and of high dimension, even dedicated solution algorithms (exact or approximate) do not apply when the dimension of the state space and the number of agents both exceed 30, except under strong assumptions about state transitions or value function. In this paper we introduce the (FMDP)-M-3 framework and associated approximate solution algorithms which can tackle much larger problems. An (FMDP)-M-3 is a collaborative multiagent MDP whose state space is factored, reward function is additively factored and solution policies are constrained to be factored and can be stochastic. The proposed algorithms belong to the family of Policy Iteration (PI) algorithms. On small problems, where the optimal policy is available, they provide policies close to optimal. On larger problems belonging to the subclass of GMDPs they compete well with state-of-the-art resolution algorithms in terms of quality. Finally, we show that our algorithms can tackle very large F(3)MDPs, with 100 agents and a state space of size 2(100).
-
Résolution de PDMF^3 : processus décisionnels de Markov à transitions, récompenses et politiques stochastiques factorisées
2015Co-Authors: Julia Radoszycki, Nathalie Peyrard, Regis SabbadinAbstract:Markov Decision Processes with factored state and action spaces, usually referred to as FA-FMDPs, provide a rich framework to model problems of sequential Decision under Uncertainty, where both the state and action spaces are of high dimension and highly structured, as in robotics, conservation biology or disease management domains. However, even dedicated solution algorithms (exact or approximate) do not apply when the dimensions of the state and action spaces both exceed 20-30, except under strong assumptions about state transitions or value function. In this paper we introduce the F^3 MDP framework and associated approximate solution algorithms which can tackle much larger problems. An F^3 MDP is an FA-FMDP whose reward function is additively factored and solution policies are constrained to be factored and can be stochastic. The proposed algorithms belong to the family of Policy Iteration (PI) algorithms and exploit continuous optimization tools. We validate them on extensive experiments. On small problems, where the optimal policy is available, they provide policies close to optimal. On larger problems belonging to the subclass of GMDPs they compete well with state-of-the-art resolution algorithms in terms of quality. Finally, we show that our algorithms can tackle very large F^3 MDPs. Indeed, they can solve problems of disease management in crop fields with state and action spaces of size 2^100.
-
Qualitative Decision under Uncertainty: back to expected utility
Artificial Intelligence, 2005Co-Authors: Hélène Fargier, Regis SabbadinAbstract:Different qualitative models have been proposed for Decision under Uncertainty in Artificial Intelligence, but they generally fail to satisfy the principle of strict Pareto dominance or principle of "efficiency", in contrast to the classical numerical criterion--expected utility. Among the most prominent examples of qualitative models are the qualitative possibilistic utilities (QPU) and the order of magnitude expected utilities (OMEU). They are both appealing but inefficient in the above sense. The question is whether it is possible to reconcile qualitative criteria and efficiency. The present paper shows that the answer is yes, and that it leads to special kinds of expected utilities. It is also shown that although numerical, these expected utilities remain qualitative: they lead to different Decision procedures based on min, max and reverse operators only, generalizing the leximin and leximax orderings of vectors.
Patrice Perny - One of the best experts on this subject based on the ideXlab platform.
-
Decision under Uncertainty
A Guided Tour of Artificial Intelligence Research, 2020Co-Authors: Christophe Gonzales, Patrice PernyAbstract:The goal of this chapter is to provide a general introduction to Decision making under Uncertainty. The mathematical foundations of the most popular models used in artificial intelligence are described, notably the Expected Utility model (EU), but also new Decision making models, like Rank Dependent Utility (RDU), which significantly extend the descriptive power of EU. Decision making under Uncertainty naturally involves risks when Decisions are made. The notion of risk is formalized as well as the attitude of agents w.r.t. risk. For this purpose, probabilities are often exploited to model uncertainties. But there exist situations in which agents do not have sufficient knowledge or data available to determine these probability distributions. In this case, more general models of Uncertainty are needed and this chapter describes some of them, notably belief functions. Finally, in most artificial intelligence problems, sequences of Decisions need be made and, to get an optimal sequence, Decisions must not be considered separately but as a whole. We thus study at the end of this chapter models of sequential Decision making under Uncertainty, notably the most widely used graphical models.
-
Qualitative Decision Theory with preference relations and comparative Uncertainty: an axiomatic approach
Artificial Intelligence, 2003Co-Authors: Didier Dubois, Hélène Fargier, Patrice PernyAbstract:This paper investigates a purely qualitative approach to Decision making under Uncertainty. Since the pioneering work of Savage, most models of Decision under Uncertainty rely on a numerical representation where utility and Uncertainty are commensurate. Giving up this tradition, we relax this assumption and introduce an axiom of ordinal invariance requiring that the Decision Maker's preference between two acts only depends on the relative position of their consequences for each state. Within this qualitative framework, we determine the only possible form of the corresponding Decision rule. Then assuming the transitivity of the strict preference, the underlying partial confidence relations are those at work in non-monotonic inference and thus satisfy one of the main properties of possibility theory. The satisfaction of additional postulates of unanimity and anonymity enforces the use of a necessity measure, unique up to a monotonic transformation, for encoding the relative likelihood of events.
Agnés Rico - One of the best experts on this subject based on the ideXlab platform.
-
New axiomatisations of discrete quantitative and qualitative possibilistic integrals
Fuzzy Sets and Systems, 2018Co-Authors: Didier Dubois, Agnés RicoAbstract:Necessity (resp. possibility) measures are very simple min-decomposable (resp. max-decomposable) representations of epistemic Uncertainty due to incomplete knowledge. They can be used in both quantitative and qualitative settings. In the present work, we revisit Choquet and Sugeno integrals as criteria for Decision under Uncertainty and propose new axioms when Uncertainty is representable in possibility theory. First, a characterization of Choquet integral with respect to a possibility or a necessity measure is proposed. We respectively add an optimism or a pessimism axiom to the axioms of the Choquet integral with respect to a general capacity. This new axiom enforces the maxitivity or the minitivity of the capacity without requiring the same property for the functional. It essentially assumes that the Decision-maker preferences only reflect the plausibility ordering between states of nature. The obtained pessimistic (resp. optimistic) criterion is an average maximin (resp. maximax) criterion of Wald across cuts of a possibility distribution on the state space. The additional axiom can be also used in the axiomatic approach to Sugeno integral and generalized forms thereof to justify possibility and necessity measures. The axiomatization of these criteria for Decision under Uncertainty in the setting of preference relations among acts is also discussed. We show that the new axiom justifying possibilistic Choquet integrals can be expressed in this setting. In the case of Sugeno integral, we correct a characterization proof for an existing set of axioms on acts, and study an alternative set of axioms based on the idea of non-compensation.
-
Extracting Decision Rules from Qualitative Data via Sugeno Utility Functionals
2018Co-Authors: Quentin Brabant, Didier Dubois, Henri Prade, Miguel Couceiro, Agnés RicoAbstract:Sugeno integrals are qualitative aggregation functions. They are used in multiple criteria Decision making and Decision under Uncertainty, for computing global evaluations of items, based on local evaluations. The combination of a Sugeno integral with unary order preserving functions on each criterion is called a Sugeno utility functionals (SUF). A noteworthy property of SUF is that they represent multi-threshold Decision rules, while Sugeno integrals represent single-threshold ones. However, not all sets of multi-threshold rules can be represented by a single SUF. In this paper, we consider functions defined as the minimum or the maximum of several SUF. These max-SUF and min-SUF can represent all functions that can be described by a set of multi-threshold rules, i.e., all order-preserving functions on finite scales. We study their potential advantages as a compact representation of a big set of rules, as well as an intermediary step for extracting rules from empirical datasets.
-
Axiomatisation of discrete fuzzy integrals with respect to possibility and necessity measures
2016Co-Authors: Didier Dubois, Agnés RicoAbstract:Necessity (resp. possibility) measures are very simple representations of epistemic Uncertainty due to incomplete knowledge. In the present work, a characterization of discrete Choquet integrals with respect to a possibility or a necessity measure is proposed, understood as a criterion for Decision under Uncertainty. This kind of criterion has the merit of being very simple to define and compute. To get our characterization, it is shown that it is enough to respectively add an optimism or a pessimism axiom to the axioms of the Choquet integral with respect to a general capacity. This additional axiom enforces the maxitivity or the minitivity of the capacity and essentially assumes that the Decision-maker preferences only reflect the plausibility ordering between states of nature. The obtained pessimistic (resp. optimistic) criterion is an average of the maximin (resp. maximax) criterion of Wald across cuts of a possibility distribution on the state space. The additional axiom can be also used in the axiomatic approach to Sugeno integral and generalized forms thereof. The possibility of axiomatising of these criteria for Decision under Uncertainty in the setting of preference relations among acts is also discussed.
