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Possibility Theory as a Basis for Qualitative Decision Theory
, 1995
"... A counterpart to von Neumann and Morgenstern' expected utility theory is proposed in the framework of possibility theory. The existence of a utility function, representing a preference ordering among possibility distributions (on the consequences of decisionmaker's actions) that satisfies a series ..."
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Cited by 101 (25 self)
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A counterpart to von Neumann and Morgenstern' expected utility theory is proposed in the framework of possibility theory. The existence of a utility function, representing a preference ordering among possibility distributions (on the consequences of decisionmaker's actions) that satisfies a series of axioms pertaining to decisionmaker's behavior, is established. The obtained utility is a generalization of Wald's criterion, which is recovered in case of total ignorance; when ignorance is only partial, the utility takes into account the fact that some situations are more plausible than others. Mathematically, the qualitative utility is nothing but the necessity measure of a fuzzy event in the sense of possibility theory (a socalled Sugeno integral). The possibilistic representation of uncertainty, which only requires a linearly ordered scale, is qualitative in nature. Only max, min and orderreversing operations are used on the scale. The axioms express a riskaverse behavior of the d...
Possibility theory in constraint satisfaction problems: Handling priority, preference and uncertainty
 Applied Intelligence
, 1996
"... In classical Constraint Satisfaction Problems (CSPs) knowledge is embedded in a set of hard constraints, each one restricting the possible values of a set of variables. However constraints in real world problems are seldom hard, and CSP's are often idealizations that do not account for the preferenc ..."
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Cited by 74 (13 self)
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In classical Constraint Satisfaction Problems (CSPs) knowledge is embedded in a set of hard constraints, each one restricting the possible values of a set of variables. However constraints in real world problems are seldom hard, and CSP's are often idealizations that do not account for the preference among feasible solutions. Moreover some constraints may have priority over others. Lastly, constraints may involve uncertain parameters. This paper advocates the use of fuzzy sets and possibility theory as a realistic approach for the representation of these three aspects. Fuzzy constraints encompass both preference relations among possible instanciations and priorities among constraints. In a Fuzzy Constraint Satisfaction Problem (FCSP), a constraint is satisfied to a degree (rather than satisfied or not satisfied) and the acceptability of a potential solution becomes a gradual notion. Even if the FCSP is partially inconsistent, best instanciations are provided owing to the relaxation of ...
DecisionTheoretic Foundations of Qualitative Possibility Theory
 European Journal of Operational Research
, 2000
"... This paper presents a justification of two qualitative counterparts of the expected utility criterion for decision under uncertainty, which only require bounded, linearly ordered, valuation sets for expressing uncertainty and preferences. This is carried out in the style of Savage, starting with ..."
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Cited by 51 (7 self)
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This paper presents a justification of two qualitative counterparts of the expected utility criterion for decision under uncertainty, which only require bounded, linearly ordered, valuation sets for expressing uncertainty and preferences. This is carried out in the style of Savage, starting with a set of acts equipped with a complete preordering relation. Conditions on acts are given that imply a possibilistic representation of the decisionmaker uncertainty. In this framework, pessimistic (i.e., uncertaintyaverse) as well as optimistic attitudes can be explicitly captured. The approach thus proposes an operationally testable description of possibility theory. 1
Handling contingency in temporal constraint networks: from consistency to controllabilities
 Journal of Experimental and Theoretical Artificial Intelligence
, 1999
"... This paper has been accepted for publication by the Journal of Experimental and Theoretical Arti cial Intelligence (JETAI) published byTaylor & Francis Ltd. Anyway, it should be pointed out that this version slightly di ers from the nal published one. Copyright 1999 T&F Ltd. Personal use of this mat ..."
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Cited by 50 (4 self)
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This paper has been accepted for publication by the Journal of Experimental and Theoretical Arti cial Intelligence (JETAI) published byTaylor & Francis Ltd. Anyway, it should be pointed out that this version slightly di ers from the nal published one. Copyright 1999 T&F Ltd. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from Taylor & Francis Ltd
Contingent Durations in Temporal CSPs: from Consistency to Controllabilities
, 1997
"... Temporal Constraint Networks (TCSP) allow to express minimal and maximal durations between timepoints. Though being used in many research areas, this model disregards the contingent nature of some constraints, whose effective duration cannot be decided by the system but is provided by the external w ..."
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Cited by 20 (2 self)
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Temporal Constraint Networks (TCSP) allow to express minimal and maximal durations between timepoints. Though being used in many research areas, this model disregards the contingent nature of some constraints, whose effective duration cannot be decided by the system but is provided by the external world. We propose an extension of TCSP in which the classical network consistency property must be redefined in terms of controllability: intuitively, we would like to say that a network is controllable iff it is consistent in any situation (i.e. any assignment of the whole set of contingent intervals) that may arise in the external world. Three levels of controllability must be distinguished, namely the Strong, the Weak and the Dynamic ones. This preliminary report mainly stresses the representation and concept issues, discussing their relevance in dynamic application domains, and partially tackles the reasoning issues (complexity, algorithms and tractable subclasses). 1 Background and ove...
Dynamic Flexible Constraint Satisfaction and its Application to AI Planning
, 2001
"... Constraint satisfaction is a fundamental Artificial Intelligence technique for knowledge representation and inference. It has, however, become clear that the original formulation of a static constraint satisfaction problem (CSP) with hard, imperative constraints is insucient to model many real prob ..."
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Cited by 19 (5 self)
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Constraint satisfaction is a fundamental Artificial Intelligence technique for knowledge representation and inference. It has, however, become clear that the original formulation of a static constraint satisfaction problem (CSP) with hard, imperative constraints is insucient to model many real problems. Recent work has addressed these shortcomings in the form of two separate extensions known as dynamic CSP and flexible CSP respectively. Little has yet been done to combine dynamic and exible CSP in order to bring to bear the benefits of both in solving more complex problems. Based on a
Uncertainty in soft temporal constraint problems: a general framework and controllability algorithms for the fuzzy case
 Journal of AI Research
, 2006
"... In reallife temporal scenarios, uncertainty and preferences are often essential and coexisting aspects. We present a formalism where quantitative temporal constraints with both preferences and uncertainty can be defined. We show how three classical notions of controllability (that is, strong, weak, ..."
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Cited by 14 (3 self)
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In reallife temporal scenarios, uncertainty and preferences are often essential and coexisting aspects. We present a formalism where quantitative temporal constraints with both preferences and uncertainty can be defined. We show how three classical notions of controllability (that is, strong, weak, and dynamic), which have been developed for uncertain temporal problems, can be generalized to handle preferences as well. After defining this general framework, we focus on problems where preferences follow the fuzzy approach, and with properties that assure tractability. For such problems, we propose algorithms to check the presence of the controllability properties. In particular, we show that in such a setting dealing simultaneously with preferences and uncertainty does not increase the complexity of controllability testing. We also develop a dynamic execution algorithm, of polynomial complexity, that produces temporal plans under uncertainty that are optimal with respect to fuzzy preferences. 1.
Reactive Scheduling  Improving the Robustness of Schedules and Restricting the . . .
 INTERNATIONAL JOURNAL ON HUMANCOMPUTER STUDIES
, 1995
"... Practical scheduling usually has to react to many unpredictable events and uncertainties in the production environment. Although often possible in theory, it is undesirable to reschedule from scratch in such cases. Since the surrounding organization will be prepared for the predicted schedule it is ..."
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Cited by 14 (4 self)
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Practical scheduling usually has to react to many unpredictable events and uncertainties in the production environment. Although often possible in theory, it is undesirable to reschedule from scratch in such cases. Since the surrounding organization will be prepared for the predicted schedule it is important to change only those features of the schedule that are necessary. We show how on one side fuzzy logic can be used to support the construction of schedules that are robust with respect to changes due to certain types of event. On the other side we show how a reaction can be restricted to a small environment by means of fuzzy constraints and a repairbased problemsolving strategy. We demonstrate the proposed representation and problemsolving method by introducing a scheduling application in a steelmaking plant. We construct a preliminary schedule by taking into account only the most likely duration of operations. This schedule is iteratively "repaired" until some threshold evaluation is found. A repair is found with a local search procedure based on Tabu Search. Finally, we show which events can lead to reactive scheduling and how this is supported by the repair strategy.
Computing Improved Optimal Solutions to MaxMin Flexible Constraint Satisfaction Problems
 European Journal of Operational Research
, 1999
"... : The formal framework for decision making in a fuzzy environment is based on a general maxmin, bottlenecklike optimization problem, proposed by Zadeh. It is also the basis for extending the constraint satisfaction paradigm of Artificial Intelligence to accommodating flexible or prioritized constra ..."
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Cited by 12 (3 self)
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: The formal framework for decision making in a fuzzy environment is based on a general maxmin, bottlenecklike optimization problem, proposed by Zadeh. It is also the basis for extending the constraint satisfaction paradigm of Artificial Intelligence to accommodating flexible or prioritized constraints. This paper surveys refinements of the ordering of solutions supplied by the maxmin formulation, namely the discrimin partial ordering and the leximin complete preordering. A general algorithm is given which computes all maximal solutions in the sense of these relations. It also sheds light on the structure of the set of best solutions. Moreover, classes of problems for which there is a unique best discrimin and leximin solution are exhibited, namely, continuous problems with convex domains, and so called isotonic problems. Noticeable examples of such problems are fuzzy linear programming problems and fuzzy PERTlike scheduling problems. Introduction Flexible constraint satisfaction p...
Fuzzy Approach for Modeling Multiple Criteria in the Job Grouping Problem
 PROCEEDINGS OF THE 25TH INTERNATIONAL CONFERENCE ON COMPUTERS & INDUSTRIAL ENGINEERING
, 1998
"... In flexible manufacturing systems (FMS), jobs (or products) are often grouped in order to improve productivity. Usually the goal is to minimize the setup size or the number of setup occasions, whereas other criteria are regarded less important and omitted from the objective function. In this paper ..."
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Cited by 5 (5 self)
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In flexible manufacturing systems (FMS), jobs (or products) are often grouped in order to improve productivity. Usually the goal is to minimize the setup size or the number of setup occasions, whereas other criteria are regarded less important and omitted from the objective function. In this paper we discuss fuzzy multiple criteria optimization of the job grouping problem in printed circuit board (PCB) assembly. The importance of the criteria is prescribed by weighting, and a poorly satisfied criterion can be compensated by other criteria. The presented method has been implemented in our production scheduling system designed for electronic industry and is currently in everyday use.