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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 100 (26 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...
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 52 (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
Object Extraction and Revision By Image Analysis Using Existing Geodata And . . .
, 2004
"... The paper focuses mainly on extraction of important topographic objects, like buildings and roads, that have received much attention the last decade. As main input data, aerial imagery is considered, although other data, like from laser scanner, SAR and highresolution satellite imagery, can be also ..."
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Cited by 47 (0 self)
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The paper focuses mainly on extraction of important topographic objects, like buildings and roads, that have received much attention the last decade. As main input data, aerial imagery is considered, although other data, like from laser scanner, SAR and highresolution satellite imagery, can be also used. After a short review of recent image analysis trends, and strategy and overall system aspects of knowledgebased image analysis, the paper focuses on aspects of knowledge that can be used for object extraction: types of knowledge, problems in using existing knowledge, knowledge representation and management, current and possible use of knowledge, upgrading and augmenting of knowledge. Finally, an overview on commercial systems regarding automated object extraction and use of a priori knowledge is given. In spite of many remaining unsolved problems and need for further research and development, use of knowledge and semiautomation are the only viable alternatives towards development of useful object extraction systems, as some commercial systems on building extraction and 3D city modelling as well as advanced, practically oriented research have shown.
Fuzzy sets and probability : Misunderstandings, bridges and gaps
 In Proceedings of the Second IEEE Conference on Fuzzy Systems
, 1993
"... This paper is meant to survey the literature pertaining to this debate, and to try to overcome misunderstandings and to supply access to many basic references that have addressed the "probability versus fuzzy set" challenge. This problem has not a single facet, as will be claimed here. Moreover it s ..."
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Cited by 42 (5 self)
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This paper is meant to survey the literature pertaining to this debate, and to try to overcome misunderstandings and to supply access to many basic references that have addressed the "probability versus fuzzy set" challenge. This problem has not a single facet, as will be claimed here. Moreover it seems that a lot of controversies might have been avoided if protagonists had been patient enough to build a common language and to share their scientific backgrounds. The main points made here are as follows. i) Fuzzy set theory is a consistent body of mathematical tools. ii) Although fuzzy sets and probability measures are distinct, several bridges relating them have been proposed that should reconcile opposite points of view ; especially possibility theory stands at the crossroads between fuzzy sets and probability theory. iii) Mathematical objects that behave like fuzzy sets exist in probability theory. It does not mean that fuzziness is reducible to randomness. Indeed iv) there are ways of approaching fuzzy sets and possibility theory that owe nothing to probability theory. Interpretations of probability theory are multiple especially frequentist versus subjectivist views (Fine [31]) ; several interpretations of fuzzy sets also exist. Some interpretations of fuzzy sets are in agreement with probability calculus and some are not. The paper is structured as follows : first we address some classical misunderstandings between fuzzy sets and probabilities. They must be solved before any discussion can take place. Then we consider probabilistic interpretations of membership functions, that may help in membership function assessment. We also point out nonprobabilistic interpretations of fuzzy sets. The next section examines the literature on possibilityprobability transformati...
Towards a unified theory of imprecise probability
 Int. J. Approx. Reasoning
, 2000
"... Belief functions, possibility measures and Choquet capacities of order 2, which are special kinds of coherent upper or lower probability, are amongst the most popular mathematical models for uncertainty and partial ignorance. I give examples to show that these models are not sufficiently general to ..."
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Cited by 40 (0 self)
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Belief functions, possibility measures and Choquet capacities of order 2, which are special kinds of coherent upper or lower probability, are amongst the most popular mathematical models for uncertainty and partial ignorance. I give examples to show that these models are not sufficiently general to represent some common types of uncertainty. Coherent lower previsions and sets of probability measures are considerably more general but they may not be sufficiently informative for some purposes. I discuss two other models for uncertainty, involving sets of desirable gambles and partial preference orderings. These are more informative and more general than the previous models, and they may provide a suitable mathematical setting for a unified theory of imprecise probability.
Possibility theory and statistical reasoning
 Computational Statistics & Data Analysis Vol
, 2006
"... Numerical possibility distributions can encode special convex families of probability measures. The connection between possibility theory and probability theory is potentially fruitful in the scope of statistical reasoning when uncertainty due to variability of observations should be distinguished f ..."
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Cited by 27 (2 self)
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Numerical possibility distributions can encode special convex families of probability measures. The connection between possibility theory and probability theory is potentially fruitful in the scope of statistical reasoning when uncertainty due to variability of observations should be distinguished from uncertainty due to incomplete information. This paper proposes an overview of numerical possibility theory. Its aim is to show that some notions in statistics are naturally interpreted in the language of this theory. First, probabilistic inequalites (like Chebychev’s) offer a natural setting for devising possibility distributions from poor probabilistic information. Moreover, likelihood functions obey the laws of possibility theory when no prior probability is available. Possibility distributions also generalize the notion of confidence or prediction intervals, shedding some light on the role of the mode of asymmetric probability densities in the derivation of maximally informative interval substitutes of probabilistic information. Finally, the simulation of fuzzy sets comes down to selecting a probabilistic representation of a possibility distribution, which coincides with the Shapley value of the corresponding consonant capacity. This selection process is in agreement with Laplace indifference principle and is closely connected with the mean interval of a fuzzy interval. It sheds light on the “defuzzification ” process in fuzzy set theory and provides a natural definition of a subjective possibility distribution that sticks to the Bayesian framework of exchangeable bets. Potential applications to risk assessment are pointed out. 1
Parameters for Utilitarian Desires in a Qualitative Decision Theory
, 2001
"... In qualitative decisiontheoretic planning, desires—qualitative abstractions of utility functions—are combined with defaults—qualitative abstractions of probability distributions—to calculate the expected utilities of actions. This paper is inspired from Lang’s framework of qualitative decision theo ..."
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Cited by 26 (10 self)
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In qualitative decisiontheoretic planning, desires—qualitative abstractions of utility functions—are combined with defaults—qualitative abstractions of probability distributions—to calculate the expected utilities of actions. This paper is inspired from Lang’s framework of qualitative decision theory, in which utility functions are constructed from desires. Unfortunately, there is no consensus about the desirable logical properties of desires, in contrast to the case for defaults. To do justice to the wide variety of desires we define parameterized desires in an extension of Lang’s framework. We introduce three parameters, which help us to implement different facets of risk. The strength parameter encodes the importance of the desire, the lifting parameter encodes how to determine the utility of a set (proposition) from the utilities of its elements (worlds), and the polarity parameter encodes the relation between gain of utility for rewards and loss of utility for violations. The parameters influence how desires interact, and they thus increase the control on the construction process of utility functions from desires.
Learning Possibilistic Networks from Data
 Proc. 5th Int. Workshop on Artificial Intelligence and Statistics, 233244, Fort Lauderdale
, 1996
"... We introduce a method for inducing the structure of (causal) possibilistic networks from databases of sample cases. In comparison to the construction of Bayesian belief networks, the proposed framework has some advantages, namely the explicit consideration of imprecise (setvalued) data, and the rea ..."
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Cited by 25 (16 self)
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We introduce a method for inducing the structure of (causal) possibilistic networks from databases of sample cases. In comparison to the construction of Bayesian belief networks, the proposed framework has some advantages, namely the explicit consideration of imprecise (setvalued) data, and the realization of a controlled form of information compression in order to increase the efficiency of the learning strategy as well as approximate reasoning using local propagation techniques. Our learning method has been applied to reconstruct a nonsingly connected network of 22 nodes and 24 arcs without the need of any a priori supplied node ordering. 14.1 Introduction Bayesian networks provide a wellfounded normative framework for knowledge representation and reasoning with uncertain, but precise data. Extending pure probabilistic settings to the treatment of imprecise (setvalued) information usually restricts the computational tractability of the corresponding inference mechanisms. It is t...
Using probability trees to compute marginals with imprecise probabilities
 INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
, 2002
"... This paper presents an approximate algorithm to obtain a posteriori intervals of probability, when available information is also given with intervals. The algorithm uses probability trees as a means of representing and computing with the convex sets of ..."
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Cited by 23 (2 self)
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This paper presents an approximate algorithm to obtain a posteriori intervals of probability, when available information is also given with intervals. The algorithm uses probability trees as a means of representing and computing with the convex sets of
Possibilistic Temporal Reasoning based on Fuzzy Temporal Constraints
 In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI
, 1995
"... In this paper we propose a propositional temporal language based on fuzzy temporal constraints which turns out to be expressive enough for domains like many coming from medicine where knowledge is of propositional nature and an explicit handling of time, imprecision and uncertainty are require ..."
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Cited by 22 (2 self)
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In this paper we propose a propositional temporal language based on fuzzy temporal constraints which turns out to be expressive enough for domains like many coming from medicine where knowledge is of propositional nature and an explicit handling of time, imprecision and uncertainty are required. The language is provided with a natural possibilistic semantics to account for the uncertainty issued by the fuzziness of temporal constraints. We also present an inference system based on specific rules dealing with the temporal constraints and a general fuzzy modus ponens rule whereby behaviour is shown to be sound. The analysis of the different choices as fuzzy operators leads us to identify the wellknown Lukasiewicz implication as very appropriate to define the notion of possibilistic entailment, an essential element of our inference system.