Decision-theoretic foundations of qualitative possibility theory
European Journal of Operational ResearchPublished 1 February 2001
Didier Dubois, Henri Prade, Régis Sabbadin
Citations260
SJR quartileQ1
SJR score2.24
SNIP2.62
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
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, and proposes an operationally testable description of possibility theory.
Abstract
International audience
Keywords
Computer ScienceDecision Sciences
American Mathematical Society eBooksTheory of games and economic behavior
16,943 Citations2019Stephan Ramon Garcia, Steven J. Miller
Fuzzy Sets and SystemsFuzzy sets as a basis for a theory of possibility
7,964 Citations1978Lotfi A. Zadeh
The Quarterly Journal of EconomicsRisk, Ambiguity, and the Savage Axioms
7,774 Citations1961Daniel Ellsberg
Fuzzy Sets and SystemsFuzzy sets as a basis for a theory of possibility
7,280 Citations1999Lotfi A. Zadeh
The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
Mathematics in Science and Engineering/Mathematics in science and engineeringFuzzy Sets and Systems - Theory and Applications
6,430 Citations1980Didier Dubois, Henri Prade
Probabilistic Metric Spaces
2,659 Citations1983B. Schweizer, A. Sklar
Subjective probability and expected utility without additivity
2,580 Citations2004David Schmeidler
EconometricaSubjective Probability and Expected Utility without Additivity
2,322 Citations1989David Schmeidler
Fuzzy Measure Theory
1,240 Citations1992Zhenyuan Wang, George J. Klir
Knowledge in Flux: Modeling the Dynamics of Epistemic States
1,219 Citations1990Peter Gärdenfors
Ordinal Conditional Functions: A Dynamic Theory of Epistemic States
914 Citations1988Wolfgang Spohn
Elsevier eBooksFUZZY MEASURES AND FUZZY INTEGRALS—A SURVEY
764 Citations1993Michio Sugeno
The concept of fuzzy sets (precisely speaking, fuzzy subsets of an ordinary set) is nothing but an extended concept of ordinary sets, and the concept of probabilities is absolutely different from that of sets.
Journal of Mathematical EconomicsExpected utility with purely subjective non-additive probabilities
693 Citations1987Itzhak Gilboa
Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference
575 Citations1995Michel Grabisch, Hung T. Nguyen +1 more
The aim of this book is to provide a rigorous background for uncertainty calculi, with an emphasis on fuzziness, and to give a complete background on uncertainty measures and integrals, especially in a fuzzy setting.
International Journal of General SystemsA CLASS OF FUZZY MEASURES BASED ON TRIANGULAR NORMS A general framework for the combination of uncertain information
330 Citations1982Didier Dubois, Henri Prade
An axiomatic approach to a broad class of fuzzy measures in the sense of Sugeno is presented via the concept of triangular norm (t-norm for short), which encompasses probability measures, Zadeh's possibility measures and the dual notion of necessity measures.
Possibility Theory: Qualitative and Quantitative Aspects
317 Citations1998Didier Dubois, Henri Prade
Possibility theory offers a simple, non-additive modelling of partial belief, which contrasts with probability theory, and provides a potentially more qualitative treatment ofpartial belief since the operations ‘max’ and ‘min’ play a role somewhat analogous to the sum and the product in probability calculus.
Applied IntelligencePossibility theory in constraint satisfaction problems: Handling priority, preference and uncertainty
281 Citations1996Didier Dubois, H�l�ne Fargier +1 more
This paper advocates the use of fuzzy sets and possibility theory as a realistic approach for the representation of these three aspects of Constraint Satisfaction Problems: preference relations among possible instantiations and priorities among constraints.
Journal of Mathematical Analysis and Applications⊥-Decomposable measures and integrals for Archimedean t-conorms ⊥
280 Citations1984Siegfried Weber
Possibility Theory as a Basis for Qualitative Decision Theory
261 Citations1995Didier Dubois, Henri Prade
A counterpart to von Neumann and Morgenstern' expected utility theory is proposed in the framework of possibility theory, representing a preference ordering among possibility distributions that satisfies a series of axioms pertaining to decision-maker's behavior.
EconometricaA Simple Axiomatization of Nonadditive Expected Utility
229 Citations1992Rakesh K. Sarin, Peter P. Wakker
Journal of Intelligent ManufacturingFuzzy constraints in job-shop scheduling
164 Citations1995Didier Dubois, H�l�ne Fargier +1 more
An extension of the constraint-based approach to job-shop scheduling that accounts for the flexibility of temporal constraints and the uncertainty of operation durations is proposed, including fuzzy extensions of well-known look-ahead schemes.
Helvetica paediatrica actaBelief structures, possibility theory and decomposable confidence measures on finite sets
156 Citations1986Didier Dubois
Fuzzy Sets and SystemsFuzzy measure of fuzzy events defined by fuzzy integrals
119 Citations1992Michel Grabisch, Toshiaki Murofushi +1 more
This work proposes a general definition of fuzzy measure of fuzzy events, which is compatible with previous definitions of Zadeh, and possesses all properties of a fuzzy measure, in particular the duality property.
Fuzzy Sets and SystemsCharacterization and comparison of sugeno and choquet integrals
111 Citations1992Luis M. de Campos, María Elena Díez Jorge
Two types of fuzzy integrals that can be defined on any kind of fuzzy measure: Sugeno and Choquet integrals are characterized, pointing out their formal similarities and their conceptual differences.
IEEE Transactions on Systems Man and CyberneticsDecisionmaking under uncertainty with various assumptions about available information
89 Citations1984Thomas Whalen
Six different varieties of methodology are surveyed for choosing one of a fixed number of alternative actions in the context of uncertainty, where the outcome of each alternative action is dependent on the state of the world.
IEEE Transactions on Systems Man and CyberneticsAxiomatization of qualitative belief structure
78 Citations1991S. K. M. Wong, Yiyu Yao +2 more
The axiomization of qualitative belief provides a foundation to develop a utility theory for decision making based on belief functions and may lead to a better understanding and useful applications of belief structures in approximate reasoning.
arXiv (Cornell University)Qualitative Decision Theory with Sugeno Integrals
76 Citations2013Didier Dubois, Henri Prade +1 more
Theory and DecisionAggregation of decomposable measures with application to utility theory
74 Citations1996Damien Dubois, János Fodor +2 more
arXiv (Cornell University)Generalized Qualitative Probability: Savage revisited
65 Citations2002Daniel Lehmann
The rationality postulates considered are weaker than Savage's on three counts, but they are shown to lead to a characterization of generalized qualitative probability that includes and blends both traditional qualitative probability and the ranked structures used in logical approaches.
Fuzzy Sets and SystemsA unified approach to define fuzzy integrals
48 Citations1991Luis M. de Campos, María Teresa Lamata +1 more
The characterization theorems of Choquet's integral can be refined, whereas the same cannot be made for Sugeno's integral, and other fuzzy integrals fitting the same formal model are obtained.
Fuzzy Sets and SystemsFuzzy integral representation
34 Citations1996Dan A. Ralescu, Sugeno Michio
Under the more restrictive condition of stochastic dominance, it is proved that a more specific representation as a fuzzy integral with respect to a distorted probability measure is useful.
INFORMS Journal on ComputingPossibilistic Linear Programming with Measurable Multiattribute Value Functions
31 Citations1989Masahiro Inuiguchi, Hidetomo Ichihashi +1 more
The possibilistic linear program in this paper is an unconstrained linear program with several objective functions whose coefficients are represented by possibility distributions whose coefficient distributions are derived from a possibility distribution.
arXiv (Cornell University)Decision-making Under Ordinal Preferences and Comparative Uncertainty
26 Citations2013Didier Dubois, Hélène Fargier +1 more
It is shown that although many axioms of Savage theory can be preserved and despite the intuitive appeal of the ordinal method, the approach is inconsistent with a probabilistic representation of uncertainty.
International Journal of General SystemsDETERMINATION OF RECONSTRUCTION FAMILIES
23 Citations1982Bush Jones
A method for obtaining the equations for the reconstruction hypothesis in linearly independent form is presented, and the resultant matrix is in triangular form.
Mathematical Social SciencesRepresentation of preferences on fuzzy measures by a fuzzy integral
16 Citations1996Jens Leth Hougaard, Hans Keiding
A system of axioms for a utility representation of preferences on the set of non-additive set functions is presented, and its usefulness with respect to decision theory is evaluated.
