Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions

Benferhat, Salem; Dubois, Didier; Kaci, Souhila; Prade, Henri

doi:10.1016/j.inffus.2005.04.001

Cited by 113 publications

(93 citation statements)

References 29 publications

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“…Other applications of possibility theory can be found in fields such as data analysis [137,132,24], database querying [25], diagnosis [27,26], belief revision [18], argumentation [4,3], case-based reasoning [56,101], learning [120,121], and information merging [19] (taking advantage of the bipolar representation setting which distinguishes between positive information of the form ∆(φ) ≥ α and negative information expressing impossibility under the form N (φ) ≥ α ⇔ 1 − Π(¬φ) ≥ α [20]). …”

Section: Some Applicationsmentioning

confidence: 99%

Possibility Theory and Its Applications: Where Do We Stand?

Dubois

Prade

2015

Springer Handbook of Computational Intelligence

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141

101

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This paper provides an overview of possibility theory, emphasizing its historical roots and its recent developments. Possibility theory lies at the crossroads between fuzzy sets, probability and non-monotonic reasoning. Possibility theory can be cast either in an ordinal or in a numerical setting. Qualitative possibility theory is closely related to belief revision theory, and common-sense reasoning with exception-tainted knowledge in Artificial Intelligence. Possibilistic logic provides a rich representation setting, which enables the handling of lower bounds of possibility theory measures, while remaining close to classical logic. Qualitative possibility theory has been axiomatically justified in a decision-theoretic framework in the style of Savage, thus providing a foundation for qualitative decision theory. Quantitative possibility theory is the simplest framework for statistical reasoning with imprecise probabilities. As such it has close connections with random set theory and confidence intervals, and can provide a tool for uncertainty propagation with limited statistical or subjective information.

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Section: Some Applicationsmentioning

confidence: 99%

Possibility Theory and Its Applications: Where Do We Stand?

Dubois

Prade

2015

Springer Handbook of Computational Intelligence

Self Cite

141

101

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“…In decision under uncertainty, let us mention a logical approach [5] where uncertain knowledge and prioritized preference are represented by means of two distinct possibilistic logic N-bases, and where the pessimistic or optimistic decision criteria that are maximized are particular cases of Sugeno integrals. In [2], a multicriteria decision problem is expressed in terms of prioritized constraints and wishes, where constraints are modelled by an N-base, and wishes by a -base, handled separately in the decision process; however the latter is not interpreted as an N-based put in disjunctive form. In [13], in a multiple criteria decision perspective, a qualitative approach, also in the spirit of possibilistic logic, is compared to a counterpart of a Choquet integral-based aggregation process.…”

Section: Related Workmentioning

confidence: 99%

The logical encoding of Sugeno integrals

Dubois¹,

Prade²,

Rico³

2014

Fuzzy Sets and Systems

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. AbstractSugeno integrals are a well-known family of qualitative multiple criteria aggregation operators. The paper investigates how the behavior of these operators can be described in a prioritized propositional logic language, namely possibilistic logic. The case of binary-valued criteria, which amounts to providing a logical description of the fuzzy measure underlying the integral, is first considered. The general case of a Sugeno integral when critersia are valued on a discrete scale is then studied.

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“…Examples showing the interest of bipolar modeling in a logical setting, in particular for combining agents' preferences, can be found e.g. in [4,22].…”

Section: Examples In Propositional Logicsmentioning

confidence: 99%

Distance to bipolar information from morphological dilation

Bloch¹,

Atif²

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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In this paper we propose definitions of distances to bipolar information. This notion is important to find a solution that matches bipolar queries, to exhibit recommendations satisfying preferences of an agent while respecting her constraints, to find an agreement between several agents. All these situations require to be able to compare candidate solutions, via their distance to some bipolar information, and several evaluation measures are proposed as well. We base distances and their comparison on mathematical morphology operators, in particular dilations and skeleton by influence zones.

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Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions

Cited by 113 publications

References 29 publications

Possibility Theory and Its Applications: Where Do We Stand?

Possibility Theory and Its Applications: Where Do We Stand?

The logical encoding of Sugeno integrals

Distance to bipolar information from morphological dilation

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