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Possibility Theory and Its Applications: Where Do We Stand?

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Springer Handbook of Computational Intelligence

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Abstract

This chapter 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 nonmonotonic 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 commonsense 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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Abbreviations

ASP:

answer-set programming

CBR:

case-based reasoning

CP  net:

conditional preference network

FCA:

formal concept analysis

MEL:

minimal epistemic logic

PERT:

program evaluation and review technique

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Authors and Affiliations

  1. IRIT – Equipe ADRIA, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 9, France

    Didier Dubois

  2. IRIT – Equipe ADRIA, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 9, France

    Henry Prade

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  1. Didier Dubois
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  1. Systems Research Inst., Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Dep. Electrical and Computer Engineering, University of Alberta, 116 Street 9107, T6J 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

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Dubois, D., Prade, H. (2015). Possibility Theory and Its Applications: Where Do We Stand?. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_3

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