Decision Theory and Multi-Agent Planning pp 89-109 | Cite as

# Possibility Theory and its Applications: a Retrospective and Prospective view

## Abstract

This paper provides an overview of possibility theory, emphasising 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. It 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.

## Keywords

Belief Function Possibility Distribution Fuzzy Random Variable Possibility Theory Possibility Measure## Preview

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