Anyone familiar with possibility theory and possibilistic analysis? I came across it during my own research on expert human reasoning/decision making.(adsbygoogle = window.adsbygoogle || []).push({});

Here is a brief description of possibility theory from a recent article behind a paywall.

As I see it, possibility theory offers a novel way to deal with chances which have some particular form of 'vagueness' to them. This makes it an alternative to probability theory, the standard canonical mathematical theory of chances, which focuses on randomness instead of vagueness. Possibility theory is the simplest uncertainty theory devoted to the modeling of incomplete information. It is characterized by the use of two basic dual set functions that respectively grade the possibility and the necessity of events. Possibility theory lies at the crossroads between fuzzy sets, probability and non‐monotonic reasoning. Possibility theory is closely related to fuzzy sets if one considers that a possibility distribution is a particular fuzzy set (of mutually exclusive) possible values. However fuzzy sets and fuzzy logic are primarily motivated by the representation of gradual properties while possibility theory handles the uncertainty of classical (or fuzzy) propositions. 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.

Possibility theory is an uncertainty theory devoted to the handling of incomplete information. To a large extent, it is similar to probability theory because it is based on set‐functions. It differs from the latter by the use of a pair of dual set functions (possibility and necessity measures) instead of only one. Besides, it is not additive and makes sense on ordinal structures. The name “Theory of Possibility” was coined by Zadeh [1], who was inspired by a paper by Gaines and Kohout [2]. In Zadeh's view, possibility distributions were meant to provide a graded semantics to natural language statements. However, possibility and necessity measures can also be the basis of a full‐fledged representation of partial belief that parallels probability. It can be seen either as a coarse, non‐numerical version of probability theory, or a framework for reasoning with extreme probabilities, or yet a simple approach to reasoning with imprecise probabilities [3].

I'm not entirely sure if the two theories are exclusionary with respect to each other, or if they are in some sense just different ways of looking at the same thing, eg. like looking at classical mechanics from a Newtonian, Hamiltonian or Lagrangian perspective.

In any case, possibility theory seems to be a powerful, and more importantly, intuitive tool, which seems to be a lot simpler to learn than probability theory and seems to more closely or more naturally model human reasoning than probability theory does.

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# I Possibility theory

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