Conditioning in possibility theory

This note is concerned with the study of the concept of conditional possibility distributions. The intuitive notion of possibility is presented as a set-function which is a special case of a precapacity. This set-function is extended to linguistic variables using general formulation of optimization under elastic constraints. We introduce a definition of conditional possibility distribution which is consistent with the notion of non-interaction, and study various properties related to marginal and joint distributions. Comparisons with probability are made. This study is essential for the analysis of situations in which the uncertainty is not statistical in nature.