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Abstract
Possibility theory is the formalization of the methods of reasoning about uncertainty and information, derived from the principles of fuzzy sets and systems. Derived possibilistic assignments can be constructed within this theory. This paper defines the notion of conditional possibility—an assignment subject to conditioning by other possibilistic random variables. The proposed definition can be based on one of the two principles: proper interaction with marginal distributions, or minimization of possibilistic information distance between the original and derived distributions. Both approaches independently lead to the same definition, thus strongly suggesting its wider applicability.