Journal
FUZZY SETS AND SYSTEMS
Volume 157, Issue 11, Pages 1491-1513Publisher
ELSEVIER
DOI: 10.1016/j.fss.2006.01.003
Keywords
possibility theory; coherence; conditional independence; logical independence; graphical models
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The subtle notion of conditioning is controversial in several contexts, for example in possibility theory where, in fact, different definitions have been introduced. We refer to a general axiomatic definition of conditional possibility and then we deal with partial assessments on (not necessarily structured) domains containing only elements of interest. We study a notion of coherence, which assures the extendability of an assessment as a conditional possibility and we introduce a procedure for checking coherence. Moreover, we propose a definition of independence for conditional possibility, which avoids some counterintuitive situations, and we study its main properties in order to compare it with other definitions introduced in literature. Then, we check which properties among the graphoid ones are satisfied: this allows to compare our definition with other independence notions given in the context of other uncertainty formalisms. This analysis is relevant for graphical models in order to single out and visualize dependence relations among random variables. (C) 2006 Elsevier B.V. All rights reserved.
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