A New Approach to Possibilistic Independence

The introduction of a notion of independence in possibility theory is a problem of long-standing interest. The definitions that have up to now been given in the literature face some difficulties as far as interpretation is concerned. Also, there are inconsistencies between the definition of independence of measurable sets and possibilistic variables. After a discussion of these definitions and their shortcomings, we suggest a new definition, that is consistent in this respect. Furthermore, we show that in the special case of classical, two-valued possibility our definition has a straightforward and natural interpretation. Keywords--- possibility theory, possibilistic variables, possibilistic independence, logical independence. I. Introduction S INCE the introduction of possibility theory by Zadeh [12] in 1978, various attempts have been made to define what we shall call here possibilistic independence, a notion which is intended to be a possibilistic analogon of the probabilistic no..