The notion of independence is of great importance in any formalism for mana
ging uncertainty, for both theoretical and practical reasons. In this paper
we study the concept of independence in the framework of possibility theor
y. Our approach to defining conditional independence relationships is based
on comparing conditional possibility measures. Different comparison criter
ia are presented, based on the ideas of 'not to modify', 'not to gain', and
'to obtain similar' information after conditioning. For each definition of
independence considered, an axiomatic study has been carried out. Moreover
, there are different operators to define conditional possibility measures,
which are related to different views of possibility theory. Particularly,
in the first part of the paper, we use Hisdal conditioning (whereas Dempste
r conditioning will be used in the second part). Finally, we study the marg
inal problem for possibility measures and, as an application, we show that
it is possible to store large n-dimensional possibility distributions effic
iently, using independence relationships among variables. (C) 1999 Elsevier
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