Independence concepts in possibility theory: Part I

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 Science B.V. All rights reserved.