Independence concepts in possibility theory: Part II

From both a theoretical and a practical point of view, the study of the concept of independence has great importance in any formalism that manages uncertainty. In Independence Concepts in Possibility Theory: Part I (de Campos and Huete, Fuzzy Sets and Systems 103 (1999) 127-152) several independence relationships were proposed, using different comparison criteria between conditional possibility measures, and using Hisdal conditioning as the conditioning operator. In this paper, we follow the same approach, but considering possibility measures as particular cases of consonant plausibility measures and, therefore, using Dempster conditioning instead of Hisdal's. We formalize several intuitive ideas to define independence relationships, namely 'not to modify', 'not to gain' and 'to obtain similar' information after conditioning, and study their properties. We also compare the results with the previous ones obtained in Part I using Hisdal conditioning. Finally, the marginal problem, i.e., how to obtain a joint possibility distribution from a set of marginals, and the problem of factorizing large possibility distributions, in terms of its conditionally independent components, are considered. © 1999 Elsevier Science B.V. All fights reserved.