Independence concepts in possibility theory: Part II

From both a theoretical and a practical point of view, the study of the con cept of independence has great importance in any formalism that manages unc ertainty. In Independence Concepts in Possibility Theory: Port I (de Campos and Huete, Fuzzy Sets and Systems 103 (1999) 127-152) several independence relationships were proposed, using different comparison criteria between c onditional possibility measures, and using Hisdal conditioning as the condi tioning operator. In this paper, we follow the same approach, but consideri ng possibility measures as particular cases of consonant plausibility measu res and, therefore, using Dempster conditioning instead of Hisdal's. We for malize several intuitive ideas to define independence relationships, namely 'not to modify', 'not to gain' and 'to obtain similar' information after c onditioning, and study their properties. We also compare the results with t he previous ones obtained in Part I using Hisdal conditioning. Finally, the marginal problem, i.e., how to obtain a joint possibility distribution fro m a set of marginals, and the problem of factorizing large possibility dist ributions, in terms of its conditionally independent components, are consid ered. (C) 1999 Elsevier Science B.V. All rights reserved.