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Independence concepts in possibility theory. I. (English) Zbl 0951.68150

Summary: The notion of independence is of great importance in any formalism for managing uncertainty, for both theoretical and practical reasons. We study the concept of independence in the framework of possibility theory. Our approach to defining conditional independence relationships is based on comparing conditional possibility measures. Different comparison criteria 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 Dempster conditioning will be used in the second part). Finally, we study the marginal problem for possibility measures and, as an application, we show that it is possible to store large \(n\)-dimensional possibility distributions efficiently, using independence relationships among variables.

MSC:

68T27 Logic in artificial intelligence
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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