Can the Minimum Rule of Possibility Theory Be Extended to Belief Functions?

When merging belief functions, Dempster rule of combination is justified only when sources can be considered as independent. When dependencies are ill-known, it is usual to ask the merging operation to satisfy the property of idempotence, as this property ensures a cautious behaviour in the face of dependent sources. There are different strategies to find such rules for belief functions. One strategy is to rely on idempotent rules used in either more general or more specific frameworks and to respectively study their particularisation or extension to belief functions. In this paper, we try to extend the minimum rule of possibility theory to belief functions. We show that such an extension is not always possible, unless we accept the idea that the result of the fusion process can be a family of belief functions.

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