Abstract
We propose and advocate basic principles for the fusion of incomplete or uncertain information items, that should apply regardless of the formalism adopted for representing pieces of information coming from several sources. This formalism can be based on sets, logic, partial orders, possibility theory, belief functions or imprecise probabilities. We propose a general notion of information item representing incomplete or uncertain information about the values of an entity of interest. It is supposed to rank such values in terms of relative plausibility, and explicitly point out impossible values. Basic issues affecting the results of the fusion process, such as relative information content and consistency of information items, as well as their mutual consistency, are discussed. For each representation setting, we present fusion rules that obey our principles, and compare them to postulates specific to the representation proposed in the past. In the crudest (Boolean) representation setting (using a set of possible values), we show that the understanding of the set in terms of most plausible values, or in terms of non-impossible ones matters for choosing a relevant fusion rule. Especially, in the latter case our principles justify the method of maximal consistent subsets, while the former is related to the fusion of logical bases. Then we consider several formal settings for incomplete or uncertain information items, where our postulates are instantiated: plausibility orderings, qualitative and quantitative possibility distributions, belief functions and convex sets of probabilities. The aim of this paper is to provide a unified picture of fusion rules across various uncertainty representation settings.
Highlights
Information fusion is a specific aggregation process which aims to extract truthful knowledge from incomplete or uncertain information coming from various sources [15]
In case all sources inform on the same issue, and are considered relevant, an intuitively natural way of making the best of such information is to consider the true situation to be in agreement with either the part of the information common to witnesses 2 and 3, or with the information provided by witness 1
In [67,68], where information items are consistent knowledge bases with sets of models Ei⊆A mT (Ei), they propose the condition that f (E1, . . . ,En ) ∩ Ei = ∅ either holds for each i, or for none. The possibility that it holds for none is a matter of debate from a knowledge fusion point of view; it may be acceptable when fusing preferences, which is a matter of building a compromise, and if the sets Ei correspond to cores of information items Ti; but it sounds strange if they correspond to supports
Summary
Information fusion is a specific aggregation process which aims to extract truthful knowledge from incomplete or uncertain information coming from various sources [15]. While the result of information fusion should be consistent with what reliable sources bring about, a good compromise in a multiagent choice problem may turn out to be some proposal no party proposed in the first stand While they share some properties and methods, we claim that information fusion and preference aggregation do not obey exactly the same principles. We will check whether known fusion rules in each theory comply with general postulates of information fusion We explain how these basic properties can be written in different representation settings ranging from set-based and logicbased representations to possibility theory, belief function theory and imprecise probabilities. When such a set basically excludes impossible values, we show that our setting characterises the method of maximal consistent subsets. We analyse postulates for merging imprecise probabilities proposed by Peter Walley [109] in the light of our general approach
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