The basic principles of uncertain information fusion: An organised review of merging rules in different representation frameworks

Didier Dubois, Weiru Liu, Jianbing Ma, Henri Prade

Research output: Contribution to journalArticle (Academic Journal)

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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.
Original languageEnglish
Pages (from-to)12-39
Number of pages28
JournalInformation Fusion
Early online date26 Feb 2016
Publication statusPublished - Nov 2016

Structured keywords

  • Jean Golding


  • Information fusion
  • Knowledge-based merging
  • Evidence theory
  • Combination rules
  • Plausibility orderings
  • Possibility theory
  • Imprecise probability

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