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Title: Belief fusion / Opinion pooling =





29 May 2007

Original author

Matthias Nickles (

Current lead

Last Modified By

Matthias Nickles

Primary Actors

Secondary Actors

Application domain

Triggering event

Purpose/Goals (Summarize what the use case is to accomplish)

If a single information artifact (e.g., a knowledge base, an ontology, or a product rating on the web) shall be created from multiple possibly contradictory information sources (e.g., expert opinions, existing ontologies, or product recommendations), the user (e.g., the knowledge engineer) applies a fusion operator in order to yield possibly uncertain fused beliefs from multiple input beliefs provided by the information sources.

Issues and Relevance to Uncertainty (Summarize how relevant to uncertainty reasoning and representation?)

This use case is especially relevant wrt. uncertainty in case the set of information acquired from multiple sources about the same fact is inconsistent (UncertaintyNature: Epistemic; UncertaintyType: Inconsistency) , or (more generally) if multiple information sources attribute multiple and mutually different grades of belief to the same statement. If the user does not want to decide in favor of a single alternative, and wants the merger to weight all input beliefs adequately (instead of discarding some of them), the single statement resulting from the fusion of multiple statements will be uncertain (UncertaintyNature: Epistemic; UncertaintyType: Empirical usually, but might also depend on the uncertainty type of the input statements.)

It might be reasonable to consider in addition factors such as the trustability of the information contributors at aggregation.

Examples for belief aggregation operators which can yield uncertain results are logarithmic and linear pools (LogOP, LinOP), and Bayesian Network Aggregation. One possible criterion for a successful fusion is the minimization of the divergence of the resulting probability distribution from the input probability distributions.

[to be added: Fuzzy approaches to belief fusion, Dempster–Shafer approaches]

In order to yield an uncertain fusion result it is of course not necessary that any of the input statements which shall be fused is already uncertain itself.

Required resources (List resources, such as data sources, ontologies, needed for scenario)

  1. An adequate aggregation of the relevant input information (opinions, ratings, source ontologies...)
  2. Optionally: Information provenance identifiers in order to distinguish the information contributions. Resources could be meta-data (provenance annotations), URIs, social networks, or contexts.

Successful End (Describe what happens if this use case is successful)

The user managed to create a single, coherent merger of the contributions such that the merger i) is in a format which supports the representation of uncertainty, ii) is consistent, and iii) reflects the support (belief grades) provided by each information source for each contained statement appropriately.

Failed End (Describe what happens if this use case fails)

\neg Successful End

Main Scenario (List the sequence of events for the basic course (numbered))

  1. The user identifies information sources she considers to be relevant.
  2. Inconsistencies and other disparities are identified, preferably automatically
  3. The system applies a belief aggregation operator, calculating possibly uncertain fused beliefs from the input beliefs.
  4. The result is represented in some appropriate formal web language (e.g., one of the existing probabilistic enhancements of OWL).

Additional background information or references (Summarize/provide references to information to further describe or characterize use case)

Uncertainty approaches to belief fusion and opinion pooling (sometimes also called probability aggregation) are researched in AI since quite a long time, although no consensus regarding the "best" approach exists.

Similar approaches, although partly on a different epistemic level, exist in research communities such as sensor fusion and database integration.

A related area is the theory of social choice, especially judgement aggregation.

Variations (List the alternatives that will not be further decomposed at this time)

Open Issues