# Valuation-based system

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**Valuation-based system** (VBS) is a framework for [knowledge representation](/source/Knowledge_representation) and inference. Real-world problems are modeled in this framework by a network of interrelated entities, called variables. The relationships between variables (possibly uncertain or imprecise) are represented by the functions called valuations. The two basic operations for performing inference in a VBS are combination and marginalization. Combination corresponds to the aggregation of knowledge, while marginalization refers to the focusing (coarsening) of it. VBSs were introduced by Prakash P. [Shenoy](/source/Shenoy) in 1989 as general frameworks for managing uncertainty in [expert systems](/source/Expert_system).

## Applications

VBS are used for knowledge representation in expert systems and data fusion.

## Bibliography

- Shenoy, Prakash P. A valuation-based language for expert systems. *Int. Journal of Approximate Reasoning*, vol. 3, no. 2, pages 383–411, 1989.

- Shenoy, Prakash P. Valuation based systems: A framework for managing uncertainty in expert systems. In L. A. Zadeh and J. Kacprzyk, editors, *Fuzzy Logic and the Management of Uncertainty*, chapter 4, pages 83–104. Wiley, New York, 1992.

- Shenoy, Prakash P. and Shafer, G. Axioms for probability and belief-function propagation. In J. Pearl G. Shafer, editor, *Readings in uncertain reasoning*, pages 575–610. San Mateo, CA: Morgan Kaufmann, 1990.

## External links

- [Application of VBS to a threat assessment problem](http://www.idsia.ch/~alessio/TAES-VBS.pdf)

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