Applications of machine reasoning and artificial intelligence in situations characterised by uncertainty (caused by randomness and imprecision) are widespread. Valuation networks are knowledge-based systems for machine reasoning under uncertainty that can be developed using any theoretical framework for uncertainty modeling which satisfies certain axioms of valuation algebra. Well known examples are the valuation networks based on probability functions, possibility functions and Demspster-Shafer belief functions. In this article, we develop a valuation network using arguably the most general theoretical framework for modeling uncertainty: the imprecise probability theory. In this context, we introduce the basic operations and prove the axioms of the valuation algebra. We demonstrate by an example that reasoning with the proposed credal valuation network provides accurate and least uncertain outcomes.

Contemporary undertakings provide limitless opportunities for widespread application of machine reasoning and artificial intelligence in situations characterized by uncertainty, hostility, and sheer volume of data. The article develops a valuation network as a graphical system for higher-level fusion and reasoning under uncertainty in support of the human operators. Valuations, which are mathematical representation of (uncertain) knowledge and collected data, are expressed as credal sets, defined as coherent interval probabilities in the framework of imprecise probability theory. The basic operations with such credal sets, combination, and marginalization, are defined to satisfy the axioms of a valuation algebra. A practical implementation of the credal valuation network is discussed and its utility demonstrated on a small scale example.