DempsterShaferlära

DempsterShaferlära is a framework for reasoning under uncertainty, developed by Arthur Dempster and Glenn Shafer. It extends classical probability theory by allowing for the representation of beliefs in terms of belief functions. A belief function assigns a degree of belief to subsets of a set of possible outcomes, reflecting the total evidence supporting that subset. This differs from traditional probability, which assigns probabilities to individual outcomes.

A key concept in Dempster-Shafer theory is the "body of evidence," which is represented by a belief assignment. This assignment must satisfy certain properties, including monotonicity. The theory allows for the combination of multiple bodies of evidence using a specific rule called the Dempster rule of combination. This rule merges the information from different sources to arrive at a refined belief.

One of the advantages of Dempster-Shafer theory is its ability to explicitly represent ignorance. Unlike probability theory, where a lack of information might be represented by assigning equal probabilities, Dempster-Shafer theory can assign zero belief to all singletons and instead assign belief to larger sets, indicating uncertainty. This makes it suitable for applications where data is incomplete or vague.

The theory has found applications in various fields, including artificial intelligence, expert systems, and information fusion. It is particularly useful in situations where dealing with conflicting or partial information is crucial. While powerful, its interpretation and application can be complex, and it is not as widely adopted as standard probability theory.