BeliefFunktion

Belief Function, also known as a mass function, is a fundamental concept in the Dempster-Shafer theory of evidence, a mathematical theory of evidence developed by Arthur P. Dempster and Glenn Shafer. It is used to represent the degree of belief that one has in a particular proposition, given the available evidence.

A belief function is defined on a set of propositions, called the frame of discernment, which is a set of mutually exclusive and exhaustive hypotheses. The belief function assigns a value to each subset of the frame of discernment, representing the degree of belief that the actual hypothesis is in that subset. This value is a number between 0 and 1, where 0 indicates no belief and 1 indicates complete belief.

The belief function is often used in situations where the available evidence is uncertain or incomplete. It allows for the representation of uncertainty in a more flexible and nuanced way than traditional probability theory, which requires a complete probability distribution over the frame of discernment.

The Dempster-Shafer theory of evidence also includes a rule for combining belief functions from different sources of evidence, known as Dempster's rule of combination. This rule allows for the aggregation of evidence from multiple sources, providing a more robust and reliable assessment of the degree of belief in a particular proposition.

In summary, the belief function is a key concept in the Dempster-Shafer theory of evidence, used to represent the degree of belief in a proposition given the available evidence. It is defined on a frame of discernment and assigns a value to each subset of the frame, representing the degree of belief that the actual hypothesis is in that subset. The belief function is often used in situations where the available evidence is uncertain or incomplete, and it can be combined with other belief functions using Dempster's rule of combination.