there are several techniques that can be used to augment knowledge representation techniques with statistical measures that describe levels of evidence and belief . an important goal for many problem solving systems is to collect evidence as the systems goes along and to modify its behavior , we need a statistical theory of evidence. Bayesian statistics is such a theory which stresses the conditional probability as fundamental notion.
In fuzzy logic, we consider what happens if we make fundamental changes to our idea of set membership and corresponding changes to our definitions of logical operations. While traditional set-theory defines set membership as a Boolean predicate, fuzzy set theory allows us to represent set membership as a possibility distribution such as tall-very for the set of tall people and the set of very tall people. This contrasts with the standard Boolean definition for tall people where one is either tall or not and there must be a specific height that defines the boundary. The same is true for very tall. In fuzzy logic, one’s tallness increases with one’s height until the value 1 is reached. So it is a distribution. Once set membership has been redefined in this way, it is possible to define a reasoning system based on techniques for combining distributions. Such reasoners have been applied in control systems for devices as diverse as trains and washing machines.