A proposal on approximate reasoning based on revision principle and fixed value law
Abstract
When a rule P Q and a fact P' that is an approximation of P are given, how to obtain the conclusion Q' approximately is an interesting topic on approximate reasoning. This paper proposes a new approach based on the revision principle and fixed value law. The basic idea on revision principle is to deduce Q' from Q based on the deviation of P' from P.
When the revision principle is applied on fuzzy set, there are two laws for obtaining a deviation from P' to P. The first law is called the fixed point law. Its basic idea is to fix an element × in the universe of discourse × of P and P' to obtain the deviation between the membership functions m̈p(x) and m̈p(x). The second law is called the fixed value law. Its basic idea is to fix a value such that the membership functions m̈p(x)= m̈p(x') to obtain the shift from point × to x' on the universe of discourse X.
According to the fixed value law, it will become possible to deduce Q' from Q by shifting the membership function. As an example of the fixed value law, a set of linear revising formulas will be given.