MP and invariant MP approximations of fuzzy inference rules
It is well-known that the composition rule of inference which was introduced by Zadeh [1973], does not satisfy the inference rule, modus ponens, in general. It seems a disadvantage of applying it. However, in this paper, we show that we can make modus ponens satisfied by slightly modifying the original IFTHEN rules in the rule base. That is, we can obtain an approximation of the original rules on which modus ponens holds. The related concepts such as MP approximations and invariant MP approximations are introduced. Their properties are investigated. The second issue of this paper is about the invariance of rule adding of a rule base. It is found that in some cases, the function of a rule base is not changed by adding a new rule into the base which is obtained from the base. The relationships between the invariant MP approximation add the invariance of rule adding are investigated.
invariant mp approximations mp approximations compositional rule of inference modus ponens invariance of rule adding rule based systems approximate reasoning