Constraints on membership functions of rules in fuzzy expert systems

The compositional rule of inference used in fuzzy expert systems is investigated for multiple rules. Constraints on membership functions of rules are analyzed under the Sub-T composition and the R-implication from the perspective of the basic requirement for fuzzy reasoning. A graphic method is suggested to obtain the bounds on overlaps between membership functions of rules. An example is given to illustrate the impact of the overlaps on the inference result.<>