On the properties of SIRMs connected type-1 and type-2 fuzzy inference systems

This paper tries to show some important proper ties of the single input rule modules (SIRMs) connected fuzzy inference systems (FIS), including both type-1 (Tl) and inter val type-2 (IT2) FISs. Three kinds of properties continuity, monotonicity and robustness are explored. First, conditions on the parameters are derived to ensure that the SIRMs connected FISs are continuous and monotonic. Then, a methodology for the robustness analysis of the SIRMs connected FISs are presented. At last, an example is given to show the correctness of the theorems on the continuity and monotonicity and to demonstrate the effectiveness of the proposed methodology for robustness analysis. These results can not only deepen our understanding of the SIRMs connected FISs, but also provide us guidelines for the design of the SIRMs connected FISs.