New Type-2 Rule Ranking Indices for Designing Parsimonious Interval Type-2 Fuzzy Logic Systems

In this paper, we propose two novel indices for type-2 fuzzy rule ranking to identify the most influential fuzzy rules in designing type-2 fuzzy logic systems, and name them as R-values and c-values of fuzzy rules separately. The R-values of type-2 fuzzy rules are obtained by applying QR decomposition in which there is no need to estimate a rank as required in the SVD-QR with column pivoting algorithm. The c-values of type-2 fuzzy rules are suggested to rank rules based on the effects of rule consequents. Experimental results on a signal recovery problem have shown that by using the proposed indices the most influential type-2 fuzzy rules can be effectively selected to construct parsimonious type-2 fuzzy models while the system performances are kept at a satisfied level.