Fuzzy Interpolative Reasoning Based on the Footprints of Uncertainty of Interval Type-2 Fuzzy Sets

In this paper, we present a new method for fuzzy interpolative reasoning in sparse fuzzy rule-based systems based on the footprints of uncertainty of interval type-2 fuzzy sets. First, the proposed method divides each interval type-2 fuzzy set appearing in the fuzzy rules and the observations into some partitioned interval type-2 fuzzy sets and calculates the uncertainty ratio of each partitioned interval type-2 fuzzy set. Then, it constructs the upper membership function of the fuzzy interpolated result based on the distance between the adjacent characteristic points of fuzzy sets and constructs the lower membership function of the fuzzy interpolated result based on the inferred uncertainty ratios of the partitioned interval type-2 fuzzy sets of the fuzzy interpolated result. The experimental results show that the results of the proposed method are more reasonable than the ones obtained by using the existing methods for fuzzy interpolative reasoning in sparse fuzzy rule-based systems.