Importance Sampling Based Defuzzification for General Type-2 Fuzzy Sets

General type-2 fuzzy logic systems (T2 FLS) constitute a powerful tool for coping with ubiquitous uncertainty in many engineering applications. However, the immense computational complexity associated with defuzzification of general T2 fuzzy sets still remains an unresolved issue and prohibits its practical use. This paper proposes a novel importance sampling based defuzzification method for general T2 FLS. Here, a subset from the domain of all embedded fuzzy sets is randomly sampled using a specific probability distribution function. The algorithm is compared with the previously published uniform sampling defuzzification method. Experimental results demonstrate that importance sampling substantially reduces the variance of the sampling defuzzification method. Comparison of T2FLS output surfaces showed that smoother and more stable response can be achieved with the proposed importance sampling based defuzzification method.