Study on sampling-based discrete noniterative algorithms for centroid type-reduction of interval type-2 fuzzy logic systems

As an emerging technology, interval type-2 fuzzy logic systems (IT2 FLSs) have drawn great attentions in the past decade years. However, the computational intensive and time consuming type-reduction (TR) block may hinder the real applications IT2 FLSs. Unlike the most popular Karnik-Mendel (KM) iterative algorithms, the noniterative algorithms decrease the computational cost greatly. The comparison between the discrete and continuous algorithms is still an open problem. This paper compares the sum operations in discrete noniterative algorithms and the integral operations in continuous noniterative algorithms, and discovers the inner relations between the discrete and continuous noniterative algorithms. Then, three types of noniterative algorithms are adopted for performing the centroid TR of IT2 FLSs. Three computer simulations show the calculation results of sampling based discrete noniterative algorithms can accurately approximate the corresponding continuous noniterative algorithms as varying the number of sampling of primary variable appropriately, in addition, the computational efficiencies of former are much higher than the latter, which provide the potential value for designing IT2 FLSs.