Study on weighted Nagar-Bardini algorithms for centroid type-reduction of interval type-2 fuzzy logic systems

Interval type-2 fuzzy logic systems (IT2 FLSs) have been applied in many areas as an emerging technology. Typereduction of IT2 FLSs is considered to be one of the most important blocks due to the involved computational complexity. Karnik-Mendel algorithms are the standard algorithms to perform the type-reduction; however, the iterative nature of these algorithms may hinder them from real applications. The IT2 FLS based on the Nagar-Bardini (NB) algorithms has been proved to make significantly improvements over a wide range of uncertainties. In this research, by comparing the sum operation in discrete version of NB algorithms and the integral operation in continuous version of NB (CNB) algorithms, we extend the NB algorithms to three different forms of weighted NB (WNB) algorithms by means of the Newton-Cotes quadrature formulas of numerical integration. Whereas the NB algorithms just become a special case of the WNB algorithms. Four simulation examples are used to show the performance of the WNB algorithms. Compared with the NB algorithms, in general, the WNB algorithms have smaller absolute error and faster convergence speed, which provide the potential value for designer and adopters of T2 FLSs.