Aggregation Using the Fuzzy Weighted Average as Computed by the Karnik–Mendel Algorithms

By connecting work from two different problems-the fuzzy weighted average (FWA) and the generalized centroid of an interval type-2 fuzzy set-a new alpha-cut algorithm for solving the FWA problem has been obtained, one that is monotonically and superexponentially convergent. This new algorithm uses the Karnik-Mendel (KM) algorithms to compute the FWA -cut end-points. It appears that the KM -cut algorithms approach for computing the FWA requires the fewest iterations to date, and may therefore be the fastest available FWA algorithm to date.