EI-FRI: Extended Incircle Fuzzy Rule Interpolation for Multidimensional Antecedents, Multiple Fuzzy Rules, and Extrapolation Using Total Weight Measurement and Shift Ratio

Traditional fuzzy reasoning techniques demand a condensed fuzzy rule base to conclude a result. Still, due to incomplete data or a deficiency of expertise and knowledge, dense rule bases are not always available. Fuzzy interpolation methods have been widely explored to reasonably allow the interpolation of a fuzzy result using the closest current rules. Fuzzy rule interpolation is a type of fuzzy inference system in which conclusions can be obtained even with a few fuzzy rules. This benefit could be used to adapt the FRI to different application areas that suffer from a lack of knowledge. Alzubi et al. [17] offered a novel interpolative method that uses a weighted average based on the center point of the Incircle of the fuzzy sets. Nevertheless, the interpolated observation does not completely define the actual observation that is provided. In our offered extension to this method, a modification weight measure calculation and a shift technique are included to guarantee that the center point of the observation and the interpolated observation are mapped together. This weight measure calculation and shift technique enabled the capability of extrapolation to be conducted implicitly, which is also improves the performance results of the algorithm in the presence of multiple fuzzy rules and multidimensional priors.