Fuzzy interpolation and extrapolation using shift ratio and overall weight measurement based on areas of fuzzy sets

Conventional fuzzy reasoning methods requires compact fuzzy rule base to infer a result, but due to incomplete data or lack of expertise knowledge, compact rule bases are not always available. Fuzzy interpolation methods have been widely researched to reasonably allow the interpolation a fuzzy result using the nearest available rules. Chang et al. [24] proposed a novel interpolation method which employs the weighted average on the area of the fuzzy set. However, the interpolated observation does not fully represent the actual observation that is given. In our proposed extension to this method, a different weight computation and a shift technique are included to ensure that the normal point of the observation and the normal point of the interpolated observation are mapped together. This weight computation and shift technique has also enabled the capability of extrapolation to be performed implicitly.