Scale and move transformation-based fuzzy interpolative reasoning: a revisit

This paper generalises the previously proposed interpolative reasoning method to cover the interpolations involving the complex polygon, Gaussian or other bell-shaped fuzzy membership functions. This can be achieved by the generality of the proposed scale and move transformations. The method works by first constructing a new inference rule via manipulating the two given adjacent rules, and then by using scale and move transformations to convert the intermediate inference results into the final derived conclusions. This generalised method has two advantages, thanks to the elegantly proposed transformations: 1) It can easily handle the interpolation of multiple antecedent variables with simple computation; and 2) It guarantees the uniqueness as well as normality and convexity of the resulting interpolated fuzzy sets. Numerical examples are provided to demonstrate the use of this method.