A general interpolation technique in fuzzy rule bases with arbitrary membership functions

Abstract

Presents a general multidimensional fuzzy rule interpolation method. This method, compared to the existing interpolation methods, can be applied to arbitrary type of fuzzy sets, and does not require convex and normal sets in the rules. Another important difference is the new method gives an interpretable conclusion in case, unlike the previously published methods. As a matter of course, to apply arbitrary type of sets, the general method makes calculation necessary for every point of the sets. A special method, based on the theory of the general method, is introduced for application in practice, which needs low computational capacity. The specialised method uses three of the most wide spread set types in practice: the crisp, the triangular, and the trapezoidal fuzzy sets. The difference between the new and the former methods is pointed out by examples and the results of different formal methods.