Spline interpolation between hyperspaces of convex of fuzzy sets
|Title:||Spline interpolation between hyperspaces of convex of fuzzy sets|
|Journal:||Fuzzy Sets and Systems|
|Pages:||2472 - 2481|
A fuzzy if-then rule base may be viewed as a partial function between universes of fuzzy sets. For the construction of a fuzzy inference module, this partial function needs to be extended to a total one.
Here, we propose a new method how to do so, making use of the method of smoothing splines. To this end, we identify the fuzzy sets with elements of a finite-dimensional real parameter space in an approximate way, using Perfilieva's fuzzy transforms. We then determine a function between two such parameter spaces by requiring that it reproduces the rule base as precise as possible and that it minimizes a parameter depending on its smoothness.