Spline interpolation between hyperspaces of convex of fuzzy sets
From Mathfuzzlog
Authors: |
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Title: | Spline interpolation between hyperspaces of convex of fuzzy sets | ||
Journal: | Fuzzy Sets and Systems | ||
Volume | 157 | ||
Number | |||
Pages: | 2472 - 2481 | ||
Year: | 2006 |
Abstract
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.