COMPLETING FUZZY IF-THEN RULE BASES BY MEANS OF SMOOTHING SPLINES
Thomas Vetterlein, Martin Štěpnička · International Journal of Uncertainty Fuzziness and Knowledge-Based Systems · 2006
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.