Efficient Decomposition of Large Fuzzy Functions and Relations
Paul Burkey, Marek A. Perkowski · PDXScholar (Portland State University) · 2003
This paper presents a new approach to decomposition of fuzzy functions. A tutorial background on fuzzy logic representations is first given to emphasize next the simplicity and generality of this new approach. Ashenhurst-like decomposition of fuzzy functions was discussed in [3] but it was not suitable for programming and was not programmed. In our approach, fuzzy functions are converted to multiple-valued functions and decomposed using an mv decomposer. Then the decomposed multiple-valued functions are converted back to fuzzy functions. This approach allows for Curtis-like decompositions with arbitrary number of intermediate fuzzy variables, that have been not presented for fuzzy functions by the previous authors. Extension of the method to fuzzy relations is also shown. The new approach is suitable for Machine Learning.