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Fuzzy transform as an additive normal form
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DOI：10.1016/j.fss.2005.11.008.png)
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In this paper, we recall a class of approximating formulas. Since they arose as a generalization of classical normal forms we denote them by the same term. Moreover, we will show that the fuzzy transform (F-transform) introduced in [Perfilieva, I., Fuzzy approach to solution of differential equations with imprecise data: application to reef growth problem, in: R.V. Demicco, G.J. Klir (Eds.), Fuzzy Logic in Geology, Academic Press, Amsterdam, 2003, pp. 275-300 (Chapter 9), Perfilieva, I., Fuzzy transforms, in: J.F. Peters, A. Skowron (Eds.), Transactions on Rough Sets II. Rough Sets and Fuzzy Sets, Lecture Notes in Computer Science, vol. 3135, 2004, pp. 63-81] as an approximation method for continuous functions can be viewed as a particular case of normal form. Therefore, the results valid for normal forms may be applied to F-transforms as well. (c) 2005 Published by Elsevier B.V.
Keyword:
disjunctive
conjunctive and additive normal forms
fuzzy relation
approximation
fuzzy transform
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