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2016 | OriginalPaper | Buchkapitel

Higher Degree F-transforms Based on B-splines of Two Variables

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Abstract

The paper deals with the higher degree fuzzy transforms (F-transforms with polynomial components) for functions of two variables in the case when two-dimensional generalized fuzzy partition is given by B-splines of two variables. We investigate properties of the direct and inverse F-transform in this case and prove that using B-splines as basic functions of fuzzy partition allows us to improve the quality of approximation.

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Fußnoten
1
In fact, this way a semi-norm \( \left\| \cdot \right\| _{i,j} \) in \( L_2(A_i \times B_j) \) is defined. The identification of functions f and g, which are almost everywhere equal in the sense \( \left\| f-g \right\| _{i,j} = 0 \), turns \( \left\| \cdot \right\| _{i,j} \) from a semi-norm into a norm and the semi-definite sesquilinear form \( \left\langle \cdot ,\cdot \right\rangle _{i,j} \) into an inner product. Further on, this technical detail will be ignored.
 
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Metadaten
Titel
Higher Degree F-transforms Based on B-splines of Two Variables
verfasst von
Martins Kokainis
Svetlana Asmuss
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-40596-4_54