Fuzzy transform and least-squares approximation: Analogies, differences, and generalizations
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Polynomial alias higher degree fuzzy transform of complex-valued functions
2018, Fuzzy Sets and SystemsMulti-dimensional fuzzy transform and projection
2017, Fuzzy Sets and SystemsA novel method of multimodal medical image fusion using fuzzy transform
2016, Journal of Visual Communication and Image RepresentationCitation Excerpt :Since FTR deals with vectors and matrices, it has low computational complexity and is faster to implement than other traditional transforms. FTR is invariant with respect to interpolating and least square approximation [33] of input data. It possess noise removing abilities as well as smoothing abilities and is also successful in preserving true image edges, hence is successful in image processing applications.
Cubic B-spline fuzzy transforms for an efficient and secure compression in wireless sensor networks
2016, Information SciencesCitation Excerpt :F–transform was proposed by Perfilieva [13] as a fuzzy approximation technique. It substantially expresses a functional dependency as a linear combination of basic functions and it can be used for the solution of direct and inverse problems or least–squares approximations [14]. The major applications of the F–transform are in image processing, e.g. [15–21].
A new reconstruction from the F-transform components
2016, Fuzzy Sets and SystemsCitation Excerpt :If we additionally demand that the inverse F-transform should be the best approximation of an original function in the space of all linear combinations of basic functions, then an intermediate transformation should be applied to the sequence of the F-transform components and converted to a sequence of coefficients in the best approximation. It is essential that this intermediate transformation can be expressed in terms of the underlying fuzzy partition (see details in [2,15]). By similar reasoning, if we demand the inverse F-transform to be coincident with the original function, we shall change its main parameter – the fuzzy partition.