Abstract The fuzzy transform setting (F-transform) is proposed as a tool for representation and approximation of type-1 and type-2 fuzzy numbers; the inverse F-transform on appropriate fuzzy partition of the membership interval [0,1] is used to characterize spaces of fuzzy numbers in such a way that arithmetic operations are de…ned and expressed in terms of the F-transform of the results. A typ...

The classical method of numerically computing the Fourier transform of digitizedfunctions in one or in ddimensions is the so-called discrete Fourier transform ( D F T ) , efficiently implemented as Fast Fourier Transform ( F F T ) algorithms. In m n y cases the D F T is not an adequate appmximation of the continuous Fourier transform. The method presented in this contribution provides accurate ...

The fuzzy transform (F-transform) is ubiquitous in different research fields and applications, such as image data compression, mining, knowledge discovery, the analysis of linguistic expressions. As a generalization F-transform, this article, we introduce continuous F-transform its inverse, an integral operator induced by kernel function. Through relation between membership functions kernels, s...

and the inverse Fourier transform is f (x) = 1 2π ∫ ∞ −∞ F(ω)e dω Recall that i = √−1 and eiθ = cos θ+ i sin θ. Think of it as a transformation into a different set of basis functions. The Fourier transform uses complex exponentials (sinusoids) of various frequencies as its basis functions. (Other transforms, such as Z, Laplace, Cosine, Wavelet, and Hartley, use different basis functions). A Fo...

Singularities of the Radon transform of a piecewise smooth function f(x), x e R" , n > 2, are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of f(x) are calculated by applying the Legendre transform to the functions, which appear in the equations of the discontinuity surfaces of the Radon transform of f(x) ; examples are gi...

Following a purely algebraic procedure, we provide an exhaustive classification of local Weyl-invariant scalar densities in dimension D = 8 .

We extend properties of the weak order on finite Coxeter groups to Weyl groupoids admitting a finite root system. In particular, we determine the topological structure of intervals with respect to weak order, and show that the set of morphisms with fixed target object forms an ortho-complemented meet semilattice. We define the Coxeter complex of a Weyl groupoid with finite root system and show ...

We find a formula that relates the Fourier transform of a radial function on R with the Fourier transform of the same function defined on R. This formula enables one to explicitly calculate the Fourier transform of any radial function f(r) in any dimension, provided one knows the Fourier transform of the one-dimensional function t 7→ f(|t|) and the two-dimensional function (x1, x2) 7→ f(|(x1, x...

We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed ...