Fuzzy integrals and linearity

Convergence theorems for monotone measures

“…Some of the results discussed in this overview are related to the Choquet integral [5] and the Sugeno integral [86] which are two prominent examples of nonlinear integrals (see also [2,7,30,61,73,96]). They are deeply discussed in the overview papers [14,27] in this issue.…”

Optimizing Signal De-Noising Algorithm for Acoustic Emission Leakage of Wavelet

“…The structure of the algorithm is simple and the calculation is speedy. Thus, the lifting method has become mainstream method of calculating scatter wavelet transformation [14][15][16]. The traditional wavelet transformation algorithm (Mallat algorithm) adopts a method of convoluting input signal and high plus low pass filters to realize separation of high frequency and low frequency information.…”

A Quantile Approach to Integration with Respect to Non-additive Measures

“…We follow the approach proposed by Greco in [13] and more recently by Ban and Fechete in [2] for lattice-valued measures and integrals and we refer to [16] and [17] for the standard case. Let (A, A) be a measurable space and L a a bounded lattice.…”

“…We denote by M the set of all fuzzy measures on A with values in L and by F the set of the measurable functions f : A → L. Following [15] and [17] we give the following definition. …”