Convergence Theorems for Sequences of (S)Fuzzy Integral

The fuzzy integral on product spaces for NSA measures

Fuzzy number-valued triangular norm-based decomposable time-stamped fuzzy measure and integration

Generalized fuzzy integrals of set-valued functions

In this study, the fundamental theory of Kurzweil integral for fuzzy-number-valued functions with two variables will be discussed. Firstly, we provide the concept and fundamental properties of this integral. Then, we prove the characterize theorem of this kind of integral by using support functions. In addition, we obtained the convergence theorem based on weak equi-integrability and dominated convergence theorem for fuzzy Kurzweil integral. Finally, we obtained some properties of primitives of fuzzy Kurzweil integrable functions by weak generalized absolutely continuity. Furthermore, we obtain the relationship between the fuzzy Kurzweil integral and the fuzzy Henstock integral based on the connection of fuzzy Kurzweil integral and the fuzzy Henstock integral in the sense of partial derivatives.

Lattice-valued fuzzy measure and lattice-valued fuzzy integral

The fuzzy integral

Pseudo-integral and generalized Choquet integral

On the convergence of sequences of fuzzy measures and generalized convergence theorems of fuzzy integrals

Fuzzy number fuzzy measures and fuzzy integrals. (I). Fuzzy integrals of functions with respect to fuzzy number fuzzy measures

The convergence of (DG) fuzzy integrals

Controlled convergence theorems for infinite dimension Henstock integrals of fuzzy valued functions based on weak equi-integrability

In the last 20 years, the theoretical as well as practical significance of nonadditive set functions and nonlinear integrals has increasingly been recognized. The Choquet integral with respect to nonadditive monotone set functions is one kind of nonlinear functionals defined on a subspace of all real-valued measurable functions. Unlike the fuzzy integral, which uses the maximum and minimum operators, the Choquet integral is defined via the common addition and multiplication and, therefore, it is a generalization of the classical Lebesgue integral. The convergence of sequences of measurable functions and relevant convergence theorems for sequences of fuzzy integrals have already been investigated by Wang (1984) and Wang and Klir (1992). In an analogous way, we investigate the convergence of sequences of Choquet integrals in this paper. This investigation is, perhaps, even more relevant to practical applications. As an application of convergent theorems, we investigate the stability of a class of nonlinear systems that can be identified by nonnegative monotone set functions with the Choquet integral.

Gaussian quadratures for approximate of fuzzy multiple integrals

On the convergence of the fuzzy valued functional defined by μ-integrable fuzzy valued functions

On retarded fuzzy functional differential equations and nonabsolute fuzzy integrals