in this paper, we apply the  homotopy analysis method (ham) for solving fuzzy  linear systems and present  the necessary and sufficient conditions for the convergence of series solution obtained via the ham. also, we present a new criterion for choosing a proper value of convergence-control parameter $hbar$ when the ham is applied to linear system of equations. comparisons are made between the ...

In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equations of the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and convert a two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equations of the second kind in crisp case. We can use Adomian decomposition method for n...

An orthogonal approach to the fuzzification of both multisets and hybridsets is presented. In particular, we introduce $L$-multi-fuzzy and$L$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. In addition, we study the properties ofthese structures. Also, the usefulness of these structures is examined inthe framework of mechanical multiset proc...

The purpose of this paper is to introduce finite convergence sequences and functions preserving convergence of series in fuzzy n-normed spaces.

In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our cat...

We prove the basic fuzzy Korovkin theorem via a fuzzy Shisha– Mond inequality given here. This determines the degree of convergence with rates of a sequence of fuzzy positive linear operators to the fuzzy unit operator. The surprising fact is that only the real case Korovkin assumptions are enough for the validity of the fuzzy Korovkin theorem, along with a natural realization condition fulfill...

We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the Hausdorff distances of the α-cuts of the fuzzy sets. We do it by dividing this metric into its lower and upper quasipseudometric parts. This characterization is given in the more general context with no assumption on the fuzzy sets. Furthermore, motivated from the theory of Convex Analysis, we also...

A new, variable structure systems theory based, algorithm has been developed for on-line training of fuzzy-neural networks. Such computationally intelligent structures are widely used for modeling, identification and control of nonlinear dynamic systems. The algorithm is applicable to fuzzy rule-based neural nets of Takagi-Sugeno-Kang type with a scalar output. Its convergence is established an...

In this paper we intend to offer new numerical methods to solvethe fuzzy Fredholm- Volterra integral equations of the firstkind $(FVFIE-1)$. Some examples are investigated to verify convergence results and to illustrate the efficiently of the methods.