Most of the existing approaches for fuzzy reliability analysis are based on fuzzy probability.  The aim of this paper is to describe fuzzy reliability using fuzzy differential equation. The reliability of a system in real world applications is affected by some uncertain parameters. Fuzzy reliability is a way to present the reliability function uncertainly using fuzzy parameters. In the proposed...

In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship between integrability, D-representability, and strict differentiability. In addition to this, we show that on any separable Banach space there is a significant family of locally Lipsc...

We provide solution of first order linear fuzzy differential equations by variation of constant formula. The differentiability concept used in this paper is the strongly generalized differentiability since a fuzzy differential equation under this differentiability can have decreasing legth of support function. Under some conditions we provide solution with decreasing support and so the behaviou...

Peano differentiability generalizes ordinary differentiability to higher order. There are two ways to define Peano differentiability for functions defined on non-open sets. For both concepts, we investigate the question under which conditions a function defined on a closed set can be extended to a Peano differentiable function on the ambient space if the sets and functions are definable in an o...

Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. We interpret a fuzzy differential equation by using the strongly generalized differentiability. Also one concrete application for ordinary fuzzy differential equation with fuzzy input data...

Recently, in their paper, the authors generalized notion of differentiability by defining it for all points functional domain (not only interior points) which can be considered meaningful. In this continuous is introduced differentiable function f:X→Rm with a not necessarily open X⊆Rn; i.e., continuity mapping df:X→HomRn,Rm considered. addition to introducing context approach differentiability,...

• Banach-Alaoglu: compactness of polars • Variant Banach-Steinhaus/uniform boundedness • Second polars • Weak boundedness implies boundedness • Weak-to-strong differentiability The comparison of weak and strong differentiability is due to Grothendieck, although the original sources are not widely available.

New elements of calculus on a complete real closed non-Archimedean field extension F of the real numbers R will be presented. It is known that the total disconnectedness of F in the topology induced by the order makes the usual (topological) notions of continuity and differentiability too weak to extend real calculus results to F . In this paper, we introduce new stronger concepts of continuity...

We study Lipschitz differentiability spaces, a class of metric measure spaces introduced by Cheeger in [8]. We show that if an Ahlfors regular Lipschitz differentiability space has charts of maximal dimension, then, at almost every point, all its tangents are uniformly rectifiable. In particular, at almost every point, such a space admits a tangent that is isometric to a finite-dimensional Bana...

Let Kn be the Lorentz/second-order cone in R. For any function f from R to R, one can define a corresponding function f soc(x) on R by applying f to the spectral values of the spectral decomposition of x ∈ R with respect to Kn. We show that this vector-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Fréchet differentiabi...