We consider Volterra and Fredholm integral equations for functions with values in L-spaces. This includes corresponding problems for set-valued functions, fuzzy-valued functions and many others. We prove theorems of existence and uniqueness of the solution for such equations and suggest some algorithms for finding approximate solutions. We get initial results in the approximation of functions w...

The purpose of this paper is to give convergence theorems both for closed convex set valued and relative fuzzy valued martingales, and suband supermartingales. These kinds of martingales, suband super-martingales are the extension of classical real valued martingales, suband super-martingales. Here we compare two kinds of convergences, in the Hausdor metric and in the Kuratowski-Mosco sense. We...

This article studies the determination of the rate of convergence to the unit of each of three newly introduced here multivariate fuzzy perturbed normalized neural network operators of one hidden layer. These are given through the multivariate fuzzy modulus of continuity of the involved multivariate fuzzy number valued function or its high order fuzzy partial derivatives and that appears in the...

The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing  m-almost everywhere convergence, where  m...

In this paper we establish a Tauberian condition under which convergence follows from H"{o}lder summability of sequences of fuzzy  numbers.

In this note, by considering the notions of the intuitionistic general L-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{L}$, there exists a minimal intuitionistic general L-fuzzy automaton recognizing $mathcal{L}$.We prove that the minimal intuitionistic general L-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, be...

In this paper, we introduce the concepts of fuzzy complex number, the operations of fuzzy complex number, the concepts of convergence for fuzzy complex number-valued sequence and the fuzzy complex numbervalued mapping. Then the fixed point of fuzzy complex number-valued mapping is discussed, some existent theorems of this mapping are given. It will establish a foundation for researching fuzzy c...

Recently we proposed a new type of fuzzy integrals defined over complete residuated lattices. These integrals are intended for the modeling of type ⟨1, 1⟩ fuzzy quantifiers. An interesting theoretical question is, how to introduce various notions of convergence of this type of fuzzy integrals. In this contribution, we would like to present some results on strong and pointwise convergence of the...

Pattern search learning is known for simplicity and faster convergence. However, one of the downfalls of this learning is the premature convergence problem. In this paper, we show how we can avoid the possibility of being trapped in a local pit by the introduction of stochastic value. This improved pattern search is then applied on a recurrent type neuro-fuzzy network (ANFIS) to solve time seri...

We are concerned with the development of a K−step method for the numerical solution of fuzzy initial value problems. Convergence and stability of the method are also proved in detail. Moreover, a specific method of order 4 is found. The numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.