in this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{ax_n+x_{n-1}}{b+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $a, b$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.

In this paper, we propose the new concept of optimal solution for fuzzy variational problems based on the possibility and necessity measures. Inspired by the well–known embedding theorem, we can transform the fuzzy variational problem into a bi–objective variational problem. Then the optimal solutions of fuzzy variational problem can be obtained by solving its corresponding biobjective variatio...

In this paper fuzzy piecewise cubic interpolation is constructed for fuzzy data based on B-spline basis functions. We add two new additional conditions which guarantee uniqueness of fuzzy B-spline interpolation.Other conditions are imposed on the interpolation data to guarantee that the interpolation function to be a well-defined fuzzy function. Finally some examples are given to illustrate the...

A novel variational algorithm is developed for video inpainting. Within a Bayesian framework, using standard maximum a posteriori to variational formulation rationale, we derive a minimum energy formulation for the estimation of a reconstructed sequence as well as motion recovery. From the EulerLagrange Equations, we propose a full multiresolution algorithm in order to compute a good local mini...

this paper investigates the stability analysis of fuzzy relational dynamic systems. a new approach is introduced and a set of sufficient conditions is derived which sustains the unique globally asymptotically stable equilibrium point in a first-order fuzzy relational dynamic system with sumproduct fuzzy composition. this approach is also investigated for other types of fuzzy relational composit...

Fuzzy queries addressed to a relational database management system are based on the expression of user preferences which leads to obtain more appropriate answers. Fuzzy set theory provides powerful tools to define such conditions (fuzzy conditions). In this context, it is possible to consider fuzzy bipolar conditions which are made of two fuzzy sets to describe user's preferences: i) a fuzzy co...

Deformable models of elastic structures have been proposed for use in image analysis. Previous work has used a variational approach, based on the EulerLagrange theory. In this paper an alternative mathematical treatment is introduced, based on a direct minimisation of the underlying energy integral using the Finite Element Method. The method is outlined and demonstrated, and its principal advan...

Using the reformulation in divergence form of the EulerLagrange equation for the Willmore functional as it was developed in the second author’s paper [Riv2], we study the limit of a local Palais-Smale sequence of weak Willmore immersions with locally square-integrable second fundamental form. We show that the limit immersion is smooth and that it satisfies the conformal Willmore equation: it is...

We give examples of systems of Partial Differential Equations that admit non-trivial, Lipschitz and one-homogeneous solutions in the form u(R, θ) = Rg(θ), where (R, θ) are plane polar coordinates and g takes values in R, m ≥ 2. The systems are singular in the sense that they arise as the EulerLagrange equations of the functionals I(u) = ∫ B W (x,∇u(x)) dx, where DFW (x, F ) behaves like 1 |x| a...