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 the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...

In the mathematical analysis, there are some theorems and definitions that established for both real and fuzzy numbers. In this study, we try to prove  Bernoulli's inequality in fuzzy real numbers with some of its applications. Also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.

in applications there occur different forms of uncertainty. the twomost important types are randomness (stochastic variability) and imprecision(fuzziness). in modelling, the dominating concept to describe uncertainty isusing stochastic models which are based on probability. however, fuzzinessis not stochastic in nature and therefore it is not considered in probabilisticmodels.since many years t...

in this paper, we introduce a function in order to measure the distancebetween two order intervals of fuzzy numbers, and show that this function isa metric. we investigate some properties of this metric, and finally presentan application. we think that this study could provide a more generalframework for researchers studying on interval analysis, fuzzy analysis andfuzzy decision making.

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.

‎A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert...