In this paper, a new approach is presented to fit a robust fuzzy regression model based on some fuzzy quantities. In this approach, we first introduce a new distance between two fuzzy numbers using the kernel function, and then, based on the least squares method, the parameters of fuzzy regression model is estimated. The proposed approach has a suitable performance to present the robust fuzzy model in the presence of different types of outliers. Using some simulated data sets and some real data sets, the application of the proposed approach in modeling some characteristics with outliers, is studied.

Kernel method is one of the most common nonparametric density estimation and recently B-spline is used for estimation of a probability density function. These two methods in some how depend on selecting a smoothing parameter that has an important effect on precision of the estimators. In this paper, we consider kernel and B-spline methods of density estimation and smoothing parameter selection for these two methods. Then, the accuracy of the obtained estimators is compared by their mean square errors. Also, the effect of the number and dispersion of data on precision of estimators are studied. The results show that for a symmetric probability density, if the dispersion of data increases, the precision of both estimators decreases, while, for an asymmetric probability density function, the precision of the estimators increases for dispersion data.

In this paper, we will present a new method for solving a class of two-dimensional linear Volterra integral equation of the second kind with weakly singular kernel from Abel type in the reproducing kernel space. The reproducing kernel function is discussed in detail. Weak singularity of problem is removed by applying integration by parts. Further, improper integral belongs to L_2 (Ω ). In our method the exact solution ϕ (x, t) is represented in the form of series in the reproducing kernel space W(ω ), and the approximate solution ϕ _n (x, t) is constructed via truncating the series to n terms. Convergence analysis of the method is proved in detail. Some numerical examples are also studied to demonstrate the efficiency and accuracy of the presented method. The obtained results show that the error of the approximate solution is monotone decreasing in the sense of the norm of W(ω ), when increasing the number of the nodes. Also, that indicate the method is simple and effective. It turns out that this method is valid.

Membership function based on probability density functionچندین روش به منظور برآورد تابع چگالی احتمال وجود دارد. از سوی دیگر، در نظریه مجموعه هایفازی یکی از روش های ساختن تابع عضویت بر پایه ی مجموعه داده، روش مبتنی بر تابع چگالی احتمال است.با توجه به روش های متداول در برآورد تابع چگالی، این مسئله می تواند به محاسبه انواع تابع عضویت بر پایهیک مجموعه داده منجر شود. در این مقاله، برخی از این روش ها بیان و با مثال عددی تشریح می شوند..