This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...

Distinct elements (F0). In this note we will consider the distinct elements problem, also known as the F0 problem, defined as follows. We are given a stream of integers i1, . . . , im ∈ [n] where [n] denotes the set {1, 2, . . . , n}. We would like to output the number of distinct elements seen in the stream. As with Morris’ approximate counting algorithm, our goal will be to minimize our space...

Fuzzy rule-based edge detection using multiscale edge images is proposed. In this method, the edge image is obtained by fuzzy approximate reasoning from multiscale edge images which are obtained by derivative operators with various window sizes. The effect of utilizing multiscale edge images for edge detection is already known, but how to design the rules for deciding edges from multiscale edge...

Nowadays, nonlinear control is a very important task because machines are playing an ever increasing role in life. Lyapunov’s 2nd method is a popular tool by the use of which various controllers can be designed like adaptive neural networks, fuzzy controllers, and neuro-fuzzy solutions, or the sliding mode controllers and the well-known PID feedback controllers. Robust Fixed Point Transformatio...

In this paper, we introduce the concept of best proximal contraction theorems in non-Archimedean fuzzy metric space for two mappings and prove some proximal theorems. As a consequence, it provides the existence of an optimal approximate solution to some equations which contains no solution. The obtained results extend further the recently development proximal contractions in non-Archimedean fuz...

Solitary wave solutions to the Broer-Kaup equations and approximate long water wave equations are considered challenging by using the rst integral method.The exact solutions obtained during the present investigation are new. This method can be applied to nonintegrable equations as well as to integrable ones.

on the basis of a reproducing kernel space, an iterative algorithm for solving the one-dimensional linear and nonlinear schrödinger equations is presented. the analytical solution is shown in a series form in the reproducing kernel space and the approximate solution is constructed by truncating the series. the convergence of the approximate solution to the analytical solution is also proved. th...

the hybrid fuzzy differential equations have a wide range of applications in science and engineering. we consider the problem of nding their numerical solutions by using a novel hybrid method based on fuzzy neural network. here neural network is considered as a part of large eld called neural computing or soft computing. the proposed algorithm is illustrated by numerical examples and the resu...