This paper presents a method of using the so-called „bacterial algorithm” [4, 5] for extracting the fuzzy rule base from a training set. The class of membership functions is restricted to trapezoidal, as it is general enough and widely used. The pseudobacterial genetic algorithm (PBGA) is show. The PBGA optimises the trapezoidal membership functions in the rules by the bacterial mutation operat...

In this paper, an integral equation for the kth moment function of a geometric process is derived as generalization lower-order moments process. We propose general solution to solve by using numerical method, namely trapezoidal integration rule. The reduced equations which will be given third and fourth functions compute skewness kurtosis To illustrate we assume gamma, Weibull lognormal distrib...

1 Motivation We want to numerically approximate coefficients in a Fourier series. The first step is to see how the trapezoidal rule applies when numerically computing the integral (2π) −1 2π 0 F (t)dt, where F (t) is a continuous, 2π-periodic function. Applying the trapezoidal rule with the stepsize taken to be h = 2π/n for some integer n ≥ 1 results in (2π) −1 2π 0 F (t)dt ≈ 1 n n−1 j=0 Y j , ...

Numerical quadrature is another name for numerical integration, which refers to the approximation of an integral ́ f (x)dx of some function f (x) by a discrete summation ∑wi f (xi) over points xi with some weights wi. There are many methods of numerical quadrature corresponding to different choices of points xi and weights wi, from Euler integration to sophisticated methods such as Gaussian quad...

A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems ...

This paper provides a product integration rule for highly oscillating integrands of the type ∫−aae−iω(x−y)f(x)dx,a>0,i=−1,y∈[−a,a],ω∈R+,based on approximation f by means Generalized Bernstein polynomials B̄m,ℓf. The involves samples at m+1 equally spaced points [−a,a], and differently from classical polynomials, suitable modulation parameter ℓ∈N allows to increase accuracy rule, as smoothness in...

Abstract. A verified automatic integration algorithm is proposed for calculating contour integration over complex field using numerical computations. The proposed algorithm is based on trapezoidal rule for angle. The error analysis of the method have been presented by several authors, however, these investigations are done basically for examining the rates of convergence, and several constants ...

We prove a Murnaghan–Nakayama rule for k-Schur functions of Lapointe and Morse. That is, we give an explicit formula for the expansion of the product of a power sum symmetric function and a k-Schur function in terms of k-Schur functions. This is proved using the noncommutative k-Schur functions in terms of the nilCoxeter algebra introduced by Lam and the affine analogue of noncommutative symmet...

We study a division problem which allocates resources to agents with single-peaked preferences, who have a right to decide for the participation. We introduce the generalized uniform rule which assigns resources to agent as equally as possible subject to the participation constraints. We present various characterizations of the generalized uniform rule on the basis of separability principle.

Using Hayashi's inequality, an Iyengar type inequality for functions with bounded second derivative is obtained. This result improves a similar result from [N. Elezovi´c, J. Pečari´c, Steffensen's inequality and estimates of error in trapezoidal rule, Appl. In 1938 Iyengar proved the following inequality in [1]: Theorem 1. Let function f be differentiable on [a, b] and | f (x)| ≤ M. Then 1 b − ...