Recently, many scholars investigated interval, triangular, and trapezoidal approximations of fuzzy numbers. These researches can be grouped into two classes: the Euclidean distance class and the non-Euclidean distance class. Most approximations in the Euclidean distance class can be calculated by formulas, but calculating approximations in the other class is more complicated. In this paper, we ...

In this paper, we consider the width invariant trapezoidal and triangularapproximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserv...

Abstract The well-known Karush-Kuhn-Tucker theorem can be used, as in the fuzzy case, to find the trapezoidal approximation of a given intuitionistic fuzzy number. The method is quite technical such that obtaining the trapezoidal approximation of an intuitionistic fuzzy numbers from the trapezoidal approximation of a fuzzy number is proposed in the present paper. Among the advantages of this me...

We derwe and analyze the properties of Euler-Maclaurin expansions for the differences / ~ / s'(log.~) " /(.~. Qilfj is a combination of one-dimensional generalized trapezoidal rule approximations. 1. ~NlKOL)UC110N In this work we are intcrcstcd in deriving Euler-Maclaurin expansions for the singular double integrals where W(X) = x'(Iog x)'. s >-l.s'=O. 1. (1.3) and f(.~,~l) is as many times dif...

Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. New algorithms for calculating the proper trapezoidal approximation of fuzzy numbers with respect to the distance based on bi-symmetrical weighted functions are proposed. It is shown that the adequate approximation operator is chosen with respect both to the global spread of a fuzzy numbe...

The problem of the nearest approximation of fuzzy numbers by piecewise linear 1-knot fuzzy numbers is discussed. By using 1-knot fuzzy numbers one may obtain approximations which are simple enough and flexible to reconstruct the input fuzzy concepts under study. They might be also perceived as a generalization of the trapezoidal approximations. Moreover, these approximations possess some desira...

The numerical computation of P{X > x} can be accomplished in a variety of ways. An appealing class of methods may be derived from the contour integral connecting P{X > x} and its Fourier representation. Statisticians have largely focused on deriving saddlepoint approximations for this contour integral. The accuracy of such approximations is generally understood in vague terms only and, perhaps ...

In this paper we propose a method for computing the Faddeeva function $w(z) := {e}^{-z^2}{erfc}(-{i}\,z)$ via truncated modified trapezoidal rule approximations to integrals on real line. Our s...

This paper focuses on modelling fuzzy numbers with meaningful membership functions. More precisely, it proposes a method to construct trapezoidal fuzzy number approximations from raw discrete data. In many applications, input information is numerical, and therefore, particular fuzzy sets, such as fuzzy numbers, hold great interest and relevance in managing data imprecision and vagueness. The pr...