Trapezoidal Approximation of a Fuzzy Number Preserving the Expected Interval and Including the Core

Trapezoidal Approximation of a Fuzzy Number Preserving the Expected Interval and Including the Core

In this paper, we introduce a method to obtain the nearest trapezoidal approximation of fuzzy numbers so that preserving conditions expect interval and include the core of a fuzzy number.

Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval

The problem to find the nearest trapezoidal approximation of a fuzzy number with respect to a well-knownmetric, which preserves the expected interval of the fuzzy number, is completely solved. The previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number. Properties of this new trapezoidal approximation operator are studied. © 2007 Elsevier B.V. ...

Discontinuity of the trapezoidal fuzzy number-valued operators preserving core

Continuity and Additivity of the Trapezoidal Approximation Preserving the Expected Interval Operator

The nearest trapezoidal fuzzy number to a fuzzy number, with respect to a well-known metric and preserving the expected interval, was determined in recent articles. In the present paper the properties of additivity and continuity of the trapezoidal approximation operator are studied. Keywords— Additivity, Approximation, Continuity, Fuzzy number, Trapezoidal fuzzy number.

Trapezoidal and triangular approximations preserving the expected interval

In this paper, an improvement of the nearest trapezoidal approximation operator preserving the expected interval is studied, which is proposed by Grzegorzewski and Mrówka. A formula for computing the improved approximation is presented. Moreover, the nearest triangular approximation operator preserving the expected interval is also investigated. © 2007 Elsevier B.V. All rights reserved.