Approximations of Fuzzy Numbers by General Trapezoidal Fuzzy Numbers - Innovative Management in Information and Production - page 364

Approximations of Fuzzy Numbers by General
Trapezoidal Fuzzy Numbers

Chi-Tsuen Yeh and Pei-Hau Lin

Abstract Recently, many scholars investigated interval, triangular, trapezoidal,
and semi-trapezoidal approximations of fuzzy numbers. These researches can be
grouped into two classes: one is to study approximations of fuzzy numbers without
any constraint; the other one is to study approximations preserving some attributes.
In this paper, we propose two general approximations of fuzzy numbers named
general f-trapezoidal approximation and general f-triangular approximation. The
two approximations will generalize those approximations of the first class under
the Euclidean distance. Finally, we propose an efficient algorithm for computing the
proposed approximations and illustrate by an example.

Keywords Trapezoidal fuzzy numbers ￿ Triangular approximation ￿ Semi-

trapezoidal approximation ￿ Hilbert space

1 Introduction

Fuzzy intervals play important roles in many applications, such as fuzzy control
systems, discrete dynamic systems, or intelligence technology. In practice, we often
used fuzzy intervals to represent uncertain or incomplete information. For shorten-
ing computation time, we usually approximate general fuzzy intervals by interval,
triangular, trapezoidal, and/or semi-trapezoidal fuzzy numbers, so as to simplify
calculations. In addition, ranking or ordering fuzzy numbers is a fundamental
problem of fuzzy optimization or fuzzy decision making. Another application is
to make the comparison of fuzzy numbers by using the order relations defined
on the approximations of fuzzy numbers. Therefore, how to approximate a fuzzy