JOURNAL OF SOFTWARE (JSW)
ISSN : 1796-217X
Volume : 4    Issue : 4    Date : June 2009

Multiplication Operation on Fuzzy Numbers
Shang Gao, Zaiyue Zhang, and Cungen Cao
Page(s): 331-338
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Abstract
A fuzzy number is simply an ordinary number whose precise value is somewhat uncertain. Fuzzy
numbers are used in statistics, computer programming, engineering, and experimental science.
The arithmetic operators on fuzzy numbers are basic content in fuzzy mathematics. Operation of
fuzzy number can be generalized from that of crisp interval. The operations of interval are discussed.
Multiplication operation on fuzzy numbers is defined by the extension principle. Based on extension
principle, nonlinear programming method, analytical method, computer drawing method and
computer simulation method are used for solving multiplication operation of two fuzzy numbers. The
nonlinear programming method is a precise method also, but it only gets a membership value as
given number and it is a difficult problem for solving nonlinear programming. The analytical method
is most precise, but it is hard to α-cuts interval when the membership function is complicated. The
computer drawing method is simple, but it need calculate the α -cuts interval. The computer
simulation method is the most simple, and it has wide applicability, but the membership function is
rough. Each method is illuminated by examples.

Index Terms
fuzzy number, membership function, extension principle, α -cuts; nonlinear programming