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

Full Text: PDF (633 KB)

**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

ISSN : 1796-217X

Volume : 4 Issue : 4 Date : June 2009

Page(s): 331-338

Full Text: PDF (633 KB)

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.