Multiplication Operation on Fuzzy Numbers

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.