Artikel : ITERATIVE SYSTEM OF FUZZY NUMBER MAX-PLUS LINEAR EQUATIONS

ITERATIVE SYSTEM OF FUZZY NUMBER MAX-PLUS LINEAR EQUATIONS

Prociding International Conference on Mathematics and Natural Science 2008. FMIPA ITB Bandung 28-30 Oktober 2008.

M. Andy Rudhito, Sri Wahyuni, Ari Suparwanto, F. Susilo

Abstract. The activity times in a network are seldom precisely known, and then could be represented into the fuzzy numbers. With max-plus algebra approach, the network dynamic could be analyzed through its iterative system of fuzzy number max-plus linear equations. This paper aims to determine the existence and uniqueness of the solution of the iterative system of fuzzy number max-plus linear equations. The finding shows that if the square matrix of the systems is semidefinite, then the solution exists. The solution of the system could be determined the solution of the alpha-cuts of the system firstly. Based on the Decomposition Theorem, we can determine the membership function of the elements of solution

vectors. Moreover, the solution is unique if the square matrix of the systems is definite.

Keywords: Max-Plus Algebra, System of Linear Equations, Fuzzy Number

FULL PAPER