A PRELIMINARY STUDY OF NUMERICAL SOLUTIONS FOR FULLY FUZZY LINEAR SYSTEM

Abstract

Fuzzy linear system (FLS) is differs from conventional linear system which is the coefficients in the linear equation are fuzzy. Fully fuzzy linear system (FFLS) is one of the important kinds of FLS which all the parameters are fuzzy numbers. This study begins with description on basic concept of Fuzzy Theory, FLS, and FFLS. This study are discussed the decomposition and extended decomposition methods in order to solve different type of FFLS problems. Decomposition method is a method to solve FFLS problems that not containing constraints whereas extended decomposition method is applicable to solve FFLS problems that contain constraints. By making use of the MATLAB programming, MAPLE programming, and LINGO solver of both methods, it speeded up the time of computation of simplex and Doolittle LU methods. The objective of the research is to compare the method of FFLS between decomposition and extended decomposition methods of FFLS equation. Three examples of FFLS problem have been chosen in this study. It is interesting that the solution obtained in Example 1 and Example 2 usually same for both methods and can be solved successfully meanwhile Example 3 only can be solved by extended decomposition method. This results show that extended decomposition method performs better than decomposition method.