Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method

This paper will discuss algebraic modification of trapezoidal fuzzy numbers with a general form of fully fuzzy numbers is with is n × n fuzzy matrix, fuzzy vector, and unknown fuzzy vector. The concept used in this paper is define positive or negative fuzzy numbers determined by the area on the left side of the x-axis and the right side of the x-axis. Furthermore, the concept will be applied to the multiplication of two fully fuzzy trapezoidal numbers to produce a new algebra that can be applied to a system of linear equations. At the end, an example of multiplication two fully fuzzy trapezoidal numbers using the Gauss-Jacobi method will be given. As a result compatible number will be obtained.