Abstract: This paper will discuss algebraic modification of trapezoidal fuzzy numbers with a general form of fully fuzzy numbers is
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with
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is n × n fuzzy matrix,
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fuzzy vector, and
![](http://article.sciencepublishinggroup.com/journal/353/3531037/image004.gif)
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.