# Linear System of Equations with Trapezoidal Fuzzy Numbers

Equation 3.63 with TRFN may be converted into left monotonically increasing and right monotonically decreasing continuous functions over [0, 1]. Then, it may be solved by the following algorithm.

**Algorithm 3.2**

Step 1. Convert the TRFN into the following form:

Step 2. Now, the intervals are transferred into the crisp form using the transformation given in Equations 3.44 through 3.47.

Step 3. We get a system of linear equations obtained with crisp values. This system may be solved by any standard method used for crisp values.

Step 4. Finally, the solution vector is

**Example 3.4**

Here, we consider the following system of linear equations with the TRFN Equation 3.67 may be transferred into the following а-cut form:

Using Algorithm 3.2, we get the following solution:

**Example 3.5**

Finally, the fully fuzzy system of linear equations with TRFN is considered:

Again, with the help of the а-cut, Equation 3.69 becomes

Finally, solving Equation 3.70 using Algorithm 3.2, we get the solution vector: