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: