Approximate Nonnegative Symmetric Solution of Fully Fuzzy Systems Using Median Interval Defuzzification

We propose an approach for computing an approximate nonnegative symmetric solution of some fully fuzzy linear system of equations, where the components of the coefficient matrix and the right hand side vector are nonnegative fuzzy numbers, considering equality of the median intervals of the left and right hand sides of the system. We convert the m×n fully fuzzy linear system to two m×n real linear systems, one being related to the cores and the other being concerned with spreads of the solution. We propose an approach for solving the real systems using the modified Huang method of the Abaffy-Broyden-Spedicato (ABS) class of algorithms. An appropriate constrained least squares problem is solved when the solution does not satisfy nonnegative fuzziness conditions, that is, when the obtained solution vector for the core system includes a negative component, or the solution of the spread system has at least one negative component, or there exists an index for which the component of the spread is greater than the corresponding component of the core. As a special case, we discuss fuzzy systems with the components of the coefficient matrix as real crisp numbers. We finally present two computational algorithms and illustrate their effectiveness by solving some randomly generated consistent as well as inconsistent systems.