A New Approach to Solve the Fuzzy Nonlinear Unconstraint Optimization Problem

This paper investigates fuzzy nonlinear system equations using an optimization approach. Here, the inner-outer direct search technique is used with fuzzy coefficients and vectors to quantify the uncertain solution. The fuzzy nonlinear system of equations is converted into an unconstrained fuzzy multivariable optimization problem with preserving the operating constraints. Then developed fuzzy inner-outer direct search is applied. The developed algorithm is demonstrated through an example problem. The obtained uncertain solutions are depicted and compared with the special case. The results are found to be in good agreement when the membership values are unity.