SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHM

A system of nonlinear equations is a collection of several interrelated non-linear equations. Currently, systems of nonlinear equations are used not only on crisp but also on fuzzy numbers. A fuzzy number is an ordered pair function that has a degree of membership [0,1]. Meanwhile, a fully fuzzy system of equations is a system of equations that applies fuzzy number arithmetic operations. The solution of non-linear equation systems is usually complicated to solve analytically, so numerical methods are used as an alternative to solve these problems. In this research, the steps to find the solution of nonlinear fully fuzzy equation systems using genetic algorithms are studied, which in the solution process is based on the theory of evolution and natural selection. The solution steps taken are first converting the fully fuzzy system of equations into a system of crisp equations, next constructing the system of strict equations as a multi-objective optimization problem, and lastly solving the optimization problem using a genetic algorithm which includes initialization, evaluation, selection, crossover, and mutation. As illustrations, several cases of nonlinear fully fuzzy and dual fully fuzzy systems of equations on triangular fuzzy numbers and trapezoidal fuzzy numbers are given. The approximate solutions obtained using genetic algorithms produce solutions that are close to their analytic solutions.