Application of Runge-Kutta method for finding multiple numerical solutions to intuitionistic fuzzy differential equations

Abstract

The present study is aimed to discuss multiple numerical solutions to first order ordinary differential equation which is intuitionistic fuzzy in nature, under the concept of generalised differentiability. The first order intuitionistic fuzzy differential equation which has been taken for the present study, is changed into four systems of ordinary differential equations by the (α, β)-cut representation of an intuitionistic fuzzy set. After the transformation, each system contains two pair of equations; one is for membership function and the other for non-membership function. Then, the fourth order Runge-Kutta method is applied in each pair and the competence of the method over Euler method and Modified Euler method are shown by solving a real time problem.