Numerical Solution of Intuitionistic Fuzzy Differential Equation by Milne's Predictor - Corrector Method Under Generalised Differentiability

Abstract

Nowadays many real life problems are identified with Fuzzy set theory. The Fuzzy set theory is a useful tool to describe the situation in which data are imprecise or vague or uncertain. This set theory is completely described by its membership function. A membership function of a classical fuzzy set assigns to each element of the universe of discourse a number from the interval $[0, 1]$ to indicate the degree of belongingness to the set under consideration. The degree of non belongingness is just automatically the complement to  "1" of the membership degree. But many times, a human being does not express the degree of non membership as the complement to  "1".There may be some hesitation about the belongingness and non-belongingness. This missing data or hesitation is accomplished by a set known as intuitionistic fuzzy set. In this paper, Milne's Predictor - Corrector method is used for finding numerical solution of an intuitionistic fuzzy differential equation (IFDE). The proposed method is based on the concept of generalized differentiability. IFDE is transformed into four ordinary differential systems and then Milne's Predictor - Corrector method is applied.Also,the convergence and stability of the proposed method is given and its applicability is illustrated by solving a first order IFDE.