# 20Differential Equations with Fuzzy Uncertainty

## 20.1 Introduction

In this chapter, a system of fuzzy linear differential equations is studied. Recently, a new technique using the triangular fuzzy numbers (TFNs) [1,2] is illustrated to model the fuzzy linear differential equations. The solution of linear differential equations with fuzzy initial conditions may be studied as a set of intervals by varying α‐cut. The term fuzzy differential equations were first introduced by Chang and Zadeh [3,4]. Later, Bede introduced a strongly generalized differentiability of fuzzy functions in Refs. [5,6]. Recently, various researchers viz. Allahviranloo et al. [7], Chakraverty et al. [8], Tapaswini and Chakraverty [9] have studied fuzzy differential equations. As such, a geometric approach to solve fuzzy linear systems of differential equations have been studied by Gasilov et al. [ 1 , 2 ,10,11]. The difference between this method and the methods offered to handle the system of fuzzy linear differential equation is that at any time the solution consists a fuzzy region in the coordinate space. In this regard, the following section presents a procedure to solve fuzzy linear system of differential equations.

## 20.2 Solving Fuzzy Linear System of Differential Equations

### 20.2.1 α‐Cut of TFN

To understand the preliminary concepts of fuzzy set theory, one can refer Refs. [12,13]. There exist various types of fuzzy numbers and among them the TFN is found to be mostly used by different authors.

A TFN ...

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