In this paper, first order linear homogeneous difference equation is evaluated in fuzzy environment. Difference equations become more notable when it is studied in conjunction with fuzzy theory. Hence, here amelioration of these equations is demonstrated by three different tactics of incorporating fuzzy numbers.Subsequently, the existence and stability analysis of the attained solutions of fuzzy difference equations (FDEs) are then discussed under different cases of impreciseness. In addition, considering triangular and generalized triangular fuzzy numbers, numerical experiments are illustrated and efficient solutions are depicted, graphically and in tabular form.

In this paper we execute the solution procedure for second order linear fuzzy difference equation by Lagrange's multiplier method. In crisp sense the difference equation are easy to solve, but when we take in fuzzy sense it forms a system of difference equation which is not so easy to solve. By the help of Lagrange's multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.

In this chapter we solve linear difference equation with intuitionistic fuzzy initial condition. All possible cases are defined and solved them to obtain the exact solutions. The intuitionistic fuzzy numbers are also taken as trapezoidal intuitionistic fuzzy number. The problems are illustrated by two different numerical examples.