Abstract
This chapter discusses techniques and applications of fuzzy set theory to difference and functional equations and their utilization in modeling diverse systems. The chapter provides the motivation for studying various models governed by functional equations in the setting of the fuzzy theory. It presents diverse systems and shows why their study in the fuzzy setting renders a better understanding of their behavior. The chapter introduces the elements of fuzzy theory and deals with a formulation of the method for casting a functional or a difference equation in the fuzzy setting. Furthermore, this chapter turns to the discussion of the method of casting a general equation in the fuzzy setting. The chapter present the steps that are needed to solve the resulting fuzzy equation. The chapter also deals with the Cauchy functional equations and a linear system of difference equations and its fuzzy analog. The chapter concludes that the technique that deals with the fuzzy analog of functional and difference equations may be applied in the study of many other diverse systems that arise in the formulation of problems in engineering, information theory, decision theory, and computer sciences.
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