Fuzzy Difference Equations: The Initial Value Problem
James J. Buckley*, Thomas Feuring** and Yoichi Hayashi***
*Department of Mathematics, University of Alabama at Birmingham Birmingham, Alabama, 35294 USA
**Department of Electrical Engineering and Computer Science, University of Siegen Holderlinstr. 3, 57068 Siegen Germany
***Department of Computer Science, Meiji University 1-1-1 Higashimita, Tama-ku, Kawasaki, 214-8571 Japan
In this paper we study fuzzy solutions to the second order, linear, difference equation with constant coefficients but having fuzzy initial conditions. We look at two methods of solution: (1) in the first method we fuzzify the crisp solution and then check to see if it solves the difference equation; and (2) in the second method we first solve the fuzzy difference equation and then check to see if the solution defines a fuzzy number. Relationships between these two solution methods are also presented. Two applications are given: (1) the first is about a second order difference equation, having fuzzy initial conditions, modeling national income; and (2) the second is from information theory modeling the transmission of information.