Linear systems of first order ordinary differential equations: fuzzy initial conditions

Abstract

 We present two types of fuzzy solutions to linear systems of first order differential equations having fuzzy initial conditions. The first solution, called the extension principle solution, fuzzifies the crisp solution and then checks to see if its α-cuts satisfy the differential equations. The second solution, called the classical solution, solves the fuzzified differential equations and then checks to see if the solution always defines a fuzzy number. Three applications are presented: (1) predator–prey models; (2) the spread of infectious diseases; and (3) modeling an arms race.