Different Solution Strategy for Solving Type-2 Fuzzy System of Differential Equations with Application in Arms Race Model

Abstract

In this article, we have considered a system of type-2 fuzzy differential equation (ST2FDE) to represent Richardson’s arms race model in type-2 fuzzy environment. A novel theorem on the type-2 fuzzy extension principle is presented here and the model has been solved by the $$gH_2$$\n -differentiability and extension principle techniques with proper numerical illustrations. Four sub-cases were addressed separately for the $$gH_2$$\n -differentiability. The solution obtained by both methods has been defuzzified using the regular weighted point defuzzification technique. Finally, the idea of the arms race model has been successfully implemented to a real-life problem on advertisement spending of competing mobile companies in the type-2 fuzzy environment.