Solving singularly perturbed differential equations in intuitionistic fuzzy environment

Abstract

In this paper, we introduce and study singularly perturbed intuitionistic fuzzy initial value and boundary value problems. We develop a method based on the intuitionistic fuzzy version of Zadeh's extension principle to compute (α,β)-cuts for solutions to singularly perturbed intuitionistic fuzzy initial value problems. This method is then adapted to compute (α,β)-cuts for solutions to singularly perturbed two-point intuitionistic fuzzy boundary value problems. We present some results regarding the difference in the end-points of (α,β)-cuts of solutions obtained by these methods as t tends to infinity. Furthermore, we apply these methods to find solutions for the perturbed Newton's law of cooling/heating model, RC-circuit model, and spring-mass model in intuitionistic fuzzy environments.

Keywords

• Intuitionistic fuzzy numbers
• Perturbed differential equations
• Extension principle
• Newton's law of cooling/heating
• RC-circuit
• Vibration of spring