Type-2 Fuzzy Initial Value Problems for Second-order T2FDEs

TL;DR

This paper extends the solution methods for type-2 fuzzy initial value problems from first-order to second-order differential equations, introduces clearer notation, and proposes new Hukuhara differential symbols for better understanding.

Contribution

It provides a novel solution method for second-order T2FIVPs and introduces clearer notation and Hukuhara differential symbols in type-2 fuzzy theory.

Findings

Solution method for second-order T2FIVPs developed

New notations for type-2 fuzzy theory proposed

Hukuhara differential symbols introduced for clarity

Abstract

Type-2 fuzzy differential equations (T2FDEs) of order 1 are already known and the solution method of type-2 fuzzy initial value problems (T2FIVPs) for them was given by M. Mazandarani and M. Najariyan \cite{MN} in 2014. We give the solution method of second-order T2FIVPs in this paper. Furthermore, we would like to propose new notations for type-2 fuzzy theory where symbols tend to be complicated and misleading. In particular, the Hukuhara differential symbols introduced experimentally in this paper will give us clearler meanings and expressions.