Generalized Seikkala Differentiability and its Application to Fuzzy initial value problem

TL;DR

This paper introduces a new generalized Seikkala derivative for fuzzy-valued functions, enabling solutions to fuzzy initial value problems that were not possible with traditional Seikkala differentiability.

Contribution

The paper proposes a novel generalized Seikkala derivative that broadens the class of fuzzy functions differentiable in the Seikkala sense and applies it to solve fuzzy initial value problems.

Findings

Many fuzzy functions not Seikkala differentiable are generalized Seikkala differentiable.

The proposed derivative helps find solutions to fuzzy initial value problems.

Properties of the generalized Seikkala differentiability are discussed.

Abstract

This paper proposes a new generalized Seikkala derivative (gS-derivative) of a fuzzy-valued function. We see that, there are many elementary fuzzy-valued functions which occur frequently as solution of fuzzy differential equation, are not Seikkala differentiable but they are generalized Seikkala differentiable. We discuss some of the properties of proposed differentiability. Using gS-differentiability, we find the solution of fuzzy initial value problem.