Intuitionistic Fuzzy Differential Equations for Economic Cycles: Theory and Indonesian Applications

Efendi Efendi; Admi Nazra; Haripamyu Haripamyu; Mahdivan Syafwan

doi:10.33476/jobs.v6i2.5850

Authors

Efendi Efendi Department of Mathematics and Data Science, Andalas University, West Sumatra
Admi Nazra Department of Mathematics and Data Science, Andalas University, West Sumatra
Haripamyu Haripamyu Department of Mathematics and Data Science, Andalas University, West Sumatra
Mahdivan Syafwan Department of Mathematics and Data Science, Andalas University, West Sumatraindo

https://doi.org/10.33476/jobs.v6i2.5850

Keywords:

second-order intuitionistic fuzzy differential equations, economic cycles, complex economic dynamics, hesitation margin, numerical simulation, Indonesian economy

Abstract

This paper reviews the literature at the intersection of Intuitionistic Fuzzy Differential Equations (IFDEs) and economic modeling, emphasizing their potential to explain economic cycle dynamics under uncertainty. The review identifies a clear research gap, as no existing studies explicitly apply IFDE-based models to economic cycles. To address this gap, the paper synthesizes two related research streams: the mathematical foundations of IFDEs and the application of Intuitionistic Fuzzy Sets (IFS) in economics and finance. The analysis shows that IFDEs extend conventional fuzzy and differential equation models by incorporating membership (µ), non-membership (ν), and hesitation (π) degrees, allowing uncertainty and behavioral ambiguity to be modeled endogenously. Based on this synthesis, a conceptual IFDE-based framework for economic cycle analysis is proposed. Simulation experiments using Indonesia’s macroeconomic data indicate that second-order IFDE models can detect expansion–contraction transition phases 20–30% earlier than classical models and uncover policy-induced uncertainty bands overlooked by standard approaches. These results suggest that IFDEs provide a valuable decision-support tool for policymakers in structurally volatile economies.

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