Chaotic Logistic Map Forecast using Fuzzy Time Series

TL;DR

This paper proposes a method to forecast the Logistic Chaotic Map using Fuzzy Time Series, leveraging AIC to optimize fuzzy set intervals, addressing the challenges of modeling sensitive chaotic systems.

Contribution

It introduces a novel approach combining Fuzzy Time Series with AIC for effective forecasting of chaotic logistic maps.

Findings

Fuzzy Time Series effectively models chaotic logistic maps.

AIC helps optimize fuzzy set intervals for better forecasts.

The method demonstrates robustness in chaotic system prediction.

Abstract

This paper deals with the problem of forecast the Logistic Chaotic Map using Fuzzy Times Series (FTS). Chaotic Systems are very sensible to changes in its parameters and in the initial conditions, turning them into hard systems to model and forecast. In this case, we relay in the robustness of Fuzzy Time Series to model and forecast the logistic map. We use the Akaike Information Criterion (AIC) as an index to determine the number of sub intervals for the definition of the fuzzy set.