Type-3 fuzzy logic and Lyapunov approach for dynamic modeling and analysis of financial markets

Chaos theory offers a new way to investigate variations in financial markets data that cannot be obtained with traditional methods. The primary approach for diagnosing chaos is the existence of positive small Lyapunov views. The positive Lyapunov index indicates the average instability and the system's chaotic nature. The negativity indicates the average rate of non-chaoticness. In this paper, a new approach on basis of type-3 fuzzy logic systems is introduced for modeling the chaotic dynamics of financial data. Also, the attracting dimension tests and the Lyapunov views in the reconstructed dynamics are used for examinations. The simulations on case-study currency market show the applicability and good accuracy of the suggested approach.