RETRACTION:Optimal type-3 fuzzy control and analysis of complicated financial systems

Abstract

The financial systems have complicated dynamics and are perturbed by various uncertainties and disturbances. Chaos theory provides a practical approach to analyzing financial systems. The chaotic systems have unpredictable random characteristics that help to analyze the financial systems better. Recently, type-3 (T3) fuzzy logic systems (FLSs) have been developed for high-uncertain systems. T3-FLSs provide a reliable tool to cope with high-noisy environments. In T3-FLSs, the upper/lower bounds of uncertainties are fuzzy values. This property results in a strong tool to model more levels of uncertainties. Control, modeling, and forecasting accuracy in financial systems are so important. Then, better systems with higher accuracy are required. In this paper, a new T3-FLS based controller is introduced for chaotic financial systems. By solving a Riccati equation, sufficient conditions are concluded for optimality and robustness. T3-FLSs are learned to minimize the error and stabilize the whole system. A new optimal learning rules are extracted for T3-FLSs. Various benchmark chaotic model of financial systems are considered for examining the efficacy of the introduced approach, and the excellent response and superiority of the suggested approach is verified. Also, a comparison with other methods demonstrates the better efficiency of the suggested scheme.