A Type‐3 Fuzzy Approach for Stabilization and Synchronization of Chaotic Systems: Applicable for Financial and Physical Chaotic Systems

Abstract

In this paper, a new approach is presented for stabilizing and synchronizing financial chaotic systems. A new type-3 (T3) fuzzy-based system (FLS) with an online optimization scheme is designed to cope with chaotic behavior, high-level uncertainties, and unknown dynamics. An adaptive compensator also eliminates the effect of approximation errors (AEs) and perturbations. The stability of the dynamics of synchronization errors is guaranteed by the use of the Lyapunov method. Several simulations and comparisons demonstrate the superiority of the suggested control and synchronization scenarios.

A New Method for the Design of Interval Type-3 Fuzzy Logic Systems With Uncertain Type-2 Non-Singleton Inputs (IT3 NSFLS-2): A Case Study in a Hot Strip Mill

“…. , ∂E ∂θ nnow T (36) Each rule of the level-α 0 uses (35) to update three θ antecedent parameters, M i q1α 0 (37), M i q2α 0 (38), and σ i qα 0 (39), and two θ consequent parameters, c i lα 0 (40), and c i rα 0 (41). Equation (35) requires finding the partial derivatives used to update all the parameters of the antecedent and consequent sections of each rule of only the IT2α 0 NFLS-2 located at level-α 0 .…”

“…In recent years, 2019-2022, important and novel papers were developed [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35],…”

“…The analysis of the state-of-the-art literature shows that IT3 models use singleton inputs [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42] and type-1, non-singleton inputs [32]. The applications of the IT3 FLS systems mainly covers the areas of: Mathematical theory [1], [2], [3], [4], [6], [11], [19], [24], [56], [57],…”

“…It is important to note that most of the publications present only a common vector of 4 or 8 fixed equations for the α kcuts calculation in the consequent section (CCS). The use of CCS appears in [7], [15], [20], [21], [22], [24], [28], [30], [34], [35], [41], and [42].…”

Stability analysis with general fuzzy measure: An application to social security organizations

“…Among them, we can mention its applications in medical issues, financial issues, encryption techniques, control systems and optimization algorithms. Tian et al [ 40 ] introduced a new deep-learned type-3 fuzzy logic system to develop a model for CO2 solubility estimation. Moreover, a new type-3 fuzzy logic system with an online optimization scheme is proposed for stabilizing and synchronizing financial chaotic systems [ 41 ].…”