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The purpose of this paper is to look at the problem of fault tolerant control (FTC) for discrete time nonlinear system described by Interval Type-2 Takagi–Sugeno (IT2 TS) fuzzy model subjected to stochastic noise and actuator faults.

An IT2 fuzzy augmented state observer is first developed to estimate simultaneously the system states and the actuator faults since this estimation is required for the design of the FTC control law. Furthermore, based on the information of the states and the faults estimate, an IT2 fuzzy state feedback controller is conceived to compensate for the faults effect and to ensure a good tracking performance between the healthy system and the faulty one. Sufficient conditions for the existence of the IT2 fuzzy controller and the IT2 fuzzy observer are given in terms of linear matrix inequalities which can be solved using a two-step computing procedure.

The paper opted for simulation results which are applied to the three-tank system. These results are presented to illustrate the effectiveness of the proposed FTC strategy.

In this paper, the problem of active FTC design for noisy and faulty nonlinear system represented by IT2 TS fuzzy model is treated. The developed IT2 fuzzy fault tolerant controller is designed such that it can guarantee the stability of the closed-loop system. Moreover, the proposed controller allows to accommodate for faults, presents a satisfactory state tracking performance and outperforms the traditional type-1 fuzzy fault tolerant controller.

The purpose of this paper is to stabilize the type-2 Takagi–Sugeno (T–S) fuzzy systems with the sufficient and guaranteed stability conditions. The given conditions efficaciously handle parameter uncertainties by the upper and lower membership functions of the type-2 fuzzy sets (FSs).

This paper reports on a relevant study of stable fuzzy controllers and type-2 T–S fuzzy systems and reported that the synthesis of controller for nonlinear systems described by the type-2 T–S fuzzy model is a key problem and it can be resolve to convex problems via linear matrix inequalities (LMIs).

The multigain fuzzy controllers are established to improve the solvability of the stability conditions, and the authors design multigain fuzzy controllers which have extensive information of upper and lower membership grades. Consequently, the authors derive the traditional stability condition in terms of LMIs. One simulation examples illustrate the effectiveness and robustness of the derived stabilization conditions.

The uncertain MIMO nonlinear system described by Type-2 Takagi-Sugeno (T-S) fuzzy model, and successively LMI approach used to determine the system stability conditions. The proposed control approach will give superior fault-tolerant control permanence under the actuator fault [partial loss of effectiveness (LOE)]. Also the controller robust against the unmeasurable process disturbances. Additionally, the statistical z-test are carried out to validate the proposed control approach against the control approach proposed by Himanshukumar and Vipul (2019a).

In recent times, fuzzy logic is gaining more and more attention, and this is because of the capability of understanding the functioning of the system as per human knowledge-based system. The main contribution of the work is dynamically adapting the important parameters throughout the execution of the flower pollination algorithm (FPA) using concepts of fuzzy logic. By adapting the main parameters of the metaheuristics, the performance and accuracy of the metaheuristic have been improving in a varied range of applications.

The fuzzy logic-based parameter adaptation in the FPA is proposed. In addition, type-2 fuzzy logic is used to design fuzzy inference system for dynamic parameter adaptation in metaheuristics, which can help in eliminating uncertainty and hence offers an attractive improvement in dynamic parameter adaption in metaheuristic method, and, in reality, the effectiveness of the interval type-2 fuzzy inference system (IT2 FIS) has shown to provide improved results as matched to type-1 fuzzy inference system (T1 FIS) in some latest work.

One case study is considered for testing the proposed approach in a fault tolerant control problem without faults and with partial loss of effectiveness of main actuator fault with abrupt and incipient nature. For comparison between the type-1 fuzzy FPA and interval type-2 fuzzy FPA is presented using statistical analysis which validates the advantages of the interval type-2 fuzzy FPA. The statistical Z-test is presented for comparison of efficiency between two fuzzy variants of the FPA optimization method.

The main contribution of the work is a dynamical adaptation of the important parameters throughout the execution of the flower pollination optimization algorithm using concepts of type-2 fuzzy logic. By adapting the main parameters of the metaheuristics, the performance and accuracy of the metaheuristic have been improving in a varied range of applications.

The two-tank level control system is one of the real-world's second-order system (SOS) widely used as the process control in industries. It is normally operated under the Proportional integral and derivative (PID) feedback control loop. The conventional PID controller performance degrades significantly in the existence of modeling uncertainty, faults and process disturbances. To overcome these limitations, the paper suggests an interval type-2 fuzzy logic based Tilt-Integral-Derivative Controller (IT2TID) which is modified structure of PID controller.

In this paper, an optimization IT2TID controller design for the conical, noninteracting level control system is presented. Regarding to modern optimization context, the flower pollination algorithm (FPA), among the most coherent population-based metaheuristic optimization techniques is applied to search for the appropriate IT2FTID's and IT2FPID's parameters. The proposed FPA-based IT2FTID/IT2FPID design framework is considered as the constrained optimization problem. System responses obtained by the IT2FTID controller designed by the FPA will be differentiated with those acquired by the IT2FPID controller also designed by the FPA.

As the results, it was found that the IT2FTID can provide the very satisfactory tracking and regulating responses of the conical two-tank noninteracting level control system superior as compared to IT2FPID significantly under the actuator and system component faults. Additionally, statistical Z-test carried out for both the controllers and an effectiveness of the proposed IT2FTID controller is proven as compared to IT2FPID and existing passive fault tolerant controller in recent literature.

Application of new metaheuristic algorithm to optimize interval type-2 fractional order TID controller for nonlinear level control system with two type of faults. Also, proposed method will compare with other method and statistical analysis will be presented.

Fuzzy-based metaheuristic algorithm is used to optimize the fuzzy controllers for the nonlinear level control system subject to uncertainty specially in the main actuator that has lost effectiveness (LOE). To optimize the fuzzy controller, type-1 harmonic search (HS) and interval type-2 (HS) will be used.

The type-1 and type-2 fuzzy-based HS algorithms are designed for optimization of fuzzy controllers for Fault-Tolerant Control (FTC) applications, and this research proposes a fuzzy-based HS metaheuristic method. The performance of a fuzzy logic-based HS algorithm applied to a nonlinear two-tank level control process with a main actuator that has lost effectiveness (LOE) and also the same controller will be tested on DC motor angular position control with and without noise.

The key contribution of this work is the discovery of the best approach for generating an optimal vector of values for the fuzzy controller's membership function optimization. This is done in order to improve the controller's performance, bringing the process value of the two-tank level control process closer to the target process value (set point). It is worth noting that the type-1 fuzzy controller that has been optimized is an interval type-2 fuzzy system, which can handle more uncertainty than a type-1 fuzzy system.

The type-1 and type-2 fuzzy-based HS algorithms are designed for optimization of fuzzy controllers for FTC applications, and this research proposes a fuzzy-based HS metaheuristic method. The performance of a fuzzy logic-based HS algorithm applied to a nonlinear two-tank level control process with a main actuator that has LOE will be tested on DC motor angular position control with noise. Two nonlinear uncertain processes are used to demonstrate the effectiveness of the proposed control scheme.

The proposed IT2FMOVMI model intends to concurrently minimize total cost and warehouse space for the single vendor-retailer, multi-item and a consolidated vendor store. Regarding demand and order quantities with the deterministic and type-1 fuzzy numbers, we have also formulated the classic/crisp MOVMI model and type-1 fuzzy MOVMI (T1FMOVMI) model. The suggested solution technique can solve both crisp MOVMI and T1FMOVMI problems. By finding the optimal ordered quantities and backorder levels, the Pareto-fronts are constructed to form the solution sets for the three models.

A multi-objective vendor managed inventory (MOVMI) is the most recognized marketing and delivery technique for the service provider and the retail in the supply chain in Industry 4.0. Due to the evolving market conditions, the characteristics of the individual product, the delivery period and the manufacturing costs, the demand rate and order quantity of the MOVMI device are highly unpredictable. In such a scenario, a MOVMI system with a deterministic demand rate and order quantity cannot be designed to estimate the highly unforeseen cost of the problem. This paper introduces a novel interval type-2 fuzzy multi-objective vendor managed inventory (IT2FMOVMI) system, which uses interval type-2 fuzzy numbers (IT2FNs) to represent demand rate and order quantities. As the model is an NP-hard, the well-known meta-heuristic algorithm named NSGA-II (Non-dominated sorted genetic algorithm-II) with EKM (Enhanced Karnink-Mendel) algorithm based solution method has been established.

The experimental simulations for the five test problems that demonstrated distinct conditions are considered from the real-datasets of SAPCO company. Experimental study concludes that T1FMOVMI and crisp MOVMI schemes are outclassed by IT2FMOVMI model, offering more accurate Pareto-Fronts and efficiency measurement values.

Using fuzzy sets theory, a significant amount of work has been already done in past decades from various points of views to model the MOVMI. However, this is the very first attempt to introduce type-2 fuzzy modelling for the problem to address the realistic implementation of the imprecise parameters.

The purpose of this paper is to present a novel intelligent backstepping sliding mode control for an experimental permanent magnet synchronous motor.

A novel recurrent radial basis function network (RBFN) is used to is used to approximate unknown nonlinear functions in permanent magnet synchronous motor (PMSM) dynamics. Then, using the functions obtained from the neural network, it is possible to design a model-based and precise controller for PMSM using the immersive modeling method.

Experimental results indicate the appropriate performance of the proposed method.

This paper presents a novel intelligent backstepping sliding mode control for an experimental permanent magnet synchronous motor. A novel recurrent RBFN is used to is used to approximate unknown nonlinear functions in PMSM dynamics.

The purpose of this article is about the design of controllers for conical two-tank noninteracting level (CTTNL) system in simulation. Local linearization around the equilibrium point has been done for the nonlinear CTTNL system to obtain a linearized model transfer function.

This article deals with the design of novel optimal fractional-order tilt-integral-derivative (TID) controller using type-1 fuzzy set for the CTTNL prototype system. In this study, type-1 fuzzy TID controller parameters have been optimized through genetic algorithm (GA) and those set of values have been employed for the design of proportional-integral-derivative (PID) controller.

A performance comparison between FTID and PID controller is then investigated. The analysis shows the superiority of FTID controller over PID controller in terms of integral absolute error (IAE), integral square error (ISE), integral of time multiplied absolute error (ITAE) and integral of time multiplied squared error (ITSE) integral errors. The transient and steady state performance of the FTID controller are superior as compared to conventional PID controller. In future, the FTID controller fault-tolerance capability tested on CTTNL system subject to actuator and system component (leak) faults. The detailed study of robustness in presence of model uncertainties will be incorporated as a scope of further research.

A performance comparison between FTID and PID controller is then investigated. The analysis shows the superiority of FTID controller over PID controller in terms of IAE, ISE, ITAE and ITSE integral errors. Additionally, fault-tolerant performance of the proposed controller evaluated with fault-recovery time (F_rt) parameter. The transient and steady state performance of the FTID controller are superior as compared to conventional PID controller.

Expert systems are computer-based systems that mimic the logical processes of human experts or organizations to give advice in a specific domain of knowledge. Fuzzy expert systems use fuzzy logic to handle uncertainties generated by imprecise, incomplete and/or vague information. The purpose of this paper is to present a comprehensive review of the methods and applications in fuzzy expert systems.

The authors have carefully reviewed 281 journal publications and 149 conference proceedings published over the past 37 years since 1982. The authors grouped the journal publications and conference proceedings separately accordingly to the methods, application domains, tools and inference systems.

The authors have synthesized the findings and proposed useful suggestions for future research directions. The authors show that the most common use of fuzzy expert systems is in the medical field.

Fuzzy logic can be used to manage uncertainty in expert systems and solve problems that cannot be solved effectively with conventional methods. In this study, the authors present a comprehensive review of the methods and applications in fuzzy expert systems which could be useful for practicing managers developing expert systems under uncertainty.

Due to the increasing size and complexity of construction projects, construction engineering and management involves the coordination of many complex and dynamic processes and relies on the analysis of uncertain, imprecise and incomplete information, including subjective and linguistically expressed information. Various modelling and computing techniques have been used by construction researchers and applied to practical construction problems in order to overcome these challenges, including fuzzy hybrid techniques. Fuzzy hybrid techniques combine the human-like reasoning capabilities of fuzzy logic with the capabilities of other techniques, such as optimization, machine learning, multi-criteria decision-making (MCDM) and simulation, to capitalise on their strengths and overcome their limitations. Based on a review of construction literature, this chapter identifies the most common types of fuzzy hybrid techniques applied to construction problems and reviews selected papers in each category of fuzzy hybrid technique to illustrate their capabilities for addressing construction challenges. Finally, this chapter discusses areas for future development of fuzzy hybrid techniques that will increase their capabilities for solving construction-related problems. The contributions of this chapter are threefold: (1) the limitations of some standard techniques for solving construction problems are discussed, as are the ways that fuzzy methods have been hybridized with these techniques in order to address their limitations; (2) a review of existing applications of fuzzy hybrid techniques in construction is provided in order to illustrate the capabilities of these techniques for solving a variety of construction problems and (3) potential improvements in each category of fuzzy hybrid technique in construction are provided, as areas for future research.