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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.

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.

This study aims to propose, as the first time, the interval type-2 adaptive network-fuzzy inference system (ANFIS) structure, which is given better results compared to previously presented in the open literature. So, the ANFIS can be used effectively for training of interval type-2 fuzzy logic system (IT2FLS) parameters.

Karnik–Mendel algorithm (KMA) is modified to use in interval type-2 ANFIS. The modified Karnik–Mendel algorithm (M-KMA) is implemented to change the uncertain ANFIS parameters into known ones. In this way, the interval type-2 ANFIS removes uncertainties of IT2FLS. Therefore, the interval type-2 ANFIS is reduced to a simple one, i.e. less mathematical operation required. Only consequent parameters are trained, and the consequent parameters are chosen in the form of crisp.

By applying the mentioned procedure, it can be shown that interval type-2 ANFIS has generally better results compared to type-1 ANFIS. However, it was noticed that the worst results obtained in the case of interval type-2 ANFIS are equal to the best result obtained in the case of type-1 ANFIS. Therefore, users in this field can use this approach in solving nonlinear problems.

The interval type-2 ANFIS can be used as controller for highly nonlinear systems such as air vehicles.

As stated in the open literature, it is ineffective to use ANFIS for IT2FLS. In this study, the KMA is modified for IT2FLS, and it is seen that the ANFIS can be used effectively for IT2FLS.

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.

With numerous and ambiguous sets of information and often conflicting requirements, construction management is a complex process involving much uncertainty. Decision makers may be challenged with satisfying multiple criteria using vague information. Fuzzy multi-criteria decision-making (FMCDM) provides an innovative approach for addressing complex problems featuring diverse decision makers’ interests, conflicting objectives and numerous but uncertain bits of information. FMCDM has therefore been widely applied in construction management. With the increase in information complexity, extensions of fuzzy set (FS) theory have been generated and adopted to improve its capacity to address this complexity. Examples include hesitant FSs (HFSs), intuitionistic FSs (IFSs) and type-2 FSs (T2FSs). This chapter introduces commonly used FMCDM methods, examines their applications in construction management and discusses trends in future research and application. The chapter first introduces the MCDM process as well as FS theory and its three main extensions, namely, HFSs, IFSs and T2FSs. The chapter then explores the linkage between FS theory and its extensions and MCDM approaches. In total, 17 FMCDM methods are reviewed and two FMCDM methods (i.e. T2FS-TOPSIS and T2FS-PROMETHEE) are further improved based on the literature. These 19 FMCDM methods with their corresponding applications in construction management are discussed in a systematic manner. This review and development of FS theory and its extensions should help both researchers and practitioners better understand and handle information uncertainty in complex decision problems.

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.

This study aims to improve the reliability of emergency safety barriers by using the subjective safety analysis based on evidential reasoning theory in order to develop on a framework for optimizing the reliability of emergency safety barriers.

The emergency event tree analysis is combined with an interval type-2 fuzzy-set and analytic hierarchy process (AHP) method. In order to the quantitative data is not available, this study based on interval type2 fuzzy set theory, trapezoidal fuzzy numbers describe the expert's imprecise uncertainty about the fuzzy failure probability of emergency safety barriers related to the liquefied petroleum gas storage prevent. Fuzzy fault tree analysis and fuzzy ordered weighted average aggregation are used to address uncertainties in emergency safety barrier reliability assessment. In addition, a critical analysis and some corrective actions are suggested to identify weak points in emergency safety barriers. Therefore, a framework decisions are proposed to optimize and improve safety barrier reliability. Decision-making in this framework uses evidential reasoning theory to identify corrective actions that can optimize reliability based on subjective safety analysis.

A real case study of a liquefied petroleum gas storage in Algeria is presented to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology provides the possibility to evaluate the values of the fuzzy failure probability of emergency safety barriers. In addition, the fuzzy failure probabilities using the fuzzy type-2 AHP method are the most reliable and accurate. As a result, the improved fault tree analysis can estimate uncertain expert opinion weights, identify and evaluate failure probability values for critical basic event. Therefore, suggestions for corrective measures to reduce the failure probability of the fire-fighting system are provided. The obtained results show that of the ten proposed corrective actions, the corrective action “use of periodic maintenance tests” prioritizes reliability, optimization and improvement of safety procedures.

This study helps to determine the safest and most reliable corrective measures to improve the reliability of safety barriers. In addition, it also helps to protect people inside and outside the company from all kinds of major industrial accidents. Among the limitations of this study is that the cost of corrective actions is not taken into account.

Our contribution is to propose an integrated approach that uses interval type-2 fuzzy sets and AHP method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers. In addition, the integration of fault tree analysis and fuzzy ordered averaging aggregation helps to improve the reliability of the fire-fighting system and optimize the corrective actions that can improve the safety practices in liquefied petroleum gas storage tanks.

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 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.

Type-2 fuzzy sets became attractive in practice because of their footprint of uncertainty that gives them more degrees of freedom. This paper aims to use genetic algorithms (GAs) to design an interval Type-2 fuzzy logic system (IT2FLS) for the purpose of predicting bankruptcy.

The shape of type-2 membership functions, the parameters giving their spread and location in the fuzzy partitions and the set of fuzzy rules are evolved at the same time by encoding all together into the chromosome representation. The enhanced Karnik–Mendel algorithms are used for the centroid type-reduction and defuzzification stage. The performance in predicting bankruptcy is evaluated by benchmarking IT2FLSs against type-1 FLSs. The experimental setup consists of evolving 100 configurations for both the T1FLS and IT2FLS and comparing their in-sample and out-of-sample average accuracy.

The experiments confirm that representing and capturing uncertainty with more degrees of freedom is an important advantage. It is this extra potential of IT2FLSs that allows them to outperform T1FLS, especially in terms of generalization capability.

The strategy followed in this paper is to train an IT2FLS from scratch rather than tuning the parameters of an existing T1FLS. Because this leads to solving a mixed integer optimization problem, the GA-based approach is specifically designed and uses genetic operators that are most suited for such a case: tournament selection, extended Laplace crossover and power mutation. Finally, the trained IT2FLS is applied to bankruptcy prediction, and its generalization capability is compared with related techniques.