Next-generation wireless networks, including 5G and beyond, have grown in complexity and scale, necessitating efficient and explainable machine-learning solutions. This paper explores how functional ANalysis Of VAriance inspired models such as Generalized Additive Models (GAMs), Explainable Boosting Machines (EBM), and GAMs with Structured Interactions (GAMI-Net) can shed light on the intricate relationships among various 5G performance metrics. Framed as a regression problem, the study aims to predict received signal strength based on a wide range of Key Performance Indicators (KPIs). Drawing on a publicly available real-time 5G dataset, we examine how each model balances predictive accuracy and interpretability. Our results reveal that although GAM and EBM generally deliver superior accuracy for tabular data, GAMI-Net offers greater transparency of both main effects and feature interactions, thanks to its neural-additive architecture. In particular, the models converge in identifying key drivers of network performance, such as Quality of Service, and location-based metrics, while differing in prioritizing additional throughput-related and mobility parameters. We conclude that combining accurate predictions with explainable frameworks is indispensable for advancing robust and trustworthy artificial intelligence applications in real-world 5G networks.

This article introduces an exploration of general Type-2 (GT2) fuzzy logic systems (FLSs) via Zadeh's (Z) GT2 fuzzy set (FS) definition, with a strong emphasis on advancing uncertainty quantification (UQ). At the heart of our contribution is the introduction of Z-GT2-FLS, formed through the integration of Z-GT2-FS with the$\alpha$-plane representation. We show that the design flexibility of GT2-FLS is increased as it takes away the dependency of the secondary membership function definition from the primary membership function. For learning, we provide a solution to the curse of dimensionality problem alongside a method to seamlessly integrate deep learning (DL) optimizers. This article further presents a dual-focused Z-GT2-FLS within a DL framework, intending to learn Z-GT2-FLSs that are capable of achieving high-quality prediction intervals alongside high precision. In this context, we assign distinct roles for$\alpha _{k}$-plane-associated interval type-2 FLSs through a composite loss function. In addition, we extend the application of Z-GT2-FLS to predictive distribution estimation, proposing a DL framework to learn the inverse cumulative distribution function by predicting entire quantile levels. We first reformulate the output of Z-GT2-FLS to represent a quantile level function, thereby offering flexibility in generating desired quantiles through$\alpha$-planes. For learning, we propose a simultaneous quantile learning method alongside an adaptation mechanism to enhance learning performance. Through comparative analyses, we show that the Z-GT2-FLS excels in UQ compared to its fuzzy and DL counterparts. The contributions of this study underscore the versatility and superior performance of Z-GT2-FLS, positioning it as a valuable tool for UQ.

This study presents an Odyssey of enhancements for interval type-2 (IT2) fuzzy logic systems (FLSs) for efficient learning in the pursuit of generating prediction intervals (PIs) for high-risk scenarios. We start by presenting enhancements to Karnik–Mendel (KM) and Nie–Tan (NT) center of sets calculation methods (CSCMs) to increase their learning capacities. The enhancements increase the flexibility of KM in the defuzzification stage while the NT in the fuzzification stage. We also present a parametric KM CSCM, aimed to reduce the inference complexity of KM while providing flexibility. To address large-scale learning challenges, we convert the constraint learning problem of IT2-FLS into an unconstrained form using parameterization tricks, allowing for the direct application of deep learning optimizers and automatic differentiation methods. In tackling the curse of dimensionality issue, we expand the high-dimensional Takagi–Sugeno–Kang method (HTSK) proposed for type-1 FLS to IT2-FLSs, resulting in the HTSK for IT2-FLSs. We also introduce an enhanced HTSK for IT2-FLSs from an alternative perspective, featuring a comparatively simpler computational nature. Finally, we introduce a framework to learn IT2-FLSs with a dual focus, aiming for high precision and PI generation. Our comprehensive statistical analysis demonstrates the effectiveness of the enhancements for uncertainty quantification via IT2-FLSs.

This study revisits the fuzzy control system design problem with the motto “Fuzzy with Conventional Control,” inspired by L.A. Zadeh’s statement in the famous debate “Some Crisp Thoughts on the Fuzzy versus Conventional Control.” Focused on single-input (SI) fuzzy PIDs (FPIDs), our approach synergizes fuzzy and conventional control, presenting similar control laws to PID and fuzzy gain-scheduled (FGS) PID. Departing from traditional fuzzy control paradigms, our design methodology enhances, rather than replaces, PID controllers with fuzzy logic controllers (FLCs). We start by analyzing the internal structure of both type-1 and type-2 SI-FPIDs and commenting on their structural properties. We address the high-design complexity of FLCs by proposing an interpretable and geometrical design method that explicitly shapes fuzzy mapping (FM) according to the desired control characteristics. To provide self-tuning (ST) capability to the FPID, like the FGS-PID, we develop ST mechanisms that adapt the FM of SI-FPID according to the operating point via the derived insights. Real-world application in speed control for an industrial permanent magnet synchronous machine validates the efficacy of our designs, showcasing improved disturbance rejection and reduced control signal variation compared to FGS-PIDs and PID. This research advocates for the wider adoption of SI-FPID as a practical enhancement to PID in industrial applications, offering design simplicity and ST capabilities.

In this article, we propose a novel composite learning framework for interval type-2 (IT2) fuzzy logic systems (FLSs) to train regression models with a high accuracy performance and capable of representing uncertainty. In this context, we identify three challenges, first, the uncertainty handling capability, second, the construction of the composite loss, and third, a learning algorithm that overcomes the training complexity while taking into account the definitions of IT2-FLSs. This article presents a systematic solution to these problems by exploiting the type-reduced set of IT2-FLS via fusing quantile regression and deep learning (DL) with IT2-FLS. The uncertainty processing capability of IT2-FLS depends on employed center-of-sets calculation methods, while its representation capability is defined via the structure of its antecedent and consequent membership functions. Thus, we present various parametric IT2-FLSs and define the learnable parameters of all IT2-FLSs alongside their constraints to be satisfied during training. To construct the loss function, we define a multiobjective loss and then convert it into a constrained composite loss composed of the log-cosh loss for accuracy purposes and a tilted loss for uncertainty representation, which explicitly uses the type-reduced set. We also present a DL approach to train IT2-FLS via unconstrained optimizers. In this context, we present parameterization tricks for converting the constraint optimization problem of IT2-FLSs into an unconstrained one without violating the definitions of fuzzy sets. Finally, we provide comprehensive comparative results for hyperparameter sensitivity analysis and an inter/intramodel comparison on various benchmark datasets.

Lane-change decision-making for vehicles is a challenging task for many reasons, including traffic rules, safety, and the stochastic nature of driving. Because of its success in solving complex problems, deep reinforcement learning (DRL) has been suggested for addressing these issues. However, the studies on DRL to date have gone no further than validation in simulation and failed to address what are arguably the most critical issues, namely, the mismatch between simulation and reality, human-likeness, and safety. This paper introduces a real-world DRL framework for decision-making to design safe and human-like agents that can operate in the real world without extra tuning. We propose a new learning paradigm for DRL integrated with Real2Sim transfer, which comprises training, validation, and testing phases. The approach involves two simulator environments with different levels of fidelity, which are parameterized via real-world data. Within the framework, a large amount of randomized experience is generated with a low-fidelity simulator, whereupon the learned skills are validated regularly in a high-fidelity simulator to avoid overfitting. Finally, in the testing phase, the agent is examined concerning safety and human-like decision-making. Extensive simulation and real-world evaluations show the superiority of the proposed approach. To the best of the authors’ knowledge, this is the first application of DRL lane-changing policy in the real world.

Adaptive cruise control (ACC) is one of the frontier functionality for highly automated vehicles and has been widely studied by both academia and industry. However, previous ACC approaches are reactive and rely on precise information about the current state of a single lead vehicle. With the advancement in the field of artificial intelligence, particularly in reinforcement learning, there is a big opportunity to enhance the current functionality. This paper presents an advanced ACC concept with unique environment representation and model-based reinforcement learning (MBRL) technique which enables predictive driving. By being predictive, we refer to the capability to handle multiple lead vehicles and have internal predictions about the traffic environment which avoids reactive short-term policies. Moreover, we propose a hybrid policy that combines classical car following policies with MBRL policy to avoid accidents by monitoring the internal model of the MBRL policy. Our extensive evaluation in a realistic simulation environment shows that the proposed approach is superior to the reference model-based and model-free algorithms. The MBRL agent requires only 150k samples (approximately 50 hours driving) to converge, which is x4 more sample efficient than model-free methods.

https://doi.org/10.1002/int.22626

In this paper, we propose a learning approach for interval Fuzzy Logic Systems (FLSs) to end up with models that are capable to cover an expected amount of uncertainty with a high accuracy by exploiting a composite learning method with quantile regression. Within this paper, we construct two interval FLSs that have a different representation of uncertainty. One of them models the uncertainty in its consequents while the other one within its antecedents that are defined with interval type-2 Fuzzy Sets (FSs). The learning approach uses a multi-objective composite loss that is formed by the mean square error for accuracy purposes along with tilted loss for enforcing the bounds of the FLSs to capture the expected amount of uncertainty. In that way, it is not only possible to learn the FLSs that represent the uncertainty within their MFs (which can be used as prediction intervals) but also to improve the regression performance since the composite loss provides a more complete representation of the data. We present the proposed learning approach alongside parameterization tricks so that they can be trained within the frameworks of deep learning while not violating the definitions of FSs. We present comparative results on benchmark datasets that have different characteristics.

Working with unlabeled data carries the burden of uncertainties especially when the data are high-dimensional. Clustering is not an exception in this aspect and it requires special treatment. In this study, we propose to cope with the uncertainties which occur during clustering high-dimensional data with Interval Type-2 (IT2) Fuzzy Sets (FSs) and Deep Learning (DL) methods. Generation of the IT2-FSs is done with different cluster similarity functions parameterized with Interval Valued Parameters (IVPs). These parameters are introduced as the representations of the uncertainty in cluster assignments. As the backbone of the proposed method, Deep Embedding Clustering (DEC) is employed. The resulting IT2 fuzzy clustering inference is integrated into DEC so that both the inference and the training of the proposed model are operational in popular DL frameworks. Therefore, for a straightforward deployment, the constraints on IT2-FSs are redefined by introducing parameterization tricks upon IVPs. The presented comparative results indicate that coping with the uncertainties through IT2-FSs is superior to their baseline type-1 counterparts.

Fuzzy Logic Systems (FLSs), especially Interval Type-2 (IT2) ones, are proven to achieve good results in various tasks, including classification problems. However, IT2-FLSs suffer from the curse of dimensionality problem, just like its Type-1 (T1) counterparts, and also training complexity since IT2-FLS have a large number of learnable parameters when compared to T1-FLSs. Deep learning (DL) architectures on the other hand can handle large learnable parameter sets for good generalizability but have their disadvantages. In this study, we present DL based approach with knowledge distillation for IT2-FLSs which transfers the generalizability features of deep models into IT2-FLS and increases its learning performance significantly by eliminating the problems that may arise from large input sizes and high rule counts. We present in detail the proposed approach with parameterization tricks so that the training of IT2-FLS can be accomplished straightforwardly within the widely employed DL frameworks without violating the definitions of IT2-FSs. We present comparative analysis to show the benefits of the inclusion knowledge distillation in the learning of IT2-FLSs with respect to rule number and input dimension size.

This article aims to provide a new perspective on how the deployment of general type-2 (GT2) fuzzy sets affects the mapping of a class of fuzzy logic controllers (FLCs). It is shown that an α-plane represented a GT2-FLC is easily designed via baseline type-1 and interval type-2 FLCs and two design parameters (DPs). The DPs are the total number of α planes and the tuning parameter of the secondary membership function that are interpreted as sensitivity and shape DPs, respectively. We provide a clear understanding and interpretation of the sensitivity and shape DPs on controller performance through various comparative analyses. We present design approaches on how to tune the shape DP by providing a tradeoff between robustness and performance. We also propose two online scheduling mechanisms to tune the shape DP. We explore the effect of the sensitivity DP on the GT2-FLC and provide practical insights on how to tune the sensitivity DP. We present an algorithm for tuning the sensitivity DP that provides a compromise between computational time and sensitivity. We validate our analyses, interpretations, and design methods with experimental results conducted on a drone. We believe that this article provides clear explanations on the role of DPs on the performance, robustness, sensitivity, and computational time of GT2-FLCs.

The emerging success of Deep Learning (DL) in various application areas comes also with the questions starting with "How"s and "Why"s. These questions can be answered if the DL methods are interpretable and thus provide a certain a degree of explanation. In this paper, we propose a DL framework that leverages the advantages of β-Variational Autoencoder (VAE) and Fuzzy Sets (FSs), which are disentanglement and linguistic representation, for the design of a novel DL based Fuzzy Classifier (FC). We first present a step-by-step design approach to construct the DL-FC which is composed of the encoder layer of β-VAE and a Fuzzy Logic System (FLS) followed by a softmax layer. The β-VAE is trained so that the semantic information of the high dimensional data is captured. The latent space of the β-VAE is clustered to extract FSs. The FSs are then used to define antecedents of the FLS that is trained with DL methods. We present results conducted on the MNIST dataset and showed that DL-FC is quite competitive with its deep neural network counterpart. We then try to provide an interpretation to the antecedents of FLS by examining the FSs, the latent traversals and heat-maps of each latent dimension. The results show that the antecedents of FLS can be defined with linguistic interpretations. Thus, for the first time in the literature, we showed that linguistic interpretations can be defined for the latent space of β-VAE with FSs.

This paper proposes a systematic approach to solve the design problem of General Type-2 (GT2) Fuzzy Logic Controllers (FLCs) with an online scheduling mechanism for performance enhancements. We firstly suggest constructing the GT2-FLC over its baseline type-1 and interval type-2 FLCs, and then to tune a single design parameter which defines the shape of the secondary membership functions. We present how the shape of the secondary membership function changes with respect to the design parameter and show resulting effect on the control surface generation. The presented comparative analysis on the control surfaces show that aggressive and smooth control surfaces can be easily generated by tuning the design parameter. We suggest tuning the design parameter by providing a tradeoff between robustness and performance of the control system. Also, to achieve satisfactory control performances for various steady-state points, we propose an online scheduling mechanism that tunes the design parameter with respect to the operating points. We perform a simulation study on a nonlinear system to validate our analyses and proposed design methods. The simulation results show that GT2-FLC has a potential to improve overall system performances in comparison to its type-1 and interval type-2 counterparts, while the developed scheduling mechanism provides an opportunity to achieve satisfactory results for various operating points.

Automated lane change is one of the most challenging task to be solved of highly automated vehicles due to its safety-critical, uncertain and multi-agent nature. This paper presents the novel deployment of the state of art Q learning method, namely Rainbow DQN, that uses a new safety driven rewarding scheme to tackle the issues in an dynamic and uncertain simulation environment. We present various comparative results to show that our novel approach of having reward feedback from the safety layer dramatically increases both the agent's performance and sample efficiency. Furthermore, through the novel deployment of Rainbow DQN, it is shown that more intuition about the agent's actions is extracted by examining the distributions of generated Q values of the agents. The proposed algorithm shows superior performance to the baseline algorithm in the challenging scenarios with only 200000 training steps (i.e. equivalent to 55 hours driving).

This paper presents a systematic and interpretable design approach to generate type-2 (T2) fuzzy logic-based linguistic pursuing strategies (PSs) and their deployment to a real-world pursuit-evasion game (PEG). First, we have developed a novel T2 fuzzy logic-based strategy planner (T2-FSP). Then, through detailed theoretical investigations on the input-output mapping of the T2-FSP, it has been shown that it is possible to design a linguistic PS which defines both pursuer's approaching behavior (aggressive, smooth) and side (left or right) to the evader by simply tuning the footprint of uncertainty (FOU) sizes of the T2 fuzzy sets. Hence, an interpretable relationship has been revealed between the FOU sizes and the PSs through comparative theoretical explorations and derivations. Additionally, as there is a need to employ different PSs in a dynamic PEG environment, a type-1 fuzzy decision making (T1-FDM) mechanism has been designed to tune the FOU sizes of the T2-FSP and, thus, adjust the PS to be employed in real time. A real-world game environment is constructed in order to validate the developed T2 fuzzy logic-based PSs and T1-FDM mechanism in real time. Comparative experimental results have been presented to show that the T2 fuzzy logic-based PSs have satisfactory performance against a human user.

In this paper, we provide a new insight on the mappings of Interval Type-2 (IT2) Fuzzy Logic Systems (FLSs) in comparison to its Type-1 (T1) counterparts. For the sake of simplicity, we focus on Single input IT2 (SIT2) FLSs that employ the Karnik Mendel (KM) or the Nie-Tan (NT) Centre of Sets Calculation Method (CSCM). Through theoretical investigations, it is shown that there does exist an equivalent SIT2-FLS representation with a Single input T1 (ST1) FLS that uses Rational Polynomial Functions (RBFs) in their rule consequents. It is concluded that SIT2-FLSs cannot be implemented with traditional ST1-FLSs. It is also revealed that the extra degree of freedom provided by IT2 fuzzy sets and CSCM results with RBFs that can generate much more complex mapping when compared to its T1 counterparts. It is also proven that SIT2-FLSs can be seen as adaptive ST1-FLSs that are tuned via a collection of ST1-FLSs. Thus, SIT2-FLSs have adaptive feature property that does not exists in ST1-FLSs. It is also shown that the SIT2-FLS employing the KM is more complex but also capable to accommodate a much wider range of mappings when compared its NT counterpart.

In this paper, we will analyze and present systematic design approaches for the most commonly employed Interval Type-2 (IT2) Fuzzy PID (FPID) controllers which are the Single input IT2 (SIT2) and Double IT2 (DIT2) FPID controllers. We will firstly start with presenting the general structure of the IT2-FPID controllers and then present internal model control based tuning approaches to calculate the scaling factors of the IT2-FPID controllers. It will be shown that, by simply tuning the Footprint of Uncertainty parameters, how to construct aggressive and smooth control curves for SIT2-FPID controllers while aggressive and smooth control surfaces for DIT2-FPID controllers. Finally, we will present real world experiments using a tricycle that will act as a platform to validate the control systems. The comparative experimental results will show that the real-time tracking control performance of both the SIT2-FPID and DIT2-FPID control structure is better in the presence of noise and unmodelled dynamics in comparison with their Type-1 fuzzy and conventional counterparts. We will also try to address the question "Which IT2-FPID controller is better?" by taking account the design simplicity and control system performance.

In this paper, we present experimental results conducted on the spherical robot Sphero 2.0 by analyzing the control surfaces of Interval Type-2 (IT2) Fuzzy PD (FPD), Type-1 (T1) FPD and conventional PD controllers in order to show how and why the IT2-FPD controllers have capability improve control performances. We firstly present the vision based position control system used in this study. We then tune the design parameters of PD, T1-FPD and IT2-FPD controllers via an optimization based design approach for a training reference trajectory. The control surfaces of the designed controllers are compared in terms of the aggressiveness and smoothness of their control actions. This analysis shows that the IT2-FPD controller has ability to produce both aggressive and smooth control actions in different input spaces, which cannot be accomplished by its conventional and T1 counterparts. To analyze the controller performances for different operating points, we present the real-time results for a testing trajectory. The control surface analysis shows that the IT2-FLC is able to generate sophisticated control surfaces by adjusting the Footprint of Uncertainty (FOU), while the experimental results validate that the potential of the IT2-FPD controller to improve control performances via tuning the FOU parameters.

Nowadays, nano quadcopters have attracted research interest since they are fast quadcopters with high maneuverability. In this study, the design and deployment of a Fuzzy PID (FPID) controller structure is presented to solve the position control problem of the Crazyflie 2.0 nano quadcopter in a real-world environment. In this context, we will firstly present an experimental environment in which a low cost camera system is implemented instead of the OptiTrack or VICON camera system. Then, we will present a fuzzy logic based position controller structure which uses a vision based positioning system that is capable to track the position of Crazyflie 2.0 through the low cost camera. In this structure, since the usage of a low cost camera might result with feedback uncertainties, we will design FPID controllers to end up with a robust and satisfactory control system performance in presence of noise and the present highly coupled nonlinearities of Crazyflie 2.0. The paper will present comparative experimental results that show the resulting performance of the FPID structure is superior in various operating points and is more robust against noise and nonlinearities when compared to its PID counterpart.

In this paper, we will present the novel application of Type-2 (T2) fuzzy logic to solve a real-time pursuit-evasion game problem with the spherical droids Sphero 2.0 and BB8 (products of the Sphero company). The game scenario is constructed as the evader droid BB8 is controlled by a human user while the pursuer droid Sphero 2.0 is navigated through the game environment via the proposed T2 fuzzy pursuing system. The proposed T2 fuzzy pursuing system structure is composed of vision based localization, the error signal generator, T2 fuzzy strategy planner and the control system. The T2 fuzzy strategy planner is the key structure of the pursuing system since it generates the reference trajectories to be followed by the pursuer droid Sphero 2.0. In this paper, we have transformed design guidelines presented for T2 fuzzy logic controllers into two pursuing strategies for the first time in literature. The performances of the proposed T2 fuzzy strategies have been examined by providing comparative experimental results performed in the real-world game environment against a human user. We believe that this pioneer application of the T2 fuzzy logic in pursuit-evasion games will be an important step for a wider deployment in the research area of real world games.

In this study, we will present the novel application of Type-2 (T2) fuzzy logic to the popular video game called Lunar Lander. The proposed T2 fuzzy moon landing system structure is composed of the error signal generator and the T2 fuzzy logic control structure which give the opportunity to transform the moon landing problem of the spaceship as a multivariable tracking control problem. The landing problem of the game can be seen as one of the classical multivariable control problems including uncertainties due to the randomization process occurring the game environment. Thus, we will employ T2 fuzzy logic controllers since they are capable of handling a high level of uncertainties. Then, by optimizing the T2 fuzzy moon landing system via the particle swarm optimization, we will show that the resulting T2 fuzzy moon landing system resulted with an adequate control and game performance in the presence of the uncertainties, disturbances and nonlinear system dynamics in comparison with its type-1 and conventional counterparts. We believe that the results of this paper will be an important step for a wider deployment of T2 fuzzy logic in the research area of computer games.

In this paper, we will present the gain analysis of an Internal Type-2 (IT2) Fuzzy Logic Controller (FLC) that employs the Nie-Tan method and validated our theoretical results on the control of realistic Electric Vehicle (EV) model. In this context, we will firstly present the analytical derivation of the employed IT2-FLC structure and its output in closed form. We will then investigate the gain variations with respect to the Footprint of Uncertainty (FOU) design parameter of the IT2-FLC. We will define aggressive and smooth control regions based on the gain of IT2 FLCs in comparison with its type-1 counterpart. We will also present the FOU parameter settings that obtain aggressive or smooth control actions based on derived controller gains. We will extend these gain analysis into controller design to achieve desired control action. We will present the simulation studies in which aggressive and smooth IT2-FLCs are compared and evaluated on the EV model for different control performance measures. The results will show that the presented gain analysis provides better understanding about the effect of the FOU parameter and an initiative way to tune IT2-FLC for control system applications.

Phone segmentation is an essential task for Automatic Speech Recognition (ASR) systems, which still lack in performance when compared to the ability of humans’ speech recognition. In this paper, we propose novel Fuzzy Logic (FL) based approaches for the prediction of phone durations using linguistic features. To the best of our knowledge, this is the first development and deployment of FL based approaches in the area of phone segmentation. In this study, we perform a case study on the Dutch IFA corpus, which consists of 50000 words. Different experiments are conducted on tuned FL Systems (FLSs) and Neural Networks (NNs). The experimental results show that FLSs are more efficient in phone duration prediction in comparison to their Neural Network counterparts. Furthermore, we observe that differentiating between the vowels and the consonants improves the performance of predictions, which can facilitate enhanced ASR systems. The FLS with the differentiation between vowels and consonants had an average Mean Average Precision Error of 43.3396% on a k=3 fold. We believe that this first attempt of the employment of FL based approaches will be an important step for a wider deployment of FL in the area of ASR systems.

The aim of this paper is to present experimental validation results to show the design simplicity of single input interval type-2 (IT2) fuzzy PID (FPID) controllers by evaluating their performance on a real-time 3 DOF helicopter testbed. In this study, we briefly show that the presented analytical design approach gives the opportunity to construct the IT2 fuzzy mappings by tuning a single parameter which constructs the footprint of uncertainty (FOU) of the IT2 fuzzy sets. Then, by employing these theoretical analyses, various single input IT2 FPID (SIT2-FPID) controllers are designed to solve the control problem of the 3 DOF helicopter. Through extensive and comparative experimental analysis, we analyze the IT2 fuzzy control system performances and validate the effect of the FOU parameter on the controller characteristics. The experimental results show that, having neither a priori knowledge about the mathematical model of the system nor its parameters, the SIT2-FPID is able to achieve a satisfactory control performance over nonlinear working regions in the presence of noise and unmodelled disturbance dynamics. We believe that the experimental validation of the SIT2-FPID controllers' theoretical analyses will open the door to a wider deployment of SIT2-FPIDs to real world control engineering applications.

In this study, we will present the novel application of Type-2 (T2) fuzzy control into the popular video game called flappy bird. To the best of our knowledge, our work is the first deployment of the T2 fuzzy control into the computer games research area. We will propose a novel T2 fuzzified flappy bird control system that transforms the obstacle avoidance problem of the game logic into the reference tracking control problem. The presented T2 fuzzy control structure is composed of two important blocks which are the reference generator and Single Input Interval T2 Fuzzy Logic Controller (SIT2-FLC). The reference generator is the mechanism which uses the bird's position and the pipes' positions to generate an appropriate reference signal to be tracked. Thus, a conventional fuzzy feedback control system can be defined. The generated reference signal is tracked via the presented SIT2-FLC that can be easily tuned while also provides a certain degree of robustness to system. We will investigate the performance of the proposed T2 fuzzified flappy bird control system by providing comparative simulation results and also experimental results performed in the game environment. It will be shown that the proposed T2 fuzzified flappy bird control system results with a satisfactory performance both in the framework of fuzzy control and computer games. We believe that this first attempt of the employment of T2-FLCs in games will be an important step for a wider deployment of T2-FLCs in the research area of computer games.

In this paper, we will present two novel self-tuning structure based on the Gradient Descent (GD) method and Extended Kalman Filter (EKF) estimation to improve the control performances of Interval Type-2 (IT2) Fuzzy PID (FPID) controllers. In this context, we will derive the analytical expressions of the output of the IT2-FPID controller as a function of the design parameter, namely the Footprint of the Uncertainty (FOU) parameters. We will present the proposed GD based Self-Tuning IT2 (STIT2) FPID controller and the EKF based STIT2-FPID controller structures. These self-tuning structures update the FOU design parameter so that the size of the FOU of the IT2 fuzzy sets is tuned in an online manner. The adjustment of the FOU parameter results with a hybrid controller behavior combining the aggressive nature of the Type-1 (T1) FPID and the robust nature of the IT2-FPID controllers. We will present simulation results where the proposed GD-STIT2-FPID and EKF-STIT2-FPID controllers are compared with their IT2 and STT1 counterparts. The results will show that the self-tuning IT2-FPID controller has ability to improve overall reference tracking and disturbance rejection performances in comparison with its T1, self-tuning T1, and IT2 counterparts.

Recent results on fuzzy control have shown that interval type-2 (IT2) fuzzy logic controllers (FLCs) might achieve better control performance due to the additional degree of freedom provided by the footprint of uncertainty (FOU) in their IT2 fuzzy sets. However, the design and robust stability analysis of the IT2-FLCs are still challenging problems due to their relatively more complex internal structure. In this paper, we will derive the explicitly fuzzy mapping (FM) of a single-input IT2-FLC (SIT2-FLC) to present design methods and investigate its robustness. The analytical information of the IT2-FM will give the opportunity to provide explanations on the roles of the FOU parameters by taking advantage of the well-developed framework of nonlinear control theory. Comparative theoretical explorations will be presented on the differences between the type-1 (T1) FM and IT2-FM to clearly show the role of the FOU on the robust control system performance. It will be proven that the robust stability of the IT2 fuzzy system is guaranteed with the aids of the well-known Popov-Lyapunov method. Moreover, analytical design methods are presented for SIT2-FLCs to generate commonly employed control curves by only tuning the size of the FOUs without a need of an optimization procedure. It will be theoretically shown that the FOU gives the opportunity to the SIT2-FLC to generate commonly employed nonlinear control curves while also providing a certain degree of robustness which cannot be accomplished by its T1 counterpart. The presented results provide theoretical explanations on the role of the FOU on the performance and robustness of the SIT2-FLC.

Computing the centroid and performing Type Reduction (TR) for type-2 fuzzy sets and systems are operations that must be taken into consideration. Karnik-Mendel Algorithms (KMAs) have been usually employed to perform these operations. In KMAs, these operations are defined as nonlinear optimization problems which are solved iteratively by finding the optimal Switching Points (SPs). In this study, we will transform these operations into Linear Fractional Programming (LFP) problems and solve them with the aids of the well-developed Linear Programming (LP) theory. It will be shown that there exists a direct relationship between the SPs of the KMAs and the solution vectors of the defined LFP problems. Thus, the meaning of the SPs will be revealed in the framework of LFP theory and the KMA will be connected a LFP method. We will then present two novel LP based TR methods which only use and employ basic built-in LP functions. Thus, these LP based TR methods will be very helpful in employing type-2 fuzzy sets and systems in different programming languages. Moreover, by taking account the connection of LFP to KMAs, a computationally efficient LP based TR method will be proposed. It will be proven that this LP based TR method can be seen as a kind of variation of the KMA (or vice versa). Simulation results have been presented to show the superiority of the LP based TR method in comparison to the KMA and Enhanced KMA.

In this paper, we will present design methods for Single input IT2-FLCs (SIT2-FLCs) and we will introduce an online tuning mechanism to enhance their control system performance. The most important feature of the SIT2-FLC is the closed form output presentation which is defined in a two dimensional domain. Based on this structural information, we will present design methods for SIT2-FLCs composed of 3 rules to produce a Smooth SIT2-FLC (S-SIT2-FLC) and an Aggressive SIT2-FLC (A-SIT2-FLC) by only tuning a single parameter. It will be shown that the S-SIT2-FLC will result in a potentially more robust control performance in comparison A-SIT2-FLC. However, the transient state and disturbance rejection performance of the S-SIT2-FLC might degrade in comparison to the A-SIT2-FLC. This drawback will be solved by tuning the FOU size of the SIT2-FLCs to provide a trade-off between the robust control performance of the S-SIT2-FLC and the acceptable transient and disturbance rejection performance of the A-SIT2-FLC structure. Thus, we will present a Gradient- Descent (GD) based online tuning mechanism to enhance both the transient state and disturbance rejection performances of the SIT2-FLCs while preserving a certain degree of the robustness against nonlinearities and disturbances. We will present simulation results where the GD based SIT2-FLC (GD-SIT2- FLC) is compared with the S-SIT2-FLC and the A-SIT2-FLC structures. Moreover, we will compare the performance GD-SIT2-FLC with a robust self-tuning Type-1 (T1) FLC which has a fuzzy based tuning mechanism. The results will show that the GD-SIT2-FLC enhances both the transient state and disturbance rejection performances when compared to the IT2 and robust self-tuning T1 counterparts.

This paper introduces an enhancement to linguistic forecast representation using Triangular Fuzzy Numbers (TFNs) called Enhanced Linguistic Generation and Representation Approach (ElinGRA). Since there is always an error margin in the predictions, there is a need to define error bounds in the forecast. The interval of the proposed presentation is generated from a Fuzzy logic based Lower and Upper Bound Estimator (FLUBE) by getting the models of forecast errors. Thus, instead of a classical statistical approaches, the level of uncertainty associated with the point forecasts will be defined within the FLUBE bounds and these bound can be used for defining fuzzy linguistic terms for the forecasts. Here, ElinGRA is proposed to generate triangular fuzzy numbers (TFNs) for the predictions. In addition to opportunity to handle the forecast as linguistic terms which will increase the interpretability, ElinGRA improved forecast accuracy of constructed TFNs by adding an extra correction term. The results of the experiments, which are conducted on two data sets, show the benefit of using ElinGRA to represent the uncertainty and the quality of the forecast.

In this paper, we will present the fundamental differences of Nie-Tan (NT) and the Karnik-Mendel (KM) Center of Sets Calculation Methods (CSCMs) on the Interval Type-2 (IT2) Fuzzy Logic Controller (FLC) performance based on analytical derivations. We will derive the Fuzzy Mappings (FMs) of the IT2-FLCs and then investigate how the IT2-FMs are affected by the CSCMs in terms of the Footprint of Uncertainty (FOU) parameters. We will also present a special case where the resulting FM of the KM reduces to its NT counterpart and show that the NT CSCM can be seen as an approximation of the KM CSCM. We will examine three different FOU parameter settings to show that for certain FOU parameter settings the IT2-FLC where the NT CSCMs is employed loses its FOU from a mathematical point of view. We will also present two necessary conditions for the design of the IT2-FLC so that the resulting controller has a symmetrical control surface and is capable to eliminate the steady state error of the system response. Then, by taking account these conditions, we will investigate the gain variations of the IT2-FLCs in terms of the control performance objectives. Based on the observations, we will recommend design guidelines for the IT2-FLCs. The presented results will show that although the NT CSCM has a relatively easier design phase and a closed form representation which might be an enabler for theoretical analyses of the IT2 FLCs, the KM CSCM seems to be superior in overall since it is capable to generate smooth and aggressive control actions which cannot be accomplished by its NT counterpart.

In this paper, the analytic formulation of the single input Fuzzy PID (FPID) controller output is derived to present an Internal Model Control (IMC) based design method. In this context, we have firstly derived the input- output relationship of the fuzzy controller and investigated the effect of the membership function (MF) parameters on the output of the Single input FPID (SFPID). Based the presented observations, design guidelines are presented on how to tune MF parameters of the controller to obtain aggressive and smooth control actions. Moreover, we have derived the analytic formulation of the SFPID controller output. It has been shown that the output formulation is analogous to the Conventional FPID (CFPID) and the PID controller ones. Moreover, we have also shown that the SFPID controller can be seen as combination of a PID controller and nonlinear compensation term. Thus, we have used this analytical information to employ the well-known IMC based design method to tune the design parameters of the SFPID structure. Comparative simulation results have been conducted on a benchmark nonlinear system to show that the SFPID improved the transient state performance while providing an identical disturbance rejection performance of the CFPID structure.

In this study, we will present a novel Internal Model Control (IMC) based Self-Tuning (ST) mechanism to tune the Scaling Factors (SFs) of the fuzzy PID controllers in an online manner. Moreover, we will present a fuzzy PI-D (FPI-D) structure in order to eliminate the derivative kick and the effect of noise on the control signal. The proposed IMC based fuzzy ST mechanism is constructed by two Fuzzy Inference Systems (FISs) and an IMC based SF (IMC-SF) parameter regulator. The two FISs will predict the current values of the system parameters by using the system output value and then the IMC-SF parameter regulator will tune the SFs of FPI-D with respect to presented tuning method. The performance of the proposed Self-Tuning FPI-D (ST-FPI-D) will be evaluated on a realtime laboratory scale extruder process with its discrete implementation via the ABB PLC PM573 industrial controller. We will compare and examine the control system performance of the proposed ST fuzzy control structure with an IMC based tuned ABB-PID and FPI-D structures. The real-time experimental results will show that the proposed ST-FPI-D structure enhanced significantly the control performance for various operating points and in the presence of uncertainties and nonlinearities when compared to the ABB-PID and FPI-D structures.

The interval type-2 fuzzy Proportional-Integral (PI) controller (IT2-FPI) might be able to handle high levels of uncertainties to produce a satisfactory control performance, which could be potentially due to the robust performance as a result of the smoother control surface around the steady state. However, the transient state and disturbance rejection performance of the IT2-FPI may degrade in comparison with the type-1 fuzzy PI (T1-FPI) counterpart. This drawback can be resolved via general type-2 fuzzy PI controllers which can provide a tradeoff between the robust control performance of the IT2-FPI and the acceptable transient and disturbance rejection performance of the type-1 PI controllers. In this paper, we will present a zSlices-based general type-2 fuzzy PI controller (zT2-FPI), where the secondary membership functions (SMFs) of the antecedent general type-2 fuzzy sets are adjusted in an online manner. We will examine the effect of the SMF on the closed-system control performance to investigate their induced performance improvements. This paper will focus on the case followed in conventional or self-tuning fuzzy controller design strategies, where the aim is to decrease the integral action sufficiently around the steady state to have robust system performance against noises and parameter variations. The zSlices approach will give the opportunity to construct the zT2-FPI controller as a collection of IT2-FPI and T1-FPI controllers. We will present a new way to design a zT2-FPI controller based on a single tuning parameter where the features of T1-FPI (speed) and IT2-FPI (robustness) are combined without increasing the computational complexity much when compared with the IT2-FPI structure. This will allow the proposed zT2-FPI controller to achieve the desired transient state response and provide an efficient disturbance rejection and robust control performance. We will present several simulation studies on benchmark systems, in addition to real-world experiments that were performed using the PIONEER 3-DX mobile robot that will act as a platform to evaluate the proposed systems. The results will show that the control performance of the self-tuning zT2-FPI control structure enhances both the transient state and disturbance rejection performances when compared with the type-1 and IT2-FPI counterparts. In addition, the self-tuning zT2-FPI is more robust to disturbances, noise, and uncertainties when compared with the type-1 and interval type-2 fuzzy counterparts.

In this paper, we will present a Boundary Function (BF) based type reduction/ denazification method for Interval Type-2 Fuzzy PID (IT2-PID) controllers. Thus, we have presented a novel representation of the optimal Switching Points (SPs) of the Karnik Mendel (KM) method by first decomposing the IT2-FPID controller into SubControllers (SCs) and then derived Boundary Functions (BFs) to determine the optimal SPs of each SCs. Since the optimal SPs are calculated without an iterative algorithm, the explicit expressions of how the SPs are determined is represented in analytical structure via the proposed BFs. We have presented comparative studies where the computational time performance of the proposed BF-KM method is compared to the KM and the decomposition based KM methods. The presented results show that proposed method is superior in comparison to the other compared methods and feasible for especially real time control applications where there is a need of small sampling times.

In this paper, the robust stability of a PD type Single input Interval Type-2 Fuzzy Logic Controller (SIT2-FLC) structure will be examined via the well-known Popov criterion and Lyapunov's direct method approach. Since a closed form formulation of the SIT2-FLC output is possible, the type-2 fuzzy functional mapping is analyzed in a two dimensional domain. Thus, mathematical derivations are presented to show that type-2 fuzzy functional mapping is a symmetrical function and always sector bounded. Consequently, the type-2 fuzzy system can be transformed into a perturbed Lur'e system to examine its robust stability. It has been proven that the stability of the PD type SIT2-FLC system is guaranteed with the aids of the Popov-Lyapunov method. A robustness measure of the type-2 fuzzy control system is also presented to give the bound of allowable uncertainties/ nonlinearities of the control system. Moreover, if this bound is known, the exact region of stability of the type-2 fuzzy system can be found since SIT2-FLC output can be presented in a closed form. An illustrate example is presented to demonstrate the robust stability analysis of the PD type SIT2-FLC system.

In this paper, we will explore whether the efficiency of the Interval Type-2 Fuzzy PID (IT2-FPID) lies in its ability to handle the high level of uncertainties rather than only having an extra degree of freedom provided by the Footprint of Uncertainty (FOU) on a highly nonlinear pH neutralization process. In order to illustrate the effect of the FOU on the control performance, the control performance of an IT2-FPID controller composed of 3×3 rules will be compared with a Type-1 Fuzzy PID (T1-FPID) controller of 5×5 rules. Moreover, in order to provide more extra degree of freedom to the T1-FPID structure, we will employ two self-tuning mechanisms where the weights of the fuzzy rules are adjusted in an online manner. Thus, we will present detailed comparative studies on how the extra degrees of freedom provided by the FOU or the employed tuning mechanisms affect the control and robustness performance. The presented analysis confirm that by tuning the FOU the performance of the IT2-FPID is better in wide range of operating points in comparison with its type-1 and self-tuning type-1 fuzzy counterparts which is not merely for the IT2-FPID use of extra parameters, but rather its different way of dealing with the disturbance, nonlinearities uncertainties and noise.

In this paper, we will present analytical derivations of the simplest the Interval Type-2 Fuzzy PID (IT2-FPID) controller output which is composed of only 4 rules. Thus, we will first propose a new visualizing method called Surface of the Switching Points (S-MAP) in order to better analyze the derivation of the Switching Points (SPs) of the Karnik-Mendel algorithms. We presented mathematical explanation of the S-MAP and showed that the SPs are determined by only two Boundary Functions (BFs) for the simplest IT2-FPID controller. We will then give the simplified analytical derivation of the simplest IT2-FPID controller around the steady state via the employed BFs and S-MAP. We have illustrated that the simplest IT2-FPID controller is in fact analogous to a conventional PID controller around the steady state. We presented the simplest IT2-FPID controller output in terms of the parameters of the antecedent IT2-FSs. We examined the effect of the design parameter over IT2-FPID control system performance. In the light of the observations, we presented a simple self-tuning mechanism to enhance the transient state and disturbance rejection performance.

In this paper, we will compare the closed loop control performance of interval type-2 fuzzy PID controller with the type-1 fuzzy PID and conventional PID controllers counterparts for the Magnetic Levitation Plant. We will also compare the control performance of the interval type-2 fuzzy PID controller with the self-tuning type-1 fuzzy PID controllers. The internal structures of implemented controllers are firstly examined and then the design parameters of each controller are optimized for a given reference trajectory. The paper also show the effect of the extra degree of freedom provided by antecedent membership functions of interval type-2 fuzzy logic controller on the closed loop system performance. The real-time experiments are accomplished on an unstable nonlinear system, QUANSER Magnetic Levitation Plant, in order to show the superiority of the optimized interval type-2 fuzzy PID controller compared to optimized PID and type-1 counterparts.

In this study, a single input interval type-2 fuzzy PID controller with a one to three inference mapping has been developed. Since it consists of a single input variable (the feedback error), a closed form formulation of the type-2 fuzzy controller output is possible. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Then, a simple strategy is proposed for a process independent type-2 fuzzy PID controller design. The developed single input type-2 fuzzy controller structure preserves the most preferred features of the PID such as simplicity, independent gain tuning and easy implementation. The one to three input mapping type-2 fuzzy controller structure has been implemented on an experimental ball and beam system. The results illustrated that the proposed type-2 fuzzy controller produces superior control performance than a one-to-one inference mapping type-2 fuzzy and conventional controllers.

In this paper, we will present a big bang-big crunch optimization (BB-BC) based approach for the design of an interval type-2 fuzzy PID controller. The implemented global optimization algorithm has a low computational cost and a high convergence speed. As a consequence, the BB-BC method is a very efficient search algorithm when the number of the optimization parameters is relatively big. The optimized type-2 fuzzy controller is compared with PID and type-1 fuzzy PID controllers which were optimized with either the BB-BC optimization method or conventional design strategies. The paper will also show the effect the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets on the closed loop system performance. We will present a comparative study performed on the highly nonlinear cascaded tank process to show the superiority of the optimized interval type-2 fuzzy PID controller compared to its optimized PID, type-1 counterparts.

In this study, a self-tuning method is proposed for interval type-2 fuzzy PID (IT2FPID) controllers. The proposed method tunes the fuzzy rule weights of the IT2FPID controllers in an on-line manner. The step response of the closed loop system is firstly taken into consideration and the response is divided into certain regions which is equal to the number of fuzzy sets defined for the error input of the IT2FPID controller. Moreover, the relative importance of the activated fuzzy rules is determined for these regions. We will present meta-rules for tuning of the fuzzy rule weights in order to obtain an appropriate control signal that will achieve a satisfactory system response. In this context, we will use two simple functions for the tuning of the rule weights of IT2FPID controller structure. The effectiveness of the proposed self-tuning IT2FPID is demonstrated on a real time ball and beam setup. The results illustrated that the proposed type-2 fuzzy controller gives a simple opportunity to enhance the control performance in comparison with the T1FPID and IT2FPID controller structures.

In this study, a novel online tuning method is proposed for fuzzy PID controllers via rule weighting. The rule weighting is performed with a fast evolutionary algorithm called Big Bang - Big Crunch (BB-BC) optimization algorithm which has a low computational time. In this study, the rule weights are selected as tuning parameter of fuzzy PID controller instead of structural parameter in order to improve the transient and steady state performance of the process. The BB-BC algorithm calculates the optimal rule weights that force the process output to follow the reference signal with an applicable control signal at each sampling period. The effectiveness of the proposed online rule weighting method is demonstrated on heat transfer process (PT-326 Process Trainer) in real time with comparisons. The results illustrate that the proposed online rule weighting method significantly improves the performance of the fuzzy PID controller structure.

The real-time path tracking control of mobile robots attracted considerable research interest since they inherit non-holonomic properties and uncertainties caused by the internal dynamics and/or feedback sensors. In this paper, we will propose a cascade control architecture, which includes the inner and outer control loops, for the path tracking control of mobile robots. In the proposed mobile robot cascade structure, interval type-2 fuzzy PID controllers are implemented as the outer and inner loop controllers to achieve a satisfactory tracking performance in presence of uncertainties. In this context, we will present a simple two stage mobile robot cascade design strategy. We will present real-time control experiments performed on the PIONEER 3-DX mobile robot to show the efficiency and the superior tracking performance of the type-2 fuzzy cascade control architecture in comparison with its conventional PID and type-1 fuzzy controllers counterparts in presence of uncertainties.

It is a known fact that type-2 fuzzy sets can represent highly nonlinear and/or uncertain systems much better than ordinary (type-1) fuzzy logic systems. Lately, interval type-2 fuzzy logic system inversion methods have been proposed and applied in various areas especially in control system design. In this study, an analytical methodology has been developed to form the inverse of the interval type-2 fuzzy models composed of four rules. However, since the interval type-2 fuzzy logic system output can not be presented in a closed form an iterative algorithm is proposed based on the developed analytical methodology. In order to demonstrate the feasibility of the proposed methodology, an illustrative study is given where the beneficial sides are shown clearly.