Footprint Of Uncertainty Research Articles

DyUnS: Dynamic and uncertainty-aware task scheduling for multiprocessor embedded systems

In this paper, an uncertainty-aware task scheduling approach capable of dynamically applying on multiprocessor embedded systems called ”DyUnS” is presented. This method is based on a type-2 fuzzy inference system to consider all design challenges of multiprocessor embedded systems along with their unavoidable uncertainty caused by the differences in models and measurements. The proposed method employs a fuzzy inference system to approximate the appropriate assignment of the application’s tasks to processing cores based on a defined rank including the main design challenges of the system including execution time, temperature, power consumption, and reliability. Moreover, an uncertainty level is defined for various design challenges as the footprint of uncertainty during the scheduling process to tackle the existing inaccuracy between the static models and dynamic environment. Thus, the generated uncertainty-aware solution could be efficiently employed as a dynamic scheduling at runtime. To demonstrate the effectiveness of DyUnS in tolerating uncertainty, several experiments on various application graphs are performed and its effectually is compared to related studies. Based on these experiments, DyUnS jointly optimizes the main design parameters, and its generated solution could be employed dynamically without violating the system’s thresholds. Moreover, its average difference compared to Monte Carlo uncertainty analysis is about 0.2 for all design parameters in three levels of uncertainty.

Optimization design of a new variable type hierarchical fuzzy system with interpretability improvement

This paper proposes a variable-type hierarchical fuzzy system (VTHFS) with high accuracy and strong interpretability. An improved rear-part direct-connected structure is used in the VTHFS, which eliminates the intermediate variables of the hierarchical fuzzy system (HFS). A new feature sorting method is proposed to find suitable input variables for each layer of subsystems of VTHFS. Under the proposed topology structure, layer by layer training of VTHFS can be achieved by changing the expected output of each layer, thereby reducing residual errors layer by layer and improving the prediction accuracy of VTHFS. Three fuzzy set distribution constraints are used in parameter optimization of VTHFS to improve the interpretability, including integrity, distinguishability, and footprint of uncertainty. The type of fuzzy set is automatically adjusted according to the uncertainty characteristics of input data measured by fuzziness, which further enhances the semantic interpretability of the VTHFS and solves the problem of requiring prior knowledge to define the fuzzy set type in existing research. Finally, the proposed VTHFS is tested on the regression data sets in the real world. Experimental results demonstrate the effectiveness of the feature sorting method and the fuzzy set type adjustment method. Through a large number of quantitative indicators, it can be confirmed that VTHFS has stronger interpretability and higher prediction accuracy compared to other fuzzy systems.

Legendre wavelet method based solution of fractional order prey–predator model in type-2 fuzzy environment

Researchers have recently examined several fractional-order prey–predator population models in a crisp or type-1 fuzzy environment. But incompleteness in the membership may also be present. In this regard, type-2 fuzzy numbers are employed in this inquiry to address the system’s imprecision since they are more realistic than type-1 fuzzy numbers in light of the uncertain membership grades. To numerically estimate the solution, the Legendre wavelet method (LWM) is used in conjunction with the r2-cut of the r1-plane form of the type-2 fuzzy parameters. To test the applicability of the present method, three cases are examined. The present solutions are quantitatively compared with the RK4 solutions in the crisp case. Approximations of the type-2 fuzzy prey and predator populations are also included. In addition, two- and three-dimensional plots are depicted to examine the behaviour of prey and predator populations in crisp and type-2 fuzzy cases. To assess the LWM’s efficacy, comparison graphs of the acquired solutions and the results of the RK4 approach are also provided. Numerical validation against the RK4 method in crisp cases demonstrates strong agreement, while revealing contrasting population behaviours in first two scenarios, whereas in the third case, both populations reduce with time. Further, the behaviour of the fuzzy solution has also been shown graphically using the footprint of uncertainty (FOU).

Derivation and characteristic investigation of a two-input, two-output interval type-2 fuzzy controller using product and operations

Interval type-2 (IT2) fuzzy logic, with the footprint of uncertainty (FOU) in membership functions, is very effective in dealing with disturbances and uncertainties of nonlinear systems. With this advantage, a two-input, two-output IT2 fuzzy controller with IT2 input and singleton type-1 fuzzy output sets is proposed for coupling systems. Firstly, the controller's input-output relationship is determined. Derivation results indicate that the controller is equivalent to the sum of a relay module and a local proportional-integral (PI) controller with variable gains. Next, analytical structure properties and gain variations are explored. It is demonstrated that the relay module is independent of the FOU, playing a dominant role in determining the control behavior of the IT2 controller. On the other hand, the control action of the PI controller diminishes when increasing the FOU and the number of fuzzy input sets. These properties contribute to the fast responsiveness of the controller and advantages in handling system uncertainty. Furthermore, the stability condition of this controller is established using the small gain theorem. Finally, both simulation and experiments are carried out to illustrate the applicability of the IT2 controller. The experimental results show that the controller's performance is embodied as the tracking errors of the two-linkage axes equal to ±4 μm, while the repeated positioning accuracy values are within ±3 μm.

A hybrid clustering-based type-2 adaptive neuro-fuzzy forecasting model for smart control systems

The practical applicability of smart control systems suffers from the existence of uncertainty in the physical parameters, sensor measurements and external excitations. Effective methods and its ease of implementation are required in the real-time active control strategies. To this end, in this research, we introduce an overlapping clusters and Multilayer Extreme Learning Machine (ML-ELM)-aided interval type-2 Takagi-Sugeno fuzzy inference system for vibration mitigation of smart structures. The combined Fuzzy C-Means (FCM) and imperialist competitive algorithm (ICA) with respect to degree of fuzzy overlap between clusters was utilized for characterizing the upper and lower membership functions forming the antecedent part. Furthermore, indeterminacy was modeled as footprint of uncertainty (FOU) and automatically formed based on statistical characteristics of soft clusters. The consequent parameters were adjusted by hybridization of ML-ELM and overlapping clusters, then the adaptivity was guaranteed. The predictive accuracy and generalization capability of the proposed method were demonstrated over the estimation of active control effort. Finally, to prove the practicability of the implemented framework, it was applied to four high-rise, mid-rise and low-rise benchmark building structures equipped with active mass damper (AMD), active tendon and active bracing system (ABS). The obtained results demonstrated the higher predictive accuracy and generalization ability of the presented data-driven control scheme compared to the other standard technical machine learning strategies. This practical guideline is easy to implement and automates control engineering tasks in real-time applications, solving one of the most challenging aspects of smart control systems.

Optimization for Interval Type-2 Polynomial Fuzzy Systems: A Deep Reinforcement Learning Approach

It is known that the interval type-2 (IT2) fuzzy controllers are superior compared to their type-1 counterparts in terms of robustness, flexibility, etc. However, how to conduct the type reduction optimally with the consideration of system stability under the fuzzy-model-based (FMB) control framework is still an open problem. To address this issue, we present a new approach through the membership-function-dependent (MFD) and deep reinforcement learning (DRL) approaches. In the proposed approach, the reduction of IT2 membership functions of the fuzzy controller is completing during optimizing the control performance. Another fundamental issue is that the stability conditions must hold subject to different type-reduction methods. It is tedious and impractical to resolve the stability conditions according to different type-reduction methods, which could lead to infinite possibility. It is more practical to guarantee the holding of stability conditions during type-reduction rather than resolving the stability conditions, the MFD approach is proposed with the imperfect premise matching (IPM) concept. Thanks to the unique merit of the MFD approach, the stability conditions according to all the different embedded type-1 membership functions within the footprint of uncertainty (FOU) are guaranteed to be valid. During the control processes, the state transitions associated with properly engineered cost/reward function can be used to approximately calculate the deterministic policy gradient to optimize the acting policy and then to improve the control performance through determining the grade of IT2 membership functions of the fuzzy controller. The detailed simulation example is provided to verify the merits of the proposed approach.

Automated blood glucose regulation for nonlinear model of type-1 diabetic patient under uncertainties: GWOCS type-2 fuzzy approach.

Regulating blood glucose level (BGL) for type-1 diabetic patient (T1DP) accurately is very important issue, an uncontrolled BGL outside the standard safe range between 70 and 180mg/dl results in dire consequences for health and can significantly increase the chance of death. So the purpose of this study is to design an optimized controller that infuses appropriate amounts of exogenous insulin into the blood stream of T1DP proportional to the amount of obtained glucose from food. The nonlinear extended Bergman minimal model is used to present glucose-insulin physiological system, an interval type-2 fuzzy logic controller (IT2FLC) is utilized to infuse the proper amount of exogenous insulin. Superiority of IT2FLC in minimizing the effect of uncertainties in the system depends primarily on the best choice of footprint of uncertainty (FOU) of IT2FLC. So a comparison includes four different optimization methods for tuning FOU including hybrid grey wolf optimizer-cuckoo search (GWOCS) and fuzzy logic controller (FLC) method is constructed to select the bestcontroller approach. The effectiveness of the proposed controller was evaluated under six different scenarios of T1DP using Matlab/Simulink platform. A 24-h scenario close to real for 100 virtual T1DPs subjected to parametric uncertainty, uncertain meal disturbance and random initial condition showed that IT2FLC accurately regulate BGL for all T1DPs within the standard safe range. The results indicated that IT2FLC using GWOCS can prevent side effect of treatment with blood-sugar-lowering medication. Also stability analysis for the system indicated that the system operates within the stability region of nonlinear system.

An application of generalized symmetric type-2 intuitionistic fuzzy variables to a transportation problem with the effect of a new ranking function

The primary objective of this study is to establish and introduce generalized symmetric type-2 intuitionistic fuzzy set, a type-2 fuzzy set extension. The major goal of such an extension is to enable the concept of fuzzy outranking relation which is known as foot print of uncertainty (FOU) to be employed in generalized symmetric type-2 intuitionistic fuzzy number (GST2IFN) for the first time. This is interesting to deal this GST2IFNs and it is complicated to find the equivalent crisp quantities due to this special structure. Hence, we have introduced a new ranking function using the mean level set of membership and non-membership functions. Besides, the arithmetic operations of the GST2IFNs are discussed. To express the effectiveness and application of the proposed GST2IF variables, a transportation problem (TP) is formulated with all cost parameters are GST2IFNs. In addition, few different algorithmic approaches are applied to find the initial basic feasible solution (IBFS) and optimal solution of the TP. Finally, the feasibility and richness of the obtained optimal solution is discussed.

Multiobjective Optimization Design of Interpretable Evolutionary Fuzzy Systems With Type Self-Organizing Learning of Fuzzy Sets

This paper proposes a new multiobjective optimization approach for designing a self-generated interpretable fuzzy logic system (FLS). The types of fuzzy sets can be constructed automatically by self-organizing method, so as to form a hybrid fuzzy system. Different from the existing evolutionary type-1 fuzzy system, which is full of type-1 fuzzy sets, and the evolutionary interval type-2 fuzzy system, which is full of interval type-2 fuzzy sets, there are both type-1 fuzzy sets and interval type-2 fuzzy sets in the hybrid fuzzy system. A new transparency-oriented objective function is defined, and the constraint of the footprint of uncertainty (FOU) of the interval type-2 (IT2) fuzzy set (FS) is considered for the first time. A new FS merging criterion focusing on the proximity of the cores of fuzzy sets is proposed, which is easy to calculate and maintains the characteristics of classical similarity measures. Combined with the new merging criterion, the online cluster and fuzzy set updating (OCFU) algorithm is employed to initialize the reference rule base and the type of fuzzy sets, as it is assumed that no training data are collected in advance. Based on the reference rule base, the advanced multiobjective front-guided continuous ant colony optimization (AMO-FCACO) algorithm is introduced to optimize all the free parameters of the FLS. With the operation mentioned above, the self-generated FLSs achieve a good balance between interpretability and performance. The effectiveness of the proposed method is verified by three nonlinear system tracking problems.

Type-2 Neutrosophic Set and Their Applications in Medical Databases Deadlock Resolution

Electronic patient data gives many advantages, but also new difficulties. Deadlocks may delay procedures like acquiring patient information. Distributed deadlock resolution solutions introduce uncertainty due to inaccurate transaction properties. Soft computing-based solutions have been developed to solve this challenge. In a single framework, ambiguous, vague, incomplete, and inconsistent transaction attribute information has received minimal attention. The work presented in this paper employed type-2 neutrosophic logic, an extension of type-1 neutrosophic logic, to handle uncertainty in real-time deadlock-resolving systems. The proposed method is structured to reflect multiple types of knowledge and relations among transactions’ features that include validation factor degree, slackness degree, degree of deadline-missed transaction based on the degree of membership of truthiness, degree of membership of indeterminacy, and degree of membership of falsity. Here, the footprint of uncertainty (FOU) for truth, indeterminacy, and falsity represents the level of uncertainty that exists in the value of a grade of membership. We employed a distributed real-time transaction processing simulator (DRTTPS) to conduct the simulations and conducted experiments using the benchmark Pima Indians diabetes dataset (PIDD). As the results showed, there is an increase in detection rate and a large drop in rollback rate when this new strategy is used. The performance of Type-2 neutrosophic-based resolution is better than the Type-1 neutrosophic-based approach on the execution ratio scale. The improvement rate has reached 10% to 20%, depending on the number of arrived transactions.

Analytical Structure and Performance of Interval Type-2 Fuzzy Two-Term Controllers with Varying Footprint of Uncertainty

While type-2 fuzzy control has gained a lot of attention in the recent years, several challenges still remain with respect to controller design. The footprint of uncertainty (FoU) plays a very important role in designing type-2 fuzzy controllers, since the performance of type-2 fuzzy controllers largely depends on the choice of FoU. In this paper, we propose a simplified model of interval type-2 (IT2) fuzzy two-term controllers of Takagi–Sugeno (TS) type with only two rules in the rule base. The controller model is derived with varying FoUs based on only two type-2 input fuzzy sets (the simplest case). An extension to multiple input fuzzy sets is also presented. We investigate the variation in control surface and computational aspects of the IT2 fuzzy two-term controller as the FoU is varied. The performance of the proposed IT2 fuzzy controller with respect to varying FoUs is evaluated in the simulation study.

Altitude control of a quadcopter using interval type-2 fuzzy controller with dynamic footprint of uncertainty

Footprint of uncertainty (FOU) characteristics of interval type-2 membership functions (IT2-MFs) play an important role in the performance and robustness of interval type-2 fuzzy controllers (IT2-FCs). In literature, fixed FOU structures are used in almost all IT2-FC designs. In this study, an IT2-FC with dynamic FOU is proposed to provide high performance and robustness in the altitude control of a quadcopter. A proportional–derivative (PD) type FC with Takagi–Sugeno rule structure is used in the design procedure of the proposed controller. Additionally, input variables (error and derivative of error) are defined by using triangular IT2-MFs. To provide a dynamic FOU structure, the height of the lower MF (LMF) of each interval type-2 fuzzy set is defined as a function of the system error. In this way, FOU levels of IT2-MFs are adjusted dynamically since the height value of the LMF directly determines the FOU level of the IT2-MF. To evaluate the effectiveness of the proposed controller, comparison studies are performed under different conditions, including unmodeled measurement noises, an external disturbance, and a system parameter uncertainty. A classical PD, a type-1 fuzzy PD, and an interval type-2 fuzzy PD with fixed FOU controllers are used in the comparisons. The comparison results demonstrate that the proposed interval type-2 fuzzy PD controller with dynamic FOU exhibits better performance and more robustness than the other controllers.

Investigation of Adjustable Radial Basis Function estimations for Non-Linear System

This paper gives idea about design method for adaptive neural controller is proposed and it is applied to the non-linear system Continuous stirred tank reactor CSTR. The investigating controller used in this paper is designed in tuned with adaptive process. To analyze the performance of effect of foot print of uncertainty on the controllers’ performance two various types of algorithms namely state feedback control and observer based control are used Radial basis function Neural network is utilized for approximation of the nonlinear function . Software validation result of suggested method is discussed below.

A Spatial Fuzzy Co-Location Pattern Mining Method Based on Interval Type-2 Fuzzy Sets

The goal of spatial co-location pattern mining is to find subsets of spatial features whose instances are often neighbors in a geographical space. In many practical cases, instances of spatial features contain not only spatial location information but also attribute information. Although there have been several studies that use type-1 fuzzy membership functions to mine spatial fuzzy co-location patterns, there is great uncertainty associated with such membership functions. To address this problem, we propose a spatial fuzzy co-location pattern mining method based on interval type-2 fuzzy sets. First, we collect the interval evaluation values of the interval data of attribute information from experts to form granular data. Next, the original type-1 fuzzy membership function is extended to a granular type-2 fuzzy membership function based on elliptic curves. We use a gradual method to adjust the parameters of the fuzzy membership function so that its footprint of uncertainty satisfies both the connectivity and the given confidence. Based on this granular type-2 fuzzy membership function, we fuzzify the attribute information of instances and define the concepts of fuzzy features and fuzzy co-location patterns. A fuzzy co-location pattern mining algorithm based on spatial cliques is then proposed, termed the FCPM-Clique algorithm. In order to improve the efficiency of the algorithm, we propose two pruning strategies. In addition, we extend two classical spatial pattern mining algorithms, the Join-based algorithm and the Joinless algorithm, to mine fuzzy co-location patterns based on interval type-2 fuzzy sets. Many experiments on synthetic and real-world datasets are conducted, the performance of the three algorithms is compared, and the effectiveness and efficiency of our proposed FCPM-Clique algorithm is demonstrated.

Development, experimental validation, and comparison of interval type-2 Mamdani fuzzy PID controllers with different footprints of uncertainty

Interval Type-2 Fuzzy PID (IT2FPID) controllers use Interval Type-2 Fuzzy Sets (IT2FSs). The difference between Type-1 Fuzzy PID (T1FPID) controllers and IT2FPID controllers is the Footprint of Uncertainty (FOU) which occurs due to the use of IT2FSs. FOU gives an extra degree of freedom to the controller structure, which is capable of handling uncertainty in the plant. However, the effect of FOU on the analytical structures of the IT2FPID controllers is not yet explored when uniformly/non-uniformly distributed multiple IT2FSs are used on the input side and uniformly/non-uniformly distributed multiple singleton fuzzy sets are considered on the output side of the controller. In this paper, controllers with three different types of FOUs and two different defuzzification methods are considered, and their analytical structures are derived. The suitability of the controllers is examined, and the properties of the suitable controllers are explored. Effects of FOU on the nonlinearity, gain, and computational aspects of the suitable controllers are studied. The applicability of proposed IT2FPID controllers is shown through simulation and real-time studies. The effectiveness of the proposed controllers is depicted by comparing their performances with that of the recently developed Integer Order Fuzzy PID (IOFPID) and Fractional Order Fuzzy PID (FOFPID) controllers.

Optimal Interval Type-2 Fuzzy Logic Control Based Closed-Loop Regulation of Mean Arterial Blood Pressure Using the Controlled Drug Administration

In pandemic times, the remote and automatic control/observation of physiological variables of the patients is the prime necessity for healthcare technologies. The closed-loop regulation of mean arterial pressure is essential for critically ill patients or post-surgery recovery patients. The physiological variables have serious issues such as parameter variations and uncertainties. In this paper, an interval type-2 fuzzy logic controller (IT2FLC) with footprints of uncertainty in the membership functions is presented in a two-layered design (TL-IT2FLC) that can efficiently deal with uncertainties and parameter variations. In this design, a pre-compensator IT2FLC is used, which deals with the uncertainties and parameter variations before the primary IT2FLC approach. The robustness analysis of the proposed method is investigated for external noise, and results are compared with traditional PID and T1-FLC techniques.

An Interval Type-2 Fuzzy Model of Computing with Words via Interval Type-2 Fuzzy Finite Rough Automata with Application in COVID-19 Deduction

Classical automata, fuzzy automata, and rough automata with input alphabets as numbers or symbols are formal computing models with values. Fuzzy automata and rough automata are computation models with uncertain or imprecise information about the next state and can only process the string of input symbols or numbers. To process words and propositions involved in natural languages, we need a computation model to model real-world problems by capturing the uncertainties involved in a word. In this paper, we have shown that computing with word methodology deals with perceptions rather than measurements and allows the use of words in place of numbers and symbols while describing the real-world problems together with interval type-2 (IT2) fuzzy sets which have the capacity to capture uncertainties involved in word using its footprint of uncertainty. The rough set theory, which has potential of modeling vagueness in the imprecise and ill-defined environment, introduces a computation model, namely, IT2 fuzzy rough finite automata, which is efficient to process uncertainties involved in words. Further, we have shown the application of introduced IT2 fuzzy finite rough automaton in the medical diagnosis of COVID-19 patients.

Observer-based interval type-2 fuzzy PID controller for PEMFC air feeding system using novel hybrid neural network algorithm-differential evolution optimizer

In this paper, a novel hybrid Neural Network Algorithm-Differential Evolution (NNA-DE) optimizer which integrates both NNA and DE is proposed. The proposed hybrid NNA-DE optimizer demonstrates better performance compared to the standard NNA and the other state-of-the-art optimization algorithms. The proposed hybrid NNA-DE algorithm is then employed for optimizing an observer-based interval type-2 fuzzy PID (OB-IT2FPID) controller applied to the proton exchange membrane fuel cell (PEMFC) air feeding system. The whole design parameters of the OB-IT2FPID controller including the scaling factors, interval type-2 membership function parameters and the footprint-of-uncertainty (FOU) are optimized using the proposed hybrid NNA-DE algorithm. The results show that the proposed NNA-DE optimized OB-IT2FPID controller achieves better performance in terms of set-point tracking, disturbance rejection and the time-domain performance indices. The robustness of the proposed NNA-DE optimized OB-IT2FPID controller against parametric uncertainty in the PEMFC air-feeding system is tested. The proposed controller demonstrated better robustness against parameter uncertainty in the system. Processor-in-the-Loop (PIL) approach is adopted to validate the performance of the proposed controller on embedded control hardware.

Modelling and analysis of an interval type-2 Mamdani fuzzy PID controller

From the last decade, modelling of Interval Type-2 (IT2) fuzzy controllers has become an exciting area of research in the field of control systems engineering. The input-output relationship of the fuzzy controller gives insights into the exact structure of the controller. From the literature, it is observed that IT2 fuzzy controllers handle plant uncertainty in a better way than their Type 1 (T1) counterparts due to the presence of additional Degree of Freedom (DoF) provided by the Footprint of Uncertainty (FoU) present in the membership functions of Interval Type-2 Fuzzy Sets (IT2FSs). Further, it is also noticed that controllers obtained with non-uniformly distributed fuzzy sets control the uncertain and nonlinear plants in a better way than their uniformly distributed counterparts. To take advantage of these two, in this study, the authors have made an attempt to unveil the exact input-output relationship of an Interval Type-2 Fuzzy PID (IT2FPID) controller, where the modelling is done using a particular type of FoU and non-uniformly distributed fuzzy sets. Apart from modelling, the properties of the newly derived controller are analysed. Moreover, to justify the theoretical development made in this manuscript, the applicability of the controller is shown through simulation, where an unstable chemical reactor plant with a large time delay is controlled. Finally, the effectiveness of the proposed controller is delineated by comparing its performance with that of some recently developed controllers.

Generating Type 2 Trapezoidal Fuzzy Membership Function Using Genetic Tuning

Fuzzy inference system (FIS) is a process of fuzzy logic reasoning to produce the output based on fuzzified inputs. The system starts with identifying input from data, applying the fuzziness to input using membership functions (MF), generating fuzzy rules for the fuzzy sets and obtaining the output. There are several types of input MFs which can be introduced in FIS, commonly chosen based on the type of real data, sensitivity of certain rule implied and computational limits. This paper focuses on the construction of interval type 2 (IT2) trapezoidal shape MF from fuzzy C Means (FCM) that is used for fuzzification process of mamdani FIS. In the process, upper MF (UMF) and lower MF (LMF) of the MF need to be identified to get the range of the footprint of uncertainty (FOU). This paper proposes Genetic tuning process, which is a part of genetic algorithm (GA), to adjust parameters in order to improve the behavior of existing system, especially to enhance the accuracy of the system model. This novel process is a hybrid approach which produces Genetic Fuzzy System (GFS) that helps to enhance fuzzy classification problems and performance. The approach provides a new method for the construction and tuning process of the IT2 MF, based on the FCM outcomes. The result is compared to Gaussian shape IT2 MF and trapezoid IT2 MF generated by the classic GA method. It is shown that the proposed approach is able to outperform the mentioned benchmarked approaches. The work implies a wider range of IT2 MF types, constructed based on FCM outcomes, and an optimum generation of the FOU so that it can be implemented in practical applications such as prediction, analytics and rule-based solutions.