General Type-2 Fuzzy Topological Spaces

In this paper, a presented definition of type-2 fuzzy sets and type-2 fuzzy set operation on it was given. The aim of this work was to introduce the concept of general topological spaces were extended in type-2 fuzzy sets with the structural properties such as open sets, closed sets, interior, closure and neighborhoods in topological spaces were extended to general type-2 fuzzy topological spaces and many related theorems are proved.

Nonsingular Terminal Sliding Mode Control With Ultra-Local Model and Single Input Interval Type-2 Fuzzy Logic Control for Pitch Control of Wind Turbines

As wind energy is becoming one of the fastestgrowing renewable energy resources,controlling large-scale wind turbines remains a challenging task due to its system model nonlinearities and high external uncertainties.The main goal of the current work is to propose an intelligent control of the wind turbine system without the need for model identification.For this purpose,a novel model-independent nonsingular terminal slidingmode control(MINTSMC)using the basic principles of the ultralocal model(ULM)and combined with the single input interval type-2 fuzzy logic control(SIT2-FLC)is developed for non-linear wind turbine pitch angle control.In the suggested control framework,the MINTSMC scheme is designed to regulate the wind turbine speed rotor,and a sliding-mode(SM)observer is adopted to estimate the unknown phenomena of the ULM.The auxiliary SIT2-FLC is added in the model-independent control structure to improve the rotor speed regulation and compensate for the SM observation estimation error.Extensive examinations and comparative analyses were made using a real-time softwarein-the-loop(RT-SiL)based on the dSPACE 1202 board to appraise the efficiency and applicability of the suggested modelindependent scheme in a real-time testbed.

Fire monitoring in coal mines using wireless underground sensor network and interval type-2 fuzzy logic controller

From the view of underground coal mining safety system, it is extremely important to continuous monitoring of coal mines for the prompt detection of fires or related problems inspite of its uncertainty and imprecise characteristics. Therefore, evaluation and inferring the data perfectly to prevent fire related accidental risk in underground coal mining (UMC) system are very necessary. In the present article, we have proposed a novel type-2 fuzzy logic system (T2FLS) for the prediction of fire intensity and its risk assessment for risk reduction in an underground coal mine. Recently, for the observation of underground coal mines, wireless underground sensor network (WUSN) are being concerned frequently. To implement this technique IT2FLS, main functional components are sensor nodes which are installed in coal mines to accumulate different imprecise environmental data like, temperature, relative humidity, different gas concentrations etc. and these are sent to a base station which is connected to the ground observation system through network. In the present context, a WUSN based fire monitoring system is developed using fuzzy logic approach to enhance the consistency in decision making system to improve the risk chances of fire during coal mining. We have taken Mamdani IT2FLS as fuzzy model on coal mine monitoring data to consider real-time decision making (DM). It is predicted from the simulated results that the recommended system is highly acceptable and amenable in the case of fire hazard safety with compared to the wired and off-line monitoring system for UMC. Legitimacy of the suggested model is prepared using statistical analysis and multiple linear regression analysis.

Type-2 Fuzzy Logic Controllers Based Genetic Algorithm for the Position Control of DC Motor

Type-2 fuzzy logic systems have recently been utilized in many control processes due to their ability to model uncertainty. This research article proposes the position control of (DC) motor. The proposed algorithm of this article lies in the application of a genetic algorithm interval type-2 fuzzy logic controller (GAIT2FLC) in the design of fuzzy controller for the position control of DC Motor. The entire system has been modeled using MATLAB R11a. The performance of the proposed GAIT2FLC is compared with that of its corresponding conventional genetic algorithm type-1 FLC in terms of several performance measures such as rise time, peak overshoot, settling time, integral absolute error (IAE) and integral of time multiplied absolute error (ITAE) and in each case, the proposed scheme shows improved performance over its conventional counterpart. Extensive simulation studies are conducted to compare the response of the given system with the conventional genetic algorithm type-1 fuzzy controller to the response given with the proposed GAIT2FLC scheme.

Optimization of Interval Type-2 Fuzzy Logic System Using Grasshopper Optimization Algorithm

The estimation of the fuzzy membership function parameters for interval type 2 fuzzy logic system(IT2-FLS)is a challenging task in the presence of uncertainty and imprecision.Grasshopper optimization algorithm(GOA)is a fresh population based meta-heuristic algorithm that mimics the swarming behavior of grasshoppers in nature,which has good convergence ability towards optima.The main objective of this paper is to apply GOA to estimate the optimal parameters of the Gaussian membership function in an IT2-FLS.The antecedent part parameters(Gaussian membership function parameters)are encoded as a population of artificial swarm of grasshoppers and optimized using its algorithm.Tuning of the consequent part parameters are accomplished using extreme learning machine.The optimized IT2-FLS(GOAIT2FELM)obtained the optimal premise parameters based on tuned consequent part parameters and is then applied on the Australian national electricity market data for the forecasting of electricity loads and prices.The forecasting performance of the proposed model is compared with other population-based optimized IT2-FLS including genetic algorithm and artificial bee colony optimization algorithm.Analysis of the performance,on the same data-sets,reveals that the proposed GOAIT2FELM could be a better approach for improving the accuracy of the IT2-FLS as compared to other variants of the optimized IT2-FLS.

Interval Type-2 Fuzzy Logic Control of Mobile Robots

Navigation of autonomous mobile robots in dynamic and unknown environments needs to take into account different kinds of uncertainties. Type-1 fuzzy logic research has been largely used in the control of mobile robots. However, type-1 fuzzy control presents limitations in handling those uncertainties as it uses precise fuzzy sets. Indeed type-1 fuzzy sets cannot deal with linguistic and numerical uncertainties associated with either the mechanical aspect of robots, or with dynamic changing environment or with knowledge used in the phase of conception of a fuzzy system. Recently many researchers have applied type-2 fuzzy logic to improve performance. As control using type-2 fuzzy sets represents a new generation of fuzzy controllers in mobile robotic issue, it is interesting to present the performances that can offer type-2 fuzzy sets by regards to type-1 fuzzy sets. The paper presented deep and new comparisons between the two sides of fuzzy logic and demonstrated the great interest in controlling mobile robot using type-2 fuzzy logic. We deal with the design of new controllers for mobile robots using type-2 fuzzy logic in the navigation process in unknown and dynamic environments. The dynamicity of the environment is depicted by the presence of other dynamic robots. The performances of the proposed controllers are represented by both simulations and experimental results, and discussed over graphical paths and numerical analysis.

Identification of Question and Non-Question Segments in Arabic Monologues Using Prosodic Features: Novel Type-2 Fuzzy Logic and Sensitivity-Based Linear Learning Approaches

In this paper, we extend our previous study of addressing the important problem of automatically identifying question and non-question segments in Arabic monologues using prosodic features. We propose here two novel classification approaches to this problem: one based on the use of the powerful type-2 fuzzy logic systems (type-2 FLS) and the other on the use of the discriminative sensitivity-based linear learning method (SBLLM). The use of prosodic features has been used in a plethora of practical applications, including speech-related applications, such as speaker and word recognition, emotion and accent identification, topic and sentence segmentation, and text-to-speech applications. In this paper, we continue to specifically focus on the Arabic language, as other languages have received a lot of attention in this regard. Moreover, we aim to improve the performance of our previously-used techniques, of which the support vector machine (SVM) method was the best performing, by applying the two above-mentioned powerful classification approaches. The recorded continuous speech is first segmented into sentences using both energy and time duration parameters. The prosodic features are then extracted from each sentence and fed into each of the two proposed classifiers so as to classify each sentence as a Question or a Non-Question sentence. Our extensive simulation work, based on a moderately-sized database, showed the two proposed classifiers outperform SVM in all of the experiments carried out, with the type-2 FLS classifier consistently exhibiting the best performance, because of its ability to handle all forms of uncertainties.

Type-2 fuzzy logic applications designed for active parameter adaptation in metaheuristic algorithm for fuzzy fault-tolerant controller

Purpose-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.Design/methodology/approach-The fuzzy logic-based parameter adaptation in the FPA is proposed.In addition,type2 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 type2 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.Findings-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 statitical analysis which validates the advantages of the interval type2 fuzzy FPA.The statistical Z-test is presented for comparison of efficiency between two fuzzy variants of the FPA optimization method.Originality/value-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 type2 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.

Interval type-2 fuzzy logic based radar task priority assignment method for detecting hypersonic-glide vehicles

A radar task priority assignment method based on interval type-2 fuzzy logic system(IT2 FLS)was designed to solve the problem of resource management for phased-array radar to detect hypersonic-glide vehicles(HGVs).The mathematical model of the radar task and the motion and detection models of HGVs are described in detail.The target threat of an HGV is divided into maneuver,speed,azimuth,and distance threats.In the radar task priority assignment method based on IT2 FLS,the maneuver factor,speed,azimuth difference,distance,and initial priority are input variables.The radar task priority is the output variable.To reduce the number of fuzzy rules and avoid rule explosion,an IT2 FLS with a hierarchical structure was designed.Finally,the feasibility of the task priority assignment method was verified by simulations.Simulation results showed that the method based on IT2 FLS has a higher precise tracking rate,mean initial priority,and target threat degree,and a shorter offset time.

Detection and classification of multiple power signal patterns with Volterra series and interval type-2 fuzzy logic system

The paper deals with the application of Volterra bound Interval type−2 fuzzy logic techniques in power quality assessment.This work proposes a new layout for detection,localization and classification of various types of power quality events.The proposed method exploits Volterra series for the extraction of relevant features,which are used to recognize different PQ events by Interval type-2 fuzzy logic based classifier.Numerous single as well as multiple powers signal disturbances have been simulated to testify the efficiency of the proposed technique.This time–frequency analysis results in the clear visual detection,localization,and classification of the different power quality events.The simulation results signify that the proposed scheme has a higher recognition rate while classifying single and multiple power quality events unlike other methods.Finally,the proposed method is compared with SVM,feed forward neural network and type−1 Fuzzy logic system based classifier to show the efficacy of the proposed technique in classifying the Power quality events.

An interval type-2 fuzzy logic controller for TCSC to improve the damping of power system oscillations

In this paper an interval type-2 fuzzy logic controller （IT2FLC） was proposed for thyristor controlled series capacitor （TCSC） to improve power system damping. For controller design, memberships of system variables were represented using interval type-2 fuzzy sets. The three-dimensional membership function of type-2 fuzzy sets provided additional degree of freedom that made it possible to directly model and handle uncertainties. Simulations conducted on a single machine infinite bus （SMIB） power system showed that the proposed controller was more effective than particle swarm optimization （PSO） tuned and type-1 fuzzy logic （T1FL） based damping controllers. Robust performance of the proposed controller was also validated at different operating conditions, various disturbances and parameter variation of the transmission line parameters.

Type-2 fuzzy description logic

Description logics （DLs） are widely employed in recent semantic web application systems. However, classical description logics are limited when dealing with imprecise concepts and roles, thus providing the motivation for this work. In this paper, we present a type-2 fuzzy attributive concept language with complements （ALC） and provide its knowledge representation and reasoning algorithms. We also propose type-2 fuzzy web ontology language （OWL） to build a fuzzy ontology based on type- 2 fuzzy ALC and analyze the soundness, completeness, and complexity of the reasoning algorithms. Compared to type-1 fuzzy ALC, type-2 fuzzy ALC can describe imprecise knowledge more meticulously by using the membership degree interval. We implement a semantic search engine based on type-2 fuzzy ALC and carry out experiments on real data to test its performance. The results show that the type-2 fuzzy ALC can improve the precision and increase the number of relevant hits for imprecise information searches.

Solving type-2 fuzzy relation equations via semi-tensor product of matrices

The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.

Fault tolerant control based on neural network interval type-2 fuzzy sliding mode controller for octorotor UAV

In this paper, a robust controller for a six degrees of freedom （6 DOF） octorotor helicopter control is proposed in presence of actuator and sensor faults. Neural networks （NN）, interval type-2 fuzzy logic control （IT2FLC） approach and sliding mode control （SMC） technique are used to design a controller, named fault tolerant neural network interval type-2 fuzzy sliding mode controll,~r （FTNNIT2FSMC）, for each subsystem of the octorotor helicopter. The proposed control scheme allows avoiding difficult modeling, attenuating the chattering effect of the SMC, reducing the number of rules for the fuzzy controller, and guaranteeing the stability and the robustness of the system. The simulation results show that the FTNNIT2FSMC can greatly alleviate the chattering effect, tracking well in presence of actuator and sensor faults.

Active fault tolerant control design for stochastic Interval Type-2 Takagi-Sugeno fuzzy model

Purpose-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.Design/methodology/approach–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.Findings–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.Originality/value–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.

Application of metaheuristic algorithms in interval type-2 fractional order fuzzy TID controller for nonlinear level control process under actuator and system component faults

Purpose–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.Design/methodology/approach–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.Findings–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.Originality/value–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.

Stable fuzzy controllers via LMI approach for non-linear systems described by type-2 T-S fuzzy model

Purpose-The purpose of this paper is to stabilize the type-2 Takagi-Sugeno(T-S)fuzzy systems with the sufficient and guaranteed stability conditions.The given conditions efficaciously handle parameter uncertainties by the upper and lower membership functions of the type-2 fuzzy sets(FSs).Design/methodology/approach-This paper reports on a relevant study of stable fuzzy controllers and type-2 T-S fuzzy systems and reported that the synthesis of controller for nonlinear systems described by the type-2 T-S fuzzy model is a key problem and it can be resolve to convex problems via linear matrix inequalities(LMIs).Findings-The multigain fuzzy controllers are established to improve the solvability of the stability conditions,and the authors design multigain fuzzy controllers which have extensive information of upper and lower membership grades.Consequently,the authors derive the traditional stability condition in terms of LMIs.One simulation examples illustrate the effectiveness and robustness of the derived stabilization conditions.Originality/value-The uncertain MIMO nonlinear system described by Type-2 Takagi-Sugeno(T-S)fuzzy model,and successively LMI approach used to determine the system stability conditions.The proposed control approach will give superior fault-tolerant control permanence under the actuator fault[partial loss of effectiveness(LOE)].Also the controller robust against the unmeasurable process disturbances.Additionally,the statistical z-test are carried out to validate the proposed control approach against the control approach proposed by Himanshukumar and Vipul(2019a).

Balanced scorecard-based analysis of customer expectations for cosmetology services:a hybrid decision modeling approach

The goal of this study is to analyze and characterize customer expectations in the cosmetics sector.Within this framework,first,the extant literature is reviewed,and 12 most prominent performance measurement criteria are identified.Then,these criteria are organized along the four different balanced scorecard dimensions.By employing an Interval Type-2 Fuzzy DEMATEL methodology,the weighted importance of these dimensions and criteria are identified.Additionally,with the Interval Type-2 Fuzzy TOPSIS approach,13 leading cosmetic service providers in Ukraine are ranked based on their relative scores.The findings of the study indicate that consumer is the most significant dimension while learning and growth seem to have the least importance.Similarly,it is also concluded that all consumerfocused criteria(i.e.diversification of services,feedback on the product and services,and customer loyalty)have the highest priorities in the complete criterion set.