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Showing papers on "Fuzzy logic published in 2018"


Journal ArticleDOI
TL;DR: With the proposed control, the stability of the closed-loop system is achieved via Lyapunov’s stability theory, and the tracking performance is guaranteed under the condition of state constraints and uncertainty.
Abstract: This paper investigates adaptive fuzzy neural network (NN) control using impedance learning for a constrained robot, subject to unknown system dynamics, the effect of state constraints, and the uncertain compliant environment with which the robot comes into contact. A fuzzy NN learning algorithm is developed to identify the uncertain plant model. The prominent feature of the fuzzy NN is that there is no need to get the prior knowledge about the uncertainty and a sufficient amount of observed data. Also, impedance learning is introduced to tackle the interaction between the robot and its environment, so that the robot follows a desired destination generated by impedance learning. A barrier Lyapunov function is used to address the effect of state constraints. With the proposed control, the stability of the closed-loop system is achieved via Lyapunov’s stability theory, and the tracking performance is guaranteed under the condition of state constraints and uncertainty. Some simulation studies are carried out to illustrate the effectiveness of the proposed scheme.

498 citations


Journal ArticleDOI
TL;DR: Comparison of three popular multi-criteria supplier selection methods in a fuzzy environment indicates that the three fuzzy methods arrive at identical supplier rankings, yet fuzzy GRA requires less computational complexity to generate the same results.

363 citations


Journal ArticleDOI
TL;DR: The results are compared with Pythagorean Fuzzy Failure Modes and Effects Analysis and it is revealed that the proposed method produces reliable and informative outcomes better representing the vagueness of decision making process.

344 citations


Journal ArticleDOI
TL;DR: This paper is concerned with dissipativity-based fuzzy integral sliding mode control (FISMC) of continuous-time Takagi-Sugeno (T-S) fuzzy systems with matched/unmatched uncertainties and external disturbance, and an appropriate integral-type fuzzy switching surface is put forward.
Abstract: This paper is concerned with dissipativity-based fuzzy integral sliding mode control (FISMC) of continuous-time Takagi-Sugeno (T-S) fuzzy systems with matched/unmatched uncertainties and external disturbance To better accommodate the characteristics of T-S fuzzy models, an appropriate integral-type fuzzy switching surface is put forward by taking the state-dependent input matrix into account, which is the key contribution of the paper Based on the utilization of Lyapunov function and property of the transition matrix for unmatched uncertainties, sufficient conditions are presented to guarantee the asymptotic stability of corresponding sliding mode dynamics with a strictly dissipative performance A FISMC law is synthesized to drive system trajectories onto the fuzzy switching surface despite matched/unmatched uncertainties and external disturbance A modified adaptive FISMC law is further designed for adapting the unknown upper bound of matched uncertainty Two practical examples are provided to illustrate the effectiveness and advantages of developed FISMC scheme

343 citations


Journal ArticleDOI
TL;DR: A novel adaptive fuzzy control scheme is proposed by a backstepping technique that can guarantee that the tracking error converges to a small neighborhood of the origin in a finite time, and the other closed-loop signals remain bounded.
Abstract: This paper addresses the finite-time tracking problem of nonlinear pure-feedback systems. Unlike the literature on traditional finite-time stabilization, in this paper the nonlinear system functions, including the bounding functions, are all totally unknown. Fuzzy logic systems are used to model those unknown functions. To present a finite-time control strategy, a criterion of semiglobal practical stability in finite time is first developed. Based on this criterion, a novel adaptive fuzzy control scheme is proposed by a backstepping technique. It is shown that the presented controller can guarantee that the tracking error converges to a small neighborhood of the origin in a finite time, and the other closed-loop signals remain bounded. Finally, two examples are used to test the effectiveness of proposed control strategy.

335 citations


Journal ArticleDOI
TL;DR: An approach to multiple attribute decision making based on q‐ROFGWHM (q‐ROFWGHM) operator is proposed and a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Abstract: The generalized Heronian mean and geometric Heronian mean operators provide two aggregation operators that consider the interdependent phenomena among the aggregated arguments. In this paper, the generalized Heronian mean operator and geometric Heronian mean operator under the q‐rung orthopair fuzzy sets is studied. First, the q‐rung orthopair fuzzy generalized Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy geometric Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy generalized weighted Heronian mean (q‐ROFGWHM) operator, and q‐rung orthopair fuzzy weighted geometric Heronian mean (q‐ROFWGHM) operator are proposed, and some of their desirable properties are investigated in detail. Furthermore, we extend these operators to q‐rung orthopair 2‐tuple linguistic sets (q‐RO2TLSs). Then, an approach to multiple attribute decision making based on q‐ROFGWHM (q‐ROFWGHM) operator is proposed. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

333 citations


Journal ArticleDOI
TL;DR: The prominent characteristic of these proposed operators are studied and some approaches to solve the Pythagorean fuzzy multiple attribute decision‐making problems are developed.
Abstract: In this paper, we utilize power aggregation operators to develop some Pythagorean fuzzy power aggregation operators: Pythagorean fuzzy power average operator, Pythagorean fuzzy power geometric operator, Pythagorean fuzzy power weighted average operator, Pythagorean fuzzy power weighted geometric operator, Pythagorean fuzzy power ordered weighted average operator, Pythagorean fuzzy power ordered weighted geometric operator, Pythagorean fuzzy power hybrid average operator, and Pythagorean fuzzy power hybrid geometric operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean fuzzy multiple attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

286 citations


Journal ArticleDOI
TL;DR: It is shown that the proposed adaptive fuzzy decentralized optimal control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of zero.
Abstract: In this paper, the problem of adaptive fuzzy decentralized optimal control is investigated for a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear large-scale systems contain the unknown nonlinear functions and unmeasured states. By utilizing the fuzzy logic systems to approximate the unknown nonlinear functions and cost functions, a fuzzy state observer is established to estimate the unmeasured states. The control design is divided into two phases. First, by using the state observer and the backstepping design technique, a feedforward decentralized controller with parameters adaptive laws is designed, by which the original controlled strict-feedback nonlinear large-scale system is transformed into an equivalent affine nonlinear large-scale system. Second, by using adaptive dynamic programming theory, a feedback decentralized optimal controller is developed for the equivalent affine nonlinear system. The whole adaptive fuzzy decentralized optimal control scheme consists of a feedforward decentralized controller and a feedback decentralized optimal controller. It is shown that the proposed adaptive fuzzy decentralized optimal control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of zero. In addition, the proposed control approach can guarantee that the cost functions are minimized. Simulation results are given to demonstrate the effectiveness of the proposed control approach.

285 citations


Journal ArticleDOI
TL;DR: A conflict bi-objective model for cost-emission based operation of industrial consumer in the presence of peak load management is proposed and fuzzy decision making approach is provided to select the trade-off solution from the Pareto solutions.

285 citations


Journal ArticleDOI
TL;DR: It is proven that distributed maneuvering errors converge to a residual set by virtue of cascade stability analysis, and an optimization-based command governor is employed to generate an optimal guidance signal for vehicle kinetics.
Abstract: This brief is concerned with the distributed maneuvering of multiple autonomous surface vehicles guided by a virtual leader moving along a parameterized path. In the guidance loop, a distributed guidance law is developed by incorporating a constant bearing strategy into a path-maneuvering design such that a prescribed formation pattern can be reached. To optimize the guidance signal under velocity constraint as well as minimize control torque during transient phase, an optimization-based command governor is employed to generate an optimal guidance signal for vehicle kinetics. The optimization problem is formulated as a bound-constrained quadratic programming problem, which is solved using a recurrent neural network. In the control loop, an estimator is developed where a fuzzy system is used to approximate unknown kinetics based on input and output data. Next, a kinetic control law is constructed based on the optimal command signal and the fuzzy-system-based estimator. By virtue of cascade stability analysis, it is proven that distributed maneuvering errors converge to a residual set. The simulation results illustrate the efficacy of the proposed method.

284 citations


Journal ArticleDOI
TL;DR: The proposed methods based on q‐ ROFWBM and q‐ROFWGBM operators are very useful to deal with MAGDM problems and are developed based on these operators.
Abstract: In the real multi-attribute group decision making (MAGDM), there will be a mutual relationship between different attributes. As we all know, the Bonferroni mean (BM) operator has the advantage of considering interrelationships between parameters. In addition, in describing uncertain information, the eminent characteristic of q-rung orthopair fuzzy sets (q-ROFs) is that the sum of the qth power of the membership degree and the qth power of the degrees of non-membership is equal to or less than 1, so the space of uncertain information they can describe is broader. In this paper, we combine the BM operator with q-rung orthopair fuzzy numbers (q-ROFNs) to propose the q-rung orthopair fuzzy BM (q-ROFBM) operator, the q-rung orthopair fuzzy weighted BM (q-ROFWBM) operator, the q-rung orthopair fuzzy geometric BM (q-ROFGBM) operator, and the q-rung orthopair fuzzy weighted geometric BM (q-ROFWGBM) operator, then the MAGDM methods are developed based on these operators. Finally, we use an example to illustrate the MAGDM process of the proposed methods. The proposed methods based on q-ROFWBM and q-ROFWGBM operators are very useful to deal with MAGDM problems.

Journal ArticleDOI
TL;DR: The design and analysis process of direct/indirect adaptive fuzzy control and fuzzy PID control in marine robotic fields are summarized and trends of the fuzzy future in Marine robotic vehicles are concluded based on its state of the art.
Abstract: Fuzzy logic control, due to its simple control structure, easy and cost-effective design, has been successfully employed to the application of guidance and control in robotic fields. This paper aims to review fuzzy-logic-based guidance and control in an important branch of robots—marine robotic vehicles. First, guidance and motion forms including the maneuvering, path following, trajectory tracking, and position stabilization are described. Subsequently, the application of three major classes of fuzzy logic control, including the conventional fuzzy control (Mamdani fuzzy control and Takagi–Sugeno–Kang fuzzy control), adaptive fuzzy control (self-tuning fuzzy control and direct/indirect adaptive fuzzy control), and hybrid fuzzy control (fuzzy PID control, fuzzy sliding mode control, and neuro-fuzzy control) are presented. In particular, we summarize the design and analysis process of direct/indirect adaptive fuzzy control and fuzzy PID control in marine robotic fields. In addition, two comparative results between hybrid fuzzy control and the corresponding single control are provided to illustrate the superiority of hybrid fuzzy control. Finally, trends of the fuzzy future in marine robotic vehicles are concluded based on its state of the art.

Journal ArticleDOI
TL;DR: A novel fuzzy hybrid model for FMEA is proposed in this paper, where fuzzy weighted risk priority number (FWRPN) is considered instead of RPN for each failure, and AFWRPNs decreased by 56% compared to ACF WRPNs.

Journal ArticleDOI
TL;DR: A novel event-triggered scheme is proposed to improve the transmission efficiency at each sampling instance and sufficient conditions for the resulting fuzzy Markovian jump systems are established in terms of coupled linear matrix inequalities.
Abstract: This paper investigates the problem of event-triggered control for a class of fuzzy Markov jump systems with general switching policies. A novel event-triggered scheme is proposed to improve the transmission efficiency at each sampling instance. Each transition rate allows to be unknown, known, or only its uncertain domains value is known. With the help of a tailored technique to bind the uncertain terms and an asynchronous operation approach to tackle the fuzzy system and fuzzy controller, sufficient conditions for the resulting fuzzy Markovian jump systems are established in terms of coupled linear matrix inequalities. Finally, an example is given to illustrate the validity of the developed technique.

Journal ArticleDOI
TL;DR: It is shown that by integrating the rough approach with the traditional fuzzy approach, the subjectivity that exists when defining the borders of fuzzy sets is eliminated.
Abstract: This paper presents a new approach for the treatment of uncertainty which is based on interval-valued fuzzy-rough numbers (IVFRN). It is shown that by integrating the rough approach with the traditional fuzzy approach, the subjectivity that exists when defining the borders of fuzzy sets is eliminated. IVFRN make decision making possible using only the internal knowledge in the operative data available to the decision makers. In this way objective uncertainties are used and there is no need to rely on models of assumptions. Instead of different external parameters in the application of IVFRN, the structure of the given data is used. On this basis an original multi-criteria model was developed based on an IVFRN approach. In this multi-criteria model the traditional steps of the BWM (Best–Worst method) and MABAC (Multi-Attributive Border Approximation area Comparison) methods are modified. The model was tested and validated on a study of the optimal selection of fire fighting helicopters. Testing demonstrated that the model based on IVFRN enabled more objective expert evaluation of the criteria in comparison with traditional fuzzy and rough approaches. A sensitivity analysis of the IVFRN BWM-MABAC model was carried out by means of 57 scenarios, the results of which showed a high degree of stability. The results of the IVFRN model were validated by comparing them with the results of the fuzzy and rough extension of the MABAC, COPRAS and VIKOR models.

Journal ArticleDOI
TL;DR: The design of a low complexity fuzzy logic controller of only 25-rules to be embedded in an energy management system for a residential grid-connected microgrid including renewable energy sources and storage capability is presented.
Abstract: This paper presents the design of a low complexity fuzzy logic controller of only 25-rules to be embedded in an energy management system for a residential grid-connected microgrid including renewable energy sources and storage capability. The system assumes that neither the renewable generation nor the load demand is controllable. The main goal of the design is to minimize the grid power profile fluctuations while keeping the battery state of charge within secure limits. Instead of using forecasting-based methods, the proposed approach use both the microgrid energy rate-of-change and the battery state of charge to increase, decrease, or maintain the power delivered/absorbed by the mains. The controller design parameters (membership functions and rule-base) are adjusted to optimize a pre-defined set of quality criteria of the microgrid behavior. A comparison with other proposals seeking the same goal is presented at simulation level, whereas the features of the proposed design are experimentally tested on a real residential microgrid implemented at the Public University of Navarre.

Journal ArticleDOI
TL;DR: A multi-expert multi-criteria decision making method to solve the innovative product design selection problem by developing an enhanced QFD method combined with the complicated fuzzy linguistic representation model, the probabilistic linguistic term set (PLTS), and the ranking method, ORESTE is proposed.

Journal ArticleDOI
Hani Hagras1
TL;DR: The author introduces XAI concepts, and gives an overview of areas in need of further exploration—such as type-2 fuzzy logic systems—to ensure such systems can be fully understood and analyzed by the lay user.
Abstract: Recent increases in computing power, coupled with rapid growth in the availability and quantity of data have rekindled our interest in the theory and applications of artificial intelligence (AI). However, for AI to be confidently rolled out by industries and governments, users want greater transparency through explainable AI (XAI) systems. The author introduces XAI concepts, and gives an overview of areas in need of further exploration—such as type-2 fuzzy logic systems—to ensure such systems can be fully understood and analyzed by the lay user.

Journal ArticleDOI
TL;DR: This paper investigates the problem of the fault detection filter design for nonhomogeneous Markovian jump systems by a Takagi–Sugeno fuzzy approach to ensure the estimation error dynamic stochastically stable, and the prescribed performance requirement can be satisfied.
Abstract: This paper investigates the problem of the fault detection filter design for nonhomogeneous Markovian jump systems by a Takagi–Sugeno fuzzy approach. Attention is focused on the construction of a fault detection filter to ensure the estimation error dynamic stochastically stable, and the prescribed performance requirement can be satisfied. The designed fuzzy model-based fault detection filter can guarantee the sensitivity of the residual signal to faults and the robustness of the external disturbances. By using the cone complementarity linearization algorithm, the existence conditions for the design of fault detection filters are provided. Meanwhile, the error between the residual signal and the fault signal is made as small as possible. Finally, a practical application is given to illustrate the effectiveness of the proposed technique.

Journal ArticleDOI
TL;DR: A novel integral-type fuzzy switching surface function is put forward, which contains singular perturbation matrix and state-dependent input matrix simultaneously in a transformed fuzzy SPSs such that the matched uncertainty/perturbation is completely compensated without amplifying the unmatched one.
Abstract: This paper presents a new sliding mode control (SMC) design methodology for fuzzy singularly perturbed systems (SPSs) subject to matched/unmatched uncertainties. To fully accommodate the model characteristics of the systems, a novel integral-type fuzzy switching surface function is put forward, which contains singular perturbation matrix and state-dependent input matrix simultaneously. Its corresponding sliding mode dynamics is a transformed fuzzy SPSs such that the matched uncertainty/perturbation is completely compensated without amplifying the unmatched one. By adopting a $\boldsymbol \varepsilon $ -dependent Lyapunov function, sufficient conditions are presented to guarantee the asymptotic stability of sliding mode dynamics, and a simple search algorithm is provided to find the stability bound. Then, a fuzzy SMC law is synthesized to ensure the reaching condition despite matched/unmatched uncertainties. A modified adaptive fuzzy SMC law is further constructed for adapting the unknown upper bound of the matched uncertainty. The applicability and superiority of obtained fuzzy SMC methodology are verified by a controller design for an electric circuit system.

Journal ArticleDOI
TL;DR: This paper extends MSM to Pythagorean fuzzy environment to propose the Pythagorian fuzzy Maclaurin symmetric mean and Pythgorean fuzzy weighted MacLaurin asymmetric mean operators and delivers a comparative analysis.
Abstract: The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among the multiinput arguments. In this paper, we extend MSM to Pythagorean fuzzy environment to propose the Pythagorean fuzzy Maclaurin symmetric mean and Pythagorean fuzzy weighted Maclaurin symmetric mean operators. Then, some desirable properties and special cases of these operators are discussed in detail. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver a comparative analysis.

Journal ArticleDOI
TL;DR: This paper proposes the intuitionistic fuzzy Dombi Bonferroni mean operators, which are very useful to deal with MAGDM problems and introduces the concept, the characteristics, the score function, the accuracy function and the operational rules of IFNs.
Abstract: The Bonferroni mean (BM) operator has the advantage of considering interrelationships between parameters, but it only can deal with crisp values. In recent years, many extended BM operators have been proposed to deal with fuzzy information. Dombi Bonferroni mean operators are special cases of general T-conorm and T-norm, which have the advantage of good flexibility with a general parameter. In this paper, we extend the BM operator based on the Dombi operations to propose the intuitionistic fuzzy Dombi Bonferroni mean (IFDBM) operator, the intuitionistic fuzzy weighted Dombi Bonferroni mean (IFWDBM) operator, the intuitionistic fuzzy Dombi geometric Bonferroni mean (IFDGBM) operator and the intuitionistic fuzzy weighted Dombi geometric Bonferroni mean (IFWDGBM) operator for dealing with the aggregation of intuitionistic fuzzy numbers (IFNs) and propose some multi-attribute group decision-making (MAGDM) methods. Firstly, we introduce the concept, the characteristics, the score function, the accuracy function and the operational rules of IFNs. Then, we propose the IFDBM operator, the IFWDBM operator, the IFDGBM operator and the IFWDGBM operator for aggregating IFNs. Then, we propose two MAGDM methods based on the proposed IFWDBM operator and the proposed IFWDGBM operator for dealing with MAGDM problems. Finally, we use an example to illustrate the MAGDM process of the proposed MAGDM methods. The proposed intuitionistic fuzzy Dombi Bonferroni mean operators are very useful to deal with MAGDM problems.

Journal ArticleDOI
TL;DR: A new model of three-way decisions and the corresponding decision-making procedure based on Pythagorean fuzzy information systems are proposed and developed and validated via the comparison analysis.

Journal ArticleDOI
TL;DR: A methodology based on fuzzy analytical hierarchy process (Fuzzy AHP and fuzzy technique for order performance by similarity to ideal solution) in which fuzzy AHP is applied to get the weights of each barrier by using pairwise comparison, and fuzzy TOPSIS is applied for the final ranking of the solutions of reverse logistics implementation.

Journal ArticleDOI
TL;DR: It is proved that the system output is driven to track the reference signal to a bounded compact set, all the signals in the closed-loop system are guaranteed to be bounded, and all the states do not transgress their constrained sets.
Abstract: In the paper, the adaptive observer and controller designs based fuzzy approximation are studied for a class of uncertain nonlinear systems in strict feedback. The main properties of the considered systems are that all the state variables are not available for measurement and at the same time, they are required to limit in each constraint set. Due to the properties of systems, it will be a difficult task for designing the controller and the stability analysis. Based on the structure of the considered systems, a fuzzy state observer is framed to estimate the unmeasured states. To ensure that all the states do not violate their constraint bounds, the Barrier type of functions will be employed in the controller and the adaptation laws. In the stability analysis, the effect caused by the constraints for all the states can be overcome by using the Barrier Lyapunov functions. Based on the proposed control approach, it is proved that the system output is driven to track the reference signal to a bounded compact set, all the signals in the closed-loop system are guaranteed to be bounded, and all the states do not transgress their constrained sets. The effectiveness of the proposed control approach can be verified by setting a simulation example.

Journal ArticleDOI
TL;DR: The results of sensitivity and comparative analyses show that the proposed integrated fuzzy MCDM approach for FMEA is valid and can provide valuable and effective information in assisting risk management decision-making.

Journal ArticleDOI
TL;DR: To identify critical success factors of project management and categorize them into five criteria groups, it is shown that the organization, external environment and sustainability are “cause” criteria, while project and project management are identified as “effects”.

Proceedings ArticleDOI
10 Sep 2018
TL;DR: After identifying the nature of noisy labels in distant supervision, a novel, more effective neural model AutoNER is proposed with a new Tie or Break scheme and how to refine distant supervision for better NER performance is discussed.
Abstract: Recent advances in deep neural models allow us to build reliable named entity recognition (NER) systems without handcrafting features. However, such methods require large amounts of manually-labeled training data. There have been efforts on replacing human annotations with distant supervision (in conjunction with external dictionaries), but the generated noisy labels pose significant challenges on learning effective neural models. Here we propose two neural models to suit noisy distant supervision from the dictionary. First, under the traditional sequence labeling framework, we propose a revised fuzzy CRF layer to handle tokens with multiple possible labels. After identifying the nature of noisy labels in distant supervision, we go beyond the traditional framework and propose a novel, more effective neural model AutoNER with a new Tie or Break scheme. In addition, we discuss how to refine distant supervision for better NER performance. Extensive experiments on three benchmark datasets demonstrate that AutoNER achieves the best performance when only using dictionaries with no additional human effort, and delivers competitive results with state-of-the-art supervised benchmarks.

Journal ArticleDOI
TL;DR: The stability and stabilization criteria are derived by taking into consideration an asynchronous difference between the normalized membership function of the T–S fuzzy DPS and that of the controller, which can stabilize states of the UMV.
Abstract: This paper is concerned with a Takagi–Sugeno (T–S) fuzzy dynamic positioning controller design for an unmanned marine vehicle (UMV) in network environments. Network-based T–S fuzzy dynamic positioning system (DPS) models for the UMV are first established. Then, stability and stabilization criteria are derived by taking into consideration an asynchronous difference between the normalized membership function of the T–S fuzzy DPS and that of the controller. The proposed stabilization criteria can stabilize states of the UMV. The dynamic positioning performance analysis verifies the effectiveness of the networked modeling and the controller design.

Journal ArticleDOI
TL;DR: By designing a novel adaptive sliding-mode controller, system perturbation or modeling error can be compensated, and the reachability of the sliding surface can be guaranteed with the ultimate uniform boundedness of the closed-loop system.
Abstract: This paper is concerned with the optimal guaranteed cost sliding-mode control problem for interval type-2 (IT2) Takagi–Sugeno fuzzy systems with time-varying delays and exogenous disturbances. In the presence of the uncertain parameters hidden in membership functions, an adaptive method is presented to handle the time-varying weight coefficients reflecting the change of the uncertain parameters. A new integral sliding surface is presented based on the system output. By designing a novel adaptive sliding-mode controller, system perturbation or modeling error can be compensated, and the reachability of the sliding surface can be guaranteed with the ultimate uniform boundedness of the closed-loop system. Optimal conditions of an $\mathcal {H}_{2}$ guaranteed cost function and an $\mathcal {H}_{\infty }$ performance index are established for the resulting time-delay control system. Finally, an inverted pendulum system represented by the IT2 fuzzy model is applied to illustrate the advantages and effectiveness of the proposed control scheme.