• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-11-16
Jun-Wei Wang; Han-Xiong Li

This paper presents a Lyapunov and partial differential equation (PDE)-based methodology to solve static collocated piecewise fuzzy control design of quasi-linear parabolic PDE systems subject to periodic boundary conditions. Two types of piecewise control, i.e., globally piecewise control and locally piecewise control are considered, respectively. A Takagi-Sugeno (T-S) fuzzy PDE model that is constructed via local sector nonlinearity method, is first employed to accurately describe spatiotemporal dynamics of quasi-linear PDEs. Based on the T-S fuzzy PDE model, a static collocated piecewise fuzzy feedback controller is constructed to guarantee the locally exponential stability of the resulting closed-loop system. Sufficient conditions for the existence of such fuzzy controller are developed by applying vector-valued Poincar\'{e}-Wirtinger inequality and its variations and a linear matrix inequality (LMI) relaxation technique. These sufficient conditions are presented in terms of standard LMIs. Finally, the performance of the suggested fuzzy controller is illustrated by numerical simulation results of a nonlinear PDE system described by quasi-linear FitzHugh-Nagumo equation with periodic boundary conditions.

更新日期：2018-11-17
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-11-16
Shi Li; Choon Ki Ahn; Zhengrong Xiang

This paper considers the problem of sampled-data adaptive output feedback fuzzy stabilization for switched uncertain nonlinear systems associated with asynchronous switching. A state observer is designed to estimate the unmeasured states, and fuzzy logic systems are employed to deal with the unknown nonlinear terms. Sampled-data controller and novel switched adaptive laws are constructed based on the recursive design method, and an average dwell time constraint is given to ensure that the closed-loop system is stable. The proposed scheme is employed in a mass-spring-damper system to demonstrate its effectiveness.

更新日期：2018-11-17
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date :
Linlin Chen; Degang Chen; Hui Wang

Fuzzy similarity relation is a function to measure the similarity between two samples. It is widely used to learn knowledge under the framework of fuzzy machine learning, and the selection of a suitable fuzzy similarity relation is obviously important for the learning task. It has been pointed out that fuzzy similarity relations can be brought into the framework of kernel functions in machine learning. This fact motivates us to study fuzzy similarity relation selection for fuzzy machine learning utilizing kernel selection methods in machine learning. Kernel alignment is a kernel selection method that is effective and has low computational complexity. In this paper we present novel methods for fuzzy similarity relation selection based on kernel alignment, and their use in attribution reduction for heterogeneous data. Firstly, we define an ideal kernel for classification problems, based on which a novel fuzzy kernel alignment model is proposed. Secondly, we present a method for fuzzy similarity relation selection based on the minimization of fuzzy alignment between the defined ideal kernel and a kernel for the learning problem at hand. In order to show the correctness of this selection method, we prove that the lower bound of the classification accuracy of a support vector machine will increase with the decrease of the fuzzy alignment value. Furthermore, we apply the proposed fuzzy similarity relation selection to attribute reduction for heterogeneous data. Finally, we present experimental results to show that the proposed method of fuzzy similarity relation selection based on fuzzy kernel alignment is effective.

更新日期：2018-11-12
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date :
Gaofeng Yu; Wei Fei; Deng-Feng Li

The purpose of this paper is to develop a compromise-typed variable weight decision method for solving hybrid multi-attribute decision making problems with multiple types of attribute values. The compromise-typed variable weight functions are defined and constructed by utility functions. Moreover, the variable weight synthesis and the orness measures based on the coefficients of absolute risk aversion are analyzed in variable weight decision making. The comprehensive values of alternatives based on the compromise-typed variable weight decision method are calculated. The decision making results are determined according to the comprehensive values. Finally, an example and a detailed comparison analysis are presented to show the applicability and validity of the proposed method.

更新日期：2018-11-12
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date :
Raul Perez-Fernandez; Bernard De Baets

Penalty functions have been a common tool in data aggregation for decades. Unfortunately, although the definition of a penalty function has evolved over the years, the use of penalty functions has been reduced to the aggregation of real numbers. However, in this 'era of aggregation', the need of generalizing the current definition in order to comply with the characteristics of new types of data arises. In this paper, we bring to the attention the notion of betweenness relation and propose to replace the currently-required property of quasi-convexity of a penalty function by the compatibility with a betweenness relation. Several construction methods for a penalty function are provided based on the use of a monometric. Interestingly, several prominent data aggregation methods are proved to fit into this new framework for penalty-based data aggregation.

更新日期：2018-11-12
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date :
Hao Sun; Rongrong Yu; Ye-Hwa Chen; Han Zhao

The optimal design problem of adaptive robust control for fuzzy mechanical systems with uncertainty is investigated in this paper. The uncertainty which may be nonlinear and (possibly fast) time-varying is assumed to be bounded, and the knowledge of the bound only lies within a prescribed fuzzy set. Based on the Udwadia and Kalaba's approach, an adaptive robust controller which is deterministic and is not the usual if-then rules-based is proposed to render the system to follow a class of pre-specified constraints approximately. The adaptive law is of leakage type which can adjust the magnitude of the adaptive parameter based on the nonlinear performance-dependent gain. The resulting controlled system is uniformly bounded and uniformly ultimately bounded, which is proved via the Lyapunov minimax approach. Furthermore, we propose a novel concept: fuzzy confidence to measure the expectation value of a fuzzy number. Then a fuzzy-based system performance index which includes the expectation value of the uniform ultimate boundedness (the average fuzzy performance) and the control cost is formulated. The optimal design problem associated with the control can then be solved by minimizing the performance index. As a result, the performance of the fuzzy mechanical system is both deterministically guaranteed and fuzzily optimized under this control.

更新日期：2018-11-12
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date :
Ke Li; Renzhi Chen; Dragan Savic; Xin Yao

Decomposition has become an increasingly popular technique for evolutionary multi-objective optimisation (EMO). A decomposition-based EMO algorithm is usually designed to approximate a whole Pareto-optimal front (PF). However, in practice, the decision maker (DM) might only be interested in her/his region of interest (ROI), i.e., a part of the PF. Solutions outside that might be useless or even noisy to the decision-making procedure. Furthermore, there is no guarantee to find the preferred solutions when tackling many-objective problems. This paper develops an interactive framework for the decomposition-based EMO algorithm to lead a DM to the preferred solutions of her/his choice. It consists of three modules, i.e., consultation, preference elicitation and optimisation. Specifically, after every several generations, the DM is asked to score a few candidate solutions in a consultation session. Thereafter, an approximated value function, which models the DM's preference information, is progressively learned from the DM's behaviour. In the preference elicitation session, the preference information learned in the consultation module is translated into the form that can be used in a decomposition-based EMO algorithm, i.e., a set of reference points that are biased toward to the ROI. The optimisation module, which can be any decomposition-based EMO algorithm in principle, utilises the biased reference points to guide its search process. Extensive experiments on benchmark problems with three to ten objectives fully demonstrate the effectiveness of our proposed method for finding the DM's preferred solutions.

更新日期：2018-11-12
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-11-09
Changzhu Zhang; Hak-Keung Lam; Jianbin Qiu; Chengju Liu; Qijun Chen

This paper is concerned with the problem of membership-function-dependent controller design for a class of discrete-time T-S fuzzy systems. Based on the partition method of premise variable space, the original T-S fuzzy model is equivalently converted into a kind of piecewise-fuzzy system. Then by employing some staircase functions, the continuous membership functions are approximated by a series of discrete values, via which the information of membership functions is brought into the stability analysis to reduce the design conservatism. With piecewise Lyapunov functions, the approaches to the piecewise-fuzzy state feedback and observer-based output feedback controller design are proposed, respectively, in terms of linear matrix inequalities such that the closed-loop system is asymptotically stable with a prescribed $\mathcal{H}_{\infty}$ performance level. It is shown that the membership functions of the fuzzy model and fuzzy controllers are not necessarily the same, which allows more design flexibility. Finally, two illustrative examples are provided to show the effectiveness of the developed methods.

更新日期：2018-11-10
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-11-09

We present an extension of the discrete basis problem, recently a profoundly studied problem, from the Boolean setting to the setting of fuzzy attributes, i.e. a setting of ordinal data. Our problem consists in finding for a given object-attribute matrix I containing truth degrees and a prescribed number k of factors the best approximate decomposition of I into an object-factor matrix A and a factor-attribute matrix B. Since such matrices represent fuzzy relations, the problem is related to but very different from that of decomposition of fuzzy relations as studied in fuzzy relational equations because neither A nor B are supposed to be known in our problem. We observe that our problem is NP-hard as an optimization problem. Consequently, we provide an approximation algorithm for solving this problem and provide its time complexity in the worst-case. The algorithm is inspired by the Asso algorithm, which is known for Boolean attributes, and is based on new considerations regarding associations among fuzzy attributes. We provide an experimental evaluation on various datasets and demonstrate that our algorithm is capable of extracting informative factors in data. We conclude with a discussion regarding future research issues.

更新日期：2018-11-10
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date :
Francesco Giannini; Michelangelo Diligenti; Marco Gori; Marco Maggini

In this paper we introduce the convex fragment of Lukasiewicz Logic and discuss its possible applications in different learning schemes. Indeed, the provided theoretical results are highly general, because they can be exploited in any learning framework involving logical constraints. The method is of particular interest since the fragment guarantees to deal with convex constraints, which are shown to be equivalent to a set of linear constraints. Within this framework, we are able to formulate learning with kernel machines as well as collective classification as a quadratic programming problem.

更新日期：2018-11-05
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date :
Bing Wang; Hanxin Xie; Xuedong Xia; Xian-Xia Zhang

This paper discusses a bi-criteria robust job-shop scheduling problem. Uncertain processing times are described by discrete scenario set. Two objectives are to minimize the mean makespan and the worst-case makespan among all scenarios, which realize solution optimality and solution robustness respectively. The well-known NSGA-II algorithm framework is incorporate with local SA operators to solve the proposed problem. The Metropolis criterion is defined by considering two objectives in order to evaluate bi-criteria individuals. United-scenario neighborhood definition is used in local SA operators to adapt to the uncertainty described by discrete scenarios. The developed hybrid algorithm was compared with four alternative algorithms for solving the proposed bi-criteria problem in an extensive experiment. The computational results show that the developed algorithm obviously outperformed other algorithms in all test instances.

更新日期：2018-11-05
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-11-02
Can Atilgan; Efendi Nasibov

The Fuzzy Joint Points (FJP) method is a density-based clustering method that uses a fuzzy neighborhood relation and eliminates the need for a neighborhood parameter. Even though the fuzzy neighborhood based clustering methods are proven to be fast enough, such that tens of thousands of data can be handled under a second, the space complexity is still a limiting factor. In this study, an FJP algorithm with reduced space complexity is proposed. The computational experiments show that the reduced space algorithm enables the method to be used for much larger data sets.

更新日期：2018-11-05
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-11-01
Carmen Torres-Blanc; Susana Cubillo; Pablo Hernandez-Varela

Type-2 fuzzy sets were introduced by L.A. Zadeh in 1975, as an extension of type-1 fuzzy sets. In this extension the degree in which an element belongs to a set is just a label of the linguistic variable "TRUTH", which allows to represent reality in a more appropriate way. On the other hand, negations play an essential role within fuzzy sets theory. In fact, they are necessary in order to obtain, for example, complements of fuzzy sets, dual of a t-norm or a t-conorm, entropies, implications, as well as to study the possible contradiction appearing in a fuzzy system. However, meanwhile negations on [0,1] (set of the membership degrees of a fuzzy set) have been deeply studied throughout the literature, the same has not happened with the negations on M = Map ([0,1], [0,1]), set of functions from [0,1] to [0,1] (and also set of the membership degrees of a type-2 fuzzy set) and so many aspects of the negations on M have not yet been investigated. In a previous paper, the authors established the axioms that an operation must satisfy to be considered a negation or a strong negation on a bounded poset (partially ordered set). They also presented a family of strong negations on L, set of normal and convex functions of M. Moreover, let us note that the main characteristic of fuzzy systems is just the flexibility in order to be able to represent knowledge according to each situation, offering different models among which the expert can choose the one that best suits his/her criteria. Thus, it seems useful to find broad sets of negations in M and in L, which, as far as we know, has not been done by other researchers. According to these ideas, in this paper the authors firstly present new negations and strong negations on L, and then they show, for the first time, some negations on M respect to each of the two partial orders defined in this set.

更新日期：2018-11-02
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-26
Chuan Li; Jose L. Valente de Oliveira; Mariela Cerrada Lozada; Diego Cabrera; Vinicio Sanchez; Grover Zurita

Bearings are fundamental mechanical components in rotary machines (engines, gearboxes, generators, radars, tur- bines, etc) that have been identified as one of the primary causes of failure in these machines. This make bearing fault diagnosis (detection, classification and prognosis) an economic very relevant topic, as well as a technically challenging one as evaluated by the extensive research literature on the subject. This paper employs a systematic methodology to identify, summarize, analyze, and interpret the primary literature on fuzzy formalisms for bearing fault diagnosis from 2000 to 2017 (March). The main contribution is an updated, unbiased and (to a higher extend) repeatable search, review and analysis (summary, classification, and critique) of the available approaches resorting to fuzzy formalisms in this trendy topic. A discussion on a new promising future research direction is provided. A comprehensive list of references is also included.

更新日期：2018-10-27
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-26
Zhenyu Lu; Panfeng Huang; Zhengxiong Liu; Haifei Chen

In this paper, a novel fuzzy-observer-based hybrid force/position control method is investigated for a bimanual teleoperation system in the presence of dynamics uncertainties, random network-induced time delays and multiple sampling rates of remote control signals and local measured data. The system structure consists of two pairs of position observers and contact force/torque estimators. The position observers are designed based on Takagi-Sugeno fuzzy inference rules to estimate delayed remote state with low sampling rates. The force/torque estimators are designed for estimating the coupled item of uncertain dynamics and contact forces without acceleration information. By adding a compensatory item based on an auxiliary model, the force estimation and motion tracking errors caused by varying dynamics uncertainties decrease, which is certified by two comparative force estimation techniques. The stability condition for the closed-loop system is also proved by the linear matrix inequality method based on the Lyapunov function. Finally, two simulations verify the effectiveness of the proposed method. The results indicate that the proposed method enables a better motion synchronization effect in soft handling environment.

更新日期：2018-10-27
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-26
Zhichao Feng; Zhi-Jie Zhou; Changhua Hu; Lei-Lei Chang; Guan-Yu Hu; Fujun Zhao

In current studies of the belief rule base (BRB) model, the attributes are assumed to be fully reliable and the observation data are directly used as input. However, in engineering practice, the observation data may be affected by some disturbance factors including the quality of the sensors and noise in the environment. Then the reliability of observation data may be affected and the modeling accuracy of BRB is influenced. As such, a new BRB model with attribute reliability (BRB-r) is proposed in this paper. In particular, a calculation method of attribute reliability is given based on the statistical method. Moreover, to integrate the attribute reliability into BRB-r, a new calculation method of matching degree is developed. The model's overall reliability denotes its ability to provide the correct result, and when the attributes are unreliable, the overall reliability of BRB-r is degraded. Thus, a calculation method for the overall reliability of BRB-r is developed to support decision making in engineering practice. A case study of the safety assessment of diesel engine is conducted to demonstrate the efficiency of the proposed BRB-r model.

更新日期：2018-10-27
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-25
Hongguang Ma; Jipeng Wu; Xiaoyang Li; Rui Kang

Condition-based maintenance has been developed as a very efficient maintenance strategy for guaranteeing multi-component system performance and preventing unexpected failures. However, there are some shortcomings in the existing condition-based maintenance optimization models. Firstly, the existing models didn't make use of the accelerated degradation testing data obtained at the stage of component development. Secondly, most of these models assumed perfect repair instead of imperfect repair. Thirdly, the degradation models used in these condition-based maintenance models cannot consider the epistemic uncertainty. Motivated by these problems, this paper presents a new condition-based maintenance optimization model for multi-component systems with imperfect repair. An integrated degradation prediction framework utilizing both accelerated degradation testing data and field data is presented to timely update the parameters in the proposed model. In order to solve the proposed multi-variable, nonlinear programming model, a novel genetic algorithm with self-crossover operation and shift-mutation operation is developed. Numerical examples and comparisons are conducted to evaluate the performance of the proposed model. Results show that the proposed model can evaluate the degradation process of components accurately and achieve lower total maintenance cost.

更新日期：2018-10-26
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-25
Honggui Han; Xiaolong Wu; Hongxu Liu; Junfei Qiao

Fuzzy neural networks (FNNs), with suitable structures, have been demonstrated to be an effective tool in approximating nonlinearity between input and output variables. However, it is time consuming to construct a FNN with appropriate number of fuzzy rules to ensure its generalization ability. To solve this problem, an efficient optimization technique is introduced in this paper. First, a self-adaptive structural optimal algorithm (SASOA) is developed to minimize the structural risk of FNN, leading to an improved generalization performance. Second, with the proposed SASOA, the fuzzy rules of SASOA-based FNN (SASOA-FNN) are generated or pruned systematically. This SASOA-FNN is able to organize the structure and adjust the parameters simultaneously in the learning process. Third, the convergence of SASOA-FNN is proved in the cases with fixed and updated structure and the guidelines for selecting the parameters are given. Finally, experimental studies of the proposed SASOA-FNN have been performed on several nonlinear systems to verify the effectiveness. The comparison with other existing methods has been made and demonstrated that the proposed SASOA-FNN is of better performance.

更新日期：2018-10-26
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-23
Rong Gao; Dan A. Ralescu

Wave equation is a commonly used tool for describing various kinds of wave phenomena in nature such as sound wave, water wave, electromagnetic wave and string vibration. It is a second-order partial differential equation and describe the wave propagation without noises. However, real world is filled with noises everywhere. So deterministic wave equation is not enough to model some problems with additive noises. As a remedy method, stochastic wave equation driven by Wiener process was presented where the noise is considered random and modeled by using Wiener process. Except for randomness, uncertainty associated belief degrees is another different type of indeterministic phenomenon. For modeling the wave phenomena with uncertain noises, this paper aims at deriving an uncertain wave equation driven by Liu process, which is a type of partial differential equation. Here, Liu process is a Lipschitz continuous uncertain process with stationary and independent increments. Then, we prove the existence and uniqueness of the solution of an uncertain wave equation. Additionally, we give the inverse uncertainty distribution of a solution of an uncertain wave equation.

更新日期：2018-10-23
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-23
Xi Wang; Shukai Li; Shuai Su; Tao Tang

This paper addresses the robust automatic train regulation problem in high-frequency metro lines with fuzzy passenger arrival rate. Due to uncertainty of passenger demand, the passenger arrival rate is assumed to be represented by fuzzy variables. A nonlinear state-space model is formulated to describe the characteristic of metro train operation. To satisfy the real-time requirement of train regulation, a fuzzy constrained predictive control approach is designed to optimize a cost function at each decision epoch subject to safety constraints on the control input. Based on Lyapunov stability theory and model predictive control(MPC) method, sufficient conditions for the existence of corresponding state feedback control law are given in a set of linear matrix inequalities (LMIs). Moreover, for reducing delays caused by the uncertain disturbances, the robust train regulation strategy is designed to guarantee that the practical train timetable tracks the nominal one with respect to certain disturbance attenuation level. The effectiveness of the proposed approach is validated by a number of experiments under the real running circumstances of Beijing Metro Yizhuang Line of China.

更新日期：2018-10-23
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-23
LeSheng Jin; Radko Mesiar; Ronald R. Yager

Given probability information, i.e., a probability measure m with a random variable x on outcome space N, the expected value of that random variable is commonly used as some valuable evaluation result for further decision making. However, there is no guarantee that the given probability information will be convincing to every decision makers. This can be because decision makers could suspect the reliability of that provided probability information, and can also be because decision makers often have their own different optimistic/pessimistic preferences. Often, such optimistic/pessimistic preferences can be easily embodied and expressed by some OWA weights functions w. This study firstly compares and analyzes some simpler methods to melt given OWA weights functions w with given probability measure m to generate a new probability measure, pointing out their respective advantages and shortcomings. Then, this study proposes the Melting Axioms which will both conform to our intuition and have mathematical reasonability. As the main finding of this study, we then propose the Crescent Method which will effectively melt given OWA weights function w with given probability measure m to generate a final resulted fuzzy measure. Based on that melted fuzzy measure we may perform Choquet Integral of x as the more convincing evaluation result to decision maker with preference w. The study also proposes several interesting mathematical results such as the orness of resulted fuzzy measure will always be equal to the orness of given OWA weights function w.

更新日期：2018-10-23
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-23
Yan Zhao; Huijun Gao; Jianbin Qiu

In this work, the fuzzy observer-based control problem is investigated for a class of nonlinear coupled systems, which consists of a hyperbolic partial differential equation (PDE) containing nonlinearities and a nonlinear ordinary differential equation (ODE). The nonlinear coupled system is represented as a Takagi-Sugeno (T-S) fuzzy coupled hyperbolic PDE-ODE model. Based on the T-S fuzzy model, a novel Lyapunov functional approach is proposed to design a fuzzy observer-based control strategy. More specifically, a fuzzy observer is presented to estimate the state variables of the fuzzy coupled PDE-ODE system with the measurements of the PDE, and the exponential convergence of the observer error is proved. Then a fuzzy controller is given utilizing the estimated states as feedback variables, and it is proved that the evolution profiles of the PDE and the trajectory of the ODE in the closed-loop fuzzy system converge exponentially to the desired values, respectively. The sufficient existence conditions of the fuzzy observer-based controller are formulated in terms of a set of space differential linear matrix inequalities (SDLMIs). A recursive algorithm based on the finite-difference approximation and the linear matrix inequality (LMI) techniques is provided to solve the SDLMIs. Finally, the results are applied to case study of a predator--prey system, and the simulations are performed to illustrate the effectiveness of the proposed observer-based control law.

更新日期：2018-10-23
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-18
Xin Wang; Jessie Ju H. Park; Kun Shi; Shouming Zhang; Lin Shi

This paper studies the problems of stability and stabilization of a class of chaotic systems (CSs) with T-S fuzzy model and nonuniform sampling. It designs for the first time a fuzzy sampled-data protocol based on a switched idea to tackle stability issue of such systems. Novel criteria on stabilization of CSs are established by employing a fuzzy membership functions (FMFs) dependent Lyapunov functional and analyzing the information of the time derivative of FMFs, which significantly utilize the available characteristics of the actual sampling pattern and FMFs simultaneously. Unlike the existing works, a larger sampling interval is obtained by this new approach. A simulation example on chaotic Rossler's system is employed to demonstrate the superiority and reduced conservatism of the proposed method.

更新日期：2018-10-19
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-18
Reza Ghanbari; Khatereh Ghorbani-Moghaddam; Mahdavi-Amiri Nezam

To solve a fuzzy linear program, we need to compare fuzzy numbers. Here, we make use of our recently proposed modified Kerre's method for comparison of LR fuzzy numbers. We give some new results on LR fuzzy numbers and show that to compare two LR fuzzy numbers, we do not need to compute the fuzzy maximum of two numbers directly. Using the modified Kerre's method, we propose a new variable neighborhood search (VNS) algorithm for solving fuzzy number linear programming problems. In our algorithm, the local search is defined based on descent directions, which are found by solving four crisp mathematical programming problems. In several methods, a fuzzy optimization problem is converted to a crisp problem but in our proposed method, using our modified Kerre's method, the fuzzy optimization problem is solved directly, without changing it to a crisp program. We give some examples to compare the performance of our proposed algorithm with some available methods. We show the effectiveness of our proposed algorithm by using the non-parametric statistical sign test.

更新日期：2018-10-19
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-18
Xia Liu; Yejun Xu; Rosana Montes; Ruxi Ding; Francisco Herrera

Recently, large scale group decision making (LSGDM) problems are becoming a hotspot. This paper focuses on the hesitant fuzzy LSGDM problems, where decision makers (DMs) use hesitant fuzzy reciprocal preference relations (HFPRs) to express their assessment information. HFPRs can represent the fuzziness and hesitancy of DM assessment information well. To improve the efficiency of hesitant fuzzy LSGDM problems, we first propose a reliability index-based consensus reaching process (RI-CRP). By assessing the ordinal consistency of DM's assessment information and measuring the deviation from collective opinion, the DM's opinion reliability index is given. To avoid unreliable information, we propose an unreliable DM management method to be used in the RI-CRP, based on the computation of DM's opinion reliability index. Moreover, an alternative ranking-based clustering (ARC) method with HFPRs is proposed to improve the efficiency of the RI-CRP. The similarity index between two DMs' opinions is provided, to ensure the ARC method can be effectively implemented. Compared with those clustering methods which need to preset several correlated parameters, the presented ARC method is more objective with a different approach based on the alternative ranking. A numerical example shows that the proposed ARC method and the RI-CRP are feasible and effective for hesitant fuzzy LSGDM problems.

更新日期：2018-10-19
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-18
Xiaomin Zhao; Ye-Hwa Chen; Fangfang Dong; Han Zhao

We consider an articial swarm mechanical system consisting of multiple agents. The agents are composed of mechanical components. The ideal kinematic performance includes mutual attractions and repulsions. This kinematic performance is embedded into the dynamics by being treated as a constraint. The Udwadia-Kalaba theory is then used to generate the required servo constraint force to assure the constraint is met for the nominal system. The system also includes uncertainty. The uncertainty in the swarm mechanical system is time-varying, whose value falls within a prescribed fuzzy set. For the robust control design, a creative β-measure based approach is introduced. The robust control guarantees uniform boundedness and uniform ultimate boundedness regardless of the actual value of the uncertainty. For the optimal choice of a control design parameter, a fuzzy-theoretic performance index is introduced. The resulting optimization problem is proven to be tractable, with the global solution to be existent and unique. Furthermore, the analytic expression of this solution is obtained. As a result, the optimal design problem is completely solved. To further demonstrate its effectiveness,we compare the performances of the swarm mechanical system under the robust control and Linear-Quadratic Regulator (LQR) control through simulation results with an illustrative example

更新日期：2018-10-19
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-04
Xiaojie Su; Yao Wen; Peng Shi; Hak-Keung Lam

This paper is concerned with the problem of generalized H2 reduced-order filter design for continuous Takagi-Sugeno fuzzy systems using an event-triggered scheme. For a continuous Takagi-Sugeno fuzzy dynamic system, we want to establish a reduced-order filter to transform the original model into a linear lower-order one. This filter can also approximate the original system with H2 performance, with a new type of event-triggered scheme used to decrease the communication loads and computation resources within the network. By transforming the filtering problem to a convex optimization one, conditions are presented to design the fuzzy reduced-order filter. Finally, two illustrative examples are used to verify the feasibility and applicability of the proposed design scheme.

更新日期：2018-10-05
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-04
Liang Cao; Hongyi Li; Ning Wang; Qi Zhou

For a class of large-scale nonlinear systems in nonstrict-feedback structure with immeasurable states, an adaptive decentralized fuzzy control strategy on the basis of event-triggered mechanism is investigated in this paper. Fuzzy logic systems are implemented to construct an observer, which approximates the unknown nonlinear function in the controller. In light of backstepping control technique and event-triggered mechanism, a decentralized adaptive fuzzy control approach is proposed to compensate for the effects of actuator faults. When the triggering condition is satisfied, the communication burden can be reduced. Moreover, the whole signals of the closed-loop system are semi-globally uniformly ultimately bounded and Zeno behavior can be successfully excluded. Furthermore, the outputs of subsystems can track the desired reference signals. Finally, some simulation results are utilized to testify the effectiveness of the proposed control scheme.

更新日期：2018-10-05
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-04
Dongrui Wu; Haitao Zhang; Jian Huang

The Representation Theorem for interval type-2 fuzzy sets (IT2 FSs), proposed by Mendel and John, states that an IT2 FS is a combination of all its embedded type-1 (T1) FSs, which can be non-convex and/or sub-normal. These non-convex and/or sub-normal embedded T1 FSs are included in developing many theoretical results for IT2 FSs, including uncertainty measures, the linguistic weighted averages (LWAs), the ordered LWAs (OLWAs), the linguistic weighted power means (LWPMs), etc.. However, convex and normal T1 FSs are used in most fuzzy logic applications, particularly computing with words. In this paper, we propose a Constrained Representation Theorem (CRT) for well-shaped IT2 FSs using only its convex and normal embedded T1 FSs, and show that IT2 FSs generated from three word encoding approaches and four computing with words engines (LWAs, OLWAs, LWPMs, and Perceptual Reasoning) are all well-shaped IT2 FSs. We also compute five constrained uncertainty measures (centroid, cardinality, fuzziness, variance, and skewness) for well-shaped IT2 FSs using the CRT. The CRT and the associated constrained uncertainty measures can be useful in computing with words, IT2 fuzzy logic system design using the principles of uncertainty, and measuring the similarity between two well-shaped IT2 FSs.

更新日期：2018-10-05
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-04
Imon Banerjee; Sankha S. Mullick; Swagatam Das

The Fuzzy $k$ -Nearest Neighbor Classifier (F $k$ NN) improves upon the flexibility of the $k$ -Nearest Neighbor Classifier ( $k$ NN) by considering each class as a fuzzy set, and estimating the membership of an unlabelled data instance for each of the classes. However, the question of validating the quality of the class memberships estimated by F $k$ NN for a regular multi-class classification problem still remains mostly unanswered. In this article we attempt to address this issue by first proposing a novel direction of evaluating a fuzzy classifier, by highlighting the importance of focusing on the class memberships estimated by F $k$ NN instead of its misclassification error. This leads us to finding novel theoretical upper bounds respectively on the bias and the mean squared error of the class memberships estimated by F $k$ NN. Additionally the proposed upper bounds are shown to converge towards zero with increasing availability of the labelled data points, under some elementary assumptions on the class distribution and membership function. The major advantages of our analysis are its simplicity, capability of a direct extension for multi-class problems, parameter independence, and practical implication in explaining the behavior of F $k$ NN in diverse situations (such as in presence of class imbalance). Furthermore, we provide a detailed simulation study on artificial and real datasets to empirically support our claims.

更新日期：2018-10-05
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-04
Shiqi Zheng; Peng Shi; Shuoyu Wang; Yan Shi

This paper concentrates on the problem of event triggered adaptive leader-following control for a class of multi-agent systems. The considered systems contain completely unknown interconnections and arbitrary asynchronously switching. To handle these nonlinearties, a new hierarchical barrier Lyapunov method is proposed. Based on this method, a novel adaptive fuzzy control strategy is designed to make the output tracking errors of the multi-agent systems converge to a small neighborhood of origin. Stability analysis shows that the proposed method can guarantee the compact set conditions of the fuzzy logic systems during the entire design process. Meanwhile, to reduce the computational burden, novel event triggered mechanisms are presented for both the transmission between two connected agents, and communication between the sensor and the controller in one agent. An illustrative example is presented to verify the effectiveness of the proposed controller.

更新日期：2018-10-05
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-04
Jay Daniel; Mohsen Naderpour; Chin-Teng Lin

Although the European Foundation for Quality Management (EFQM) is one of the best-known business excellence frameworks, its inherent self-assessment approaches have several limitations. A critical review of self-assessment models reveals that most models are ambiguous and limited to precise data. In addition, the impact of expert knowledge on scoring is overly subjective, and most methodologies assume the relationships between variables are linear. This paper presents a new fuzzy multi-layer assessment method that relies on fuzzy inference systems (FISs) to accommodate imprecise data and varying assessor experiences to overcome uncertainty and complexity in the EFQM model. The method was implemented, tested, and verified under real conditions in a regional electricity company. The case was assessed by internal company experts and external assessors from an EFQM business excellence organization, and the model was implemented using Matlab software. When comparing the classical model with the new model, assessors and experts favored outputs from the new model.

更新日期：2018-10-05
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-10-04
Shih-Pin Chen; Yu-Wen Chen

Because of the lack of available historical data resulting from increasing market turbulence and increasingly short product life cycles (PLCs), the demand for an inventory system has varied non-stochastically and must be subjectively determined. This paper investigates the economic production lot size (EPLS) inventory problem with fuzzy demands but without explicit membership functions, in which a positive lead time and shortages are allowed. An analysis method based on an cut representation and fuzzy ranking is proposed to derive the optimal inventory policy. In addition, the necessary and sufficient conditions for the optimal inventory policy are determined. The merits of the proposed approach include the ability to obtain a numeric and precise optimal policy rather than a fuzzy policy and no requirement for explicit forms of the membership functions of the fuzzy demands, which increases the generality of the proposed model. Additionally, practical insights are provided.

更新日期：2018-10-05
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-02-15
Jinwu Gao; Kai Yao; Jian Zhou; Hua Ke

The uncertain variable is used to model a quantity under human uncertainty, and the weighted $k$ -out-of- $n$ system is used to model a system of $n$ components, which functions if and only if the total weights of functioning components is greater than $k$ . Considering the human uncertainty in operating the system, this paper introduces the uncertain variable to the weighted $k$ -out-of- $n$ system, and proposes a concept of uncertain weighted $k$ -out-of- $n$ system. Some formulas are derived to calculate the reliability index of such a system. As a generalization, this paper also studies an uncertain weighted $k$ -out-of- $n$ system whose weights are estimated by experts and modeled by uncertain variables instead of crisp numbers. In addition, this paper analyzes the importance measure of the components in the uncertain weighted $k$ -out-of- $n$ systems.

更新日期：2018-10-04
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-03-09
Yanli Liu; Hongjun Ma; Hui Ma

Adaptive fuzzy fault-tolerant control problem for a class of uncertain switched stochastic nonlinear systems with time-varying asymmetric output constraints is addressed in this study. Under the action of well-designed asymmetric nonlinear mapping, fuzzy control technology, and backstepping recursive design scheme; the actuator faults of both loss of effectiveness and lock-in-place are considered to develop the adaptive fuzzy controller. The boundedness of all signals as well as the convergence of the output tracking error of the closed-loop plant to an arbitrary small neighborhood about zero are guaranteed by the developed fuzzy adaptive control strategy, and the time-varying output constraints are not violated. A simulation example is worked out to demonstrate the validity of the proposed control scheme.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-03-08
Xiubin Zhu; Witold Pedrycz; Zhiwu Li

Fuzzy models have been commonly used in system modeling and model-based control. Among various fuzzy models, Takagi–Sugeno (TS) fuzzy models form one of the intensively studied and applied categories of models. In this study, we are concerned with a development of a granular TS fuzzy model realized on a basis of numerical evidence and completed through a combination of fuzzy subspace clustering and the principle of optimal allocation of information granularity. The TS fuzzy models are built with the use of the fuzzy subspace clustering algorithm. Information granularity is regarded as a crucial design asset whose optimal allocation gives rise to granular fuzzy models and makes the constructed models to become better in rapport with experimental data. In comparison with fuzzy models, granular fuzzy models produce results (outputs) that are information granules rather than numeric entities being encountered in fuzzy models. In contrast with the commonly used optimization criteria, which emphasize the highest accuracy encountered at the numeric level, the performance of the granular TS fuzzy model is quantified in terms of the coverage and specificity criteria where such criteria are of interest in the evaluation of quality of information granules vis-à-vis experimental (numeric) data. Experimental results are reported for both synthetic datasets and publicly available data sets coming from the UCI machine learning repository.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-01-11
Qian-Fang Liao; Da Sun

Interaction measure determines decentralized and sparse control configurations for a multivariable process control. This paper investigates interval type-2 Takagi–Sugeno fuzzy (IT2TSF) model based interaction measures using two different criteria, one is controllability and observability gramians, the other is relative normalized gain array (RNGA). The main contributions are: first, a data-driven IT2TSF modeling method is introduced; second, explicit formulas to execute the two measures based on IT2TSF models are given; third, two interaction indexes are defined from RNGA to select sparse control configuration; fourth, the calculations to derive sensitivities of the two measures with respect to parametric variations in the IT2TSF models are developed; and fifth, the discussion to compare the two measures is presented. Three multivariable processes are used as examples to show that the results calculated from IT2TSF models are more accurate than that from their type-1 counterparts, and compared to gramian-based measure, RNGA selects more reasonable control configurations and is more robust to the parametric uncertainties.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-02-27
Luefeng Chen; Mengtian Zhou; Min Wu; Jinhua She; Zhentao Liu; Fangyan Dong; Kaoru Hirota

A three-layer weighted fuzzy support vector regression (TLWFSVR) model is proposed for understanding human intention, and it is based on the emotion-identification information in human–robot interaction. The TLWFSVR model consists of three layers, including adjusted weighted kernel fuzzy c -means for data clustering, fuzzy support vector regressions (FSVR) for information understanding, and weighted fusion for intention understanding. It aims to guarantee the quick convergence and satisfactory performance of the local FSVR via adjusting the weights of each feature in each cluster, in such a way that importance of different emotion-identification information is represented. Moreover, smooth human-oriented interaction can be obtained by endowing robot with human intention understanding capability. Experimental results show that the proposed TLWFSVR model obtains higher intention understanding accuracy and less computational time than that of two-layer fuzzy support vector regression, support vector regression, and back propagation neural network (BPNN), respectively. Additionally, the preliminary application experiments are performed in the developing human–robot interaction system, called emotional social robot system, where 12 volunteers and 2 mobile robots experience a scenario of “drinking at a bar.” Application results indicate that the bartender robot is able to understand customers’ order intentions.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2017-12-22

This paper presents the formulation of a flocking control algorithm for a group of autonomous underwater vehicles (AUVs). A leader–follower control strategy is employed to flock a group of AUVs along a predefined desired path. In this approach, leader AUVs are assumed to have global knowledge of the desired trajectory and the follower AUVs are not provided with this information. For keeping all the AUVs connected in a group, a flocking center is estimated. This flocking center is a virtual point whose position at any instant of time can be predicted by using a consensus algorithm. The controllers for the leader and follower AUVs are developed by implementing mathematical and fuzzy artificial potential functions. A group of four AUVs is considered for analyzing the efficacy of the developed control algorithm. Simulations are carried out both in obstacle-free and obstacle-rich environments. From the obtained results, it is observed that the proposed fuzzy flocking control algorithm provides effective cooperative motion control of multiple AUVs along the desired paths and avoid obstacles successively. It is also observed that the flocking controller developed based on fuzzy artificial potential function outperforms the controller with mathematical potential functions despite uncertainties owing to external disturbances.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-01-23
Mahardhika Pratama; Witold Pedrycz; Edwin Lughofer

The concept of ensemble learning offers a promising avenue in learning from data streams under complex environments because it better addresses the bias and variance dilemma than its single-model counterpart and features a reconfigurable structure, which is well suited to the given context. While various extensions of ensemble learning for mining nonstationary data streams can be found in the literature, most of them are crafted under static base-classifier and revisit preceding samples in the sliding window for a retraining step. This feature causes computationally prohibitive complexity and is not flexible enough to cope with rapidly changing environments. Their complexities are often demanding because they involve a large collection of offline classifiers due to the absence of structural complexities reduction mechanisms and lack of an online feature selection mechanism. A novel evolving ensemble classifier, namely Parsimonious Ensemble (pENsemble), is proposed in this paper. pENsemble differs from existing architectures in the fact that it is built upon an evolving classifier from data streams, termed Parsimonious Classifier. pENsemble is equipped by an ensemble pruning mechanism, which estimates a localized generalization error of a base classifier. A dynamic online feature selection scenario is integrated into the pENsemble. This method allows for dynamic selection and deselection of input features on the fly. pENsemble adopts a dynamic ensemble structure to output a final classification decision where it features a novel drift detection scenario to grow the ensemble's structure. The efficacy of the pENsemble has been numerically demonstrated through rigorous numerical studies with dynamic and evolving data streams, where it delivers the most encouraging performance in attaining a tradeoff between accuracy and complexity.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-01-23

In this paper, a fuzzy agglomerative (FuzAg) approach is proposed for community detection that iteratively updates membership degree of nodes. Earlier approaches assign membership degree to nodes based on communities only. We introduce the notion of self-membership in addition to the membership of different communities. The essence of self-membership is to give opportunity to all nodes in growing their own community. Nodes having higher self-membership degree are referred as anchors , and they get a chance to expand their associated community. Meanwhile, some new anchors may emerge in successive iterations, whereas false or redundant anchors get removed. The time complexity of the proposed algorithm is shown to be $O(n^2)$ . We compare the results of the proposed FuzAg algorithm with those of state-of-the-art fuzzy community detection algorithms on ten real-world datasets as well as on synthetic networks. Results indicated by various quality and accuracy metrics show impressive performance of FuzAg in identifying both disjoint communities and fuzzy communities.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-01-01
Huchang Liao; Xiaomei Mi; Zeshui Xu; Jiuping Xu; Francisco Herrera

Since the analytic network process (ANP) is much more flexible than the analytic hierarchy process in handling the multiple criteria decision making (MCDM) problems in which the criteria or subcriteria are interdependent, it has attracted many scholars’ attention and has been applied into many different areas. Given the powerfulness of intuitionistic fuzzy set in representing positive, negative, and indeterminate information, this paper investigates the ANP framework for the MCDM problems in which all the pairwise comparison judgment information over the objects are represented by intuitionistic fuzzy numbers. We first justify the way to decompose the MCDM problem into a holarchy and network structure, based on which, the intuitionistic fuzzy preference relations (IFPRs) can be constructed through pairwise comparisons over the goals, criteria, clusters as well as the elements. Considering that not all the IFPRs are consistent, we then propose a new method to derive the priorities from the IFPRs no matter the IFPRs are consistent or not. After that, we address the way to construct the supermatrix for those interdependent elements. The complete algorithm of intuitionistic fuzzy ANP (IFANP) is given and illustrated by a flow chart. To show the applicability and efficiency of the IFANP, we implement the method to a case study concerning the brand management of the six golden flowers of Sichuan liquor. Some comparative analyses are given to clarify the advantages and invalidation of the IFANP.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2017-12-15
Yin Sheng; Hao Zhang; Zhigang Zeng

In this paper, stabilization for a class of Takagi–Sugeno (T–S) fuzzy memristive neural networks (FMNNs) with mixed time delays is investigated. By virtue of theories of differential equations with discontinuous right-hand sides, inequality techniques, and the comparison method, an algebraic criterion is derived to stabilize the addressed FMNNs with bounded discrete and distributed time delays via a designed fuzzy state feedback controller in Filippov's sense. The result can be reinforced to stabilize FMNNs with unbounded discrete time delays. Meanwhile, exponential stabilization of FMNNs with bounded discrete time delays and unbounded continuously distributed delays is also discussed. FMNNs in this study are general since fuzzy logics and hybrid time delays are all considered, and the obtained conditions enhance and extend some existing ones. Finally, four numerical simulations are carried out to substantiate the efficiency and merits of developed theoretical results.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-01-26
Yan-Jun Liu; Mingzhe Gong; Shaocheng Tong; C. L. Philip Chen; Dong-Juan Li

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.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-02-28
Chang-Shing Lee; Mei-Hui Wang; Chi-Shiang Wang; Olivier Teytaud; Jialin Liu; Su-Wei Lin; Pi-Hsia Hung

Fuzzy relationships exist between students’ learning performance with various abilities and a test item. However, the challenges in implementing adaptive assessment agents are obtaining sufficient items, efficient and accurate computerized estimation, and a substantial feedback agent. Additionally, the agent must immediately estimate students’ ability item by item, which places a considerable burden on the server, especially for a group test. Hence, the implementation of an adaptive assessment agent is more difficult in practice. This paper proposes an agent with particle swarm optimization (PSO) based on a fuzzy markup language (FML) for students’ learning performance evaluation and educational applications, and the proposed agent is according to the response data from a conventional test and an item response theory (IRT)-based three-parameter logistic model. First, we apply a Gauss–Seidel based parameter estimation mechanism to estimate the items’ parameters according to the response data, and then to compare its results with those of an IRT-based Bayesian parameter estimation mechanism. In addition, we propose a static-IRT test assembly mechanism to assemble a form for the conventional test. The presented FML-based dynamic assessment mechanism infers the probability of making a correct response to the item for a student with various abilities. Moreover, this paper also proposes a novel PSO-based FML (PFML) learning mechanism for optimizing the parameters between items and students. Finally, we adopt a K -fold cross-validation mechanism to evaluate the performance of the proposed agent. Experimental results show that the novel PFML learning mechanism for the parameter estimation and learning optimization performs favorably. We believe the proposed PFML will be a reference for education research and pedagogy and an important colearning mechanism for future human–machine educational applications.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-02-16
Pascual Julián-Iranzo; Fernando Sáenz-Pérez

This paper describes a proposal for a deductive database system with fuzzy ${{\small \mathsf{Datalog}}}$ as its query language. Concepts supporting the fuzzy logic programming system ${\small{\mathsf{Bousi}}}{\sim} {{\small \mathsf{Prolog}}}$ are tailored to the needs of the deductive database system ${{\small \mathsf{DES}}}$ . We develop a version of fuzzy ${{\small \mathsf{Datalog}}}$ where programs and queries are compiled to the ${{\small \mathsf{DES}}}$ core ${{\small \mathsf{Datalog}}}$ language. Weak unification and weak SLD resolution are adapted for this setting, and extended to allow rules with truth degree annotations. We provide a public implementation in ${{\small \mathsf{Prolog}}}$ , which is open source, multiplatform, portable, and in-memory, featuring a graphical user interface. A distinctive feature of this system is that, unlike others, we have formally demonstrated that our implementation techniques fit the proposed operational semantics. We also study the efficiency of these implementation techniques through a series of detailed experiments. Moreover, a database example for a recommender system is used to illustrate some of the features of the system and its usefulness.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2017-12-22
Jesús Alberto Meda-Campaña; Araceli Grande-Meza; José de Jesús Rubio; Ricardo Tapia-Herrera; Tonatiuh Hernández-Cortés; Airam V. Curtidor-López; Luis Alberto Páramo-Carranza; Irving Omar Cázares-Ramírez

An approach to design stabilizers and observers for a class of multiple-input multiple-output (MIMO) Takagi–Sugeno (T–S) fuzzy models is developed on the basis of local gains and the searching for a set of interpolation functions capable of properly combining the aforementioned local gains. As expected, the existence of such interpolation functions depends on the controllability and observability properties of the overall multivariable T–S fuzzy model. For that reason, practical controllability and observability tests are also proposed for MIMO T–S fuzzy systems. Some numerical simulations are used in order to validate the efficacy of the method. Besides, the results are compared with an approach based on linear matrix inequalities, namely parallel distributed compensation.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-02-08
Imo Eyoh; Robert John; Geert De Maere; Erdal Kayacan

This paper presents a novel application of a hybrid learning approach to the optimisation of membership and nonmembership functions of a newly developed interval type-2 intuitionistic fuzzy logic system (IT2 IFLS) of a Takagi–Sugeno–Kang (TSK) fuzzy inference system with neural network learning capability. The hybrid algorithms consisting of decoupled extended Kalman filter (DEKF) and gradient descent (GD) are used to tune the parameters of the IT2 IFLS for the first time. The DEKF is used to tune the consequent parameters in the forward pass while the GD method is used to tune the antecedents parts during the backward pass of the hybrid learning. The hybrid algorithm is described and evaluated, prediction and identification results together with the runtime are compared with similar existing studies in the literature. Performance comparison is made among the proposed hybrid learning model of IT2 IFLS, a TSK-type-1 intuitionistic fuzzy logic system (IFLS-TSK), and a TSK-type interval type-2 fuzzy logic system (IT2 FLS-TSK) on two instances of the datasets under investigation. The empirical comparison is made on the designed systems using three artificially generated datasets and three real world datasets. Analysis of results reveal that IT2 IFLS outperforms its type-1 variants, IT2 FLS and most of the existing models in the literature. Moreover, the minimal run time of the proposed hybrid learning model for IT2 IFLS also puts this model forward as a good candidate for application in real time systems.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-02-01
Quan-Yong Fan; Guang-Hong Yang

This paper presents a novel event-triggered adaptive fuzzy fault-tolerant control approach for a class of uncertain nonlinear systems without the requirement for the online fault estimation. The main objective is to guarantee the stability of the faulty systems consuming less communication resources. Different from the existing results, a specific event-trigger error is designed, which is expected to reduce the amount of communications further. The generalized fuzzy hyperbolic model is employed to approximate the ideal fault-tolerant control policy in the framework of event-based sampled-data control. Based on the stability theory for nonlinear impulsive dynamical systems, the fuzzy adaptive control policy with a novel event-based weight update law is proposed to guarantee the stability of the closed-loop faulty system. In addition, the existence of a positive lower bound of the interevent interval is ensured to avoid the Zeno phenomenon. Finally, the simulation results are provided to show the effectiveness and better performance of the proposed scheme.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-02-01
Faxiang Zhang; Jing Hua; Yimin Li

In this paper, a design method of indirect adaptive fuzzy controller is proposed for a class of single-input single-output (SISO) nonlinear systems with input–output nonlinear relationship. In this method, fuzzy systems are utilized to approximate unknown nonlinear functions, and a state observer is designed to estimate the unmeasured state. Under the given constraint conditions of the system parameters, the adaptive law is given. Meanwhile, the stability of the closed-loop system is proven with all state variables being uniformly bounded in the Lyapunov sense. Moreover, the convergence of the fuzzy control system is analyzed. The simulation results show the feasibility, effectiveness, and universality of the designed method.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-01-01
Juan Carlos Figueroa-García; Yurilev Chalco-Cano; Heriberto Román-Flores

This paper presents a ranking method, two distances, and some definitions for ordering interval type-2 fuzzy numbers based on the Yager index for type-1 fuzzy numbers. The proposed Yager index provides closed equations for the central tendency of well-defined interval type-2 fuzzy numbers. Some numerical examples are given, a comparison to the centroid of an interval type-2 fuzzy number is performed, and some interpretation issues are discussed.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2017-12-27
Guoxing Wen; C. L. Philip Chen; Jun Feng; Ning Zhou

The paper proposes an optimized leader–follower formation control for the multi-agent systems with unknown nonlinear dynamics. Usually, optimal control is designed based on the solution of the Hamilton–Jacobi–Bellman equation, but it is very difficult to solve the equation because of the unknown dynamic and inherent nonlinearity. Specifically, to multi-agent systems, it will become more complicated owing to the state coupling problem in control design. In order to achieve the optimized control, the reinforcement learning algorithm of the identifier–actor–critic architecture is implemented based on fuzzy logic system (FLS) approximators. The identifier is designed for estimating the unknown multi-agent dynamics; the actor and critic FLSs are constructed for executing control behavior and evaluating control performance, respectively. According to Lyapunov stability theory, it is proven that the desired optimizing performance can be arrived. Finally, a simulation example is carried out to further demonstrate the effectiveness of the proposed control approach.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-03-12
Bożena Małysiak-Mrozek; Marek Stabla; Dariusz Mrozek

In recent years, many fields that experience a sudden proliferation of data, which increases the volume of data that must be processed and the variety of formats the data is stored in have been identified. This causes pressure on existing compute infrastructures and data analysis methods, as more and more data are considered as a useful source of information for making critical decisions in particular fields. Among these fields exist several areas related to human life, e.g., various branches of medicine, where the uncertainty of data complicates the data analysis, and where the inclusion of fuzzy expert knowledge in data processing brings many advantages. In this paper, we show how fuzzy techniques can be incorporated in big data analytics carried out with the declarative U-SQL language over a big data lake located on the cloud. We define the concept of big data lake together with the Extract, Process, and Store process performed while schematizing and processing data from the Data Lake, and while storing results of the processing. Our solution, developed as a Fuzzy Search Library for Data Lake, introduces the possibility of massively parallel, declarative querying of big data lake with simple and complex fuzzy search criteria, using fuzzy linguistic terms in various data transformations, and fuzzy grouping. Presented ideas are exemplified by a distributed analysis of large volumes of biomedical data on Microsoft Azure cloud. Results of performed tests confirm that the presented solution is highly scalable on the Cloud and is a successful step toward soft and declarative processing of data on a large scale. The solution presented in this paper directly addresses three characteristics of big data, i.e., volume , variety , and velocity , and indirectly addresses, veracity and value .

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-02-08
Bo Li; Yuanguo Zhu; Yufei Sun; Grace Aw; Kok Lay Teo

Manpower planning is a very important component of human resource management. However, there are many indeterminate factors that should be taken into consideration in manpower planning. For example, the decision of employees to quit the job is determined by their preference, which is beyond the control of human resource department. It can be realistically modeled as a random variable when the historical data of quitting rate are large enough. Otherwise, it can only be regarded as an uncertain variable when the historical data are inadequate. In this paper, we discuss a manpower planning optimization problem for a manufacturing company with hierarchical system, where the quitting rate of employees is modeled as an uncertain variable. First, we formulate a mathematical model for this uncertain manpower planning optimization problem, where the influence on the production outputs by employees is taken into consideration. Second, we present a deterministic conversion method to transform this uncertain manpower planning optimization problem into an equivalent deterministic discrete-time optimization problem. It is further converted into an equivalent linear programming model with an equality constraint and an inequality constraint. Finally, we use the real data from Singapore, Denmark, and China to carry out a numerical simulation and make a comparison with the results obtained based on stochastic model to show the advantages of our method.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-03-12
Fangyi Li; Changjing Shang; Ying Li; Jing Yang; Qiang Shen

Using fuzzy rule interpolation (FRI) interpolative reasoning can be effectively performed with a sparse rule base where a given system observation does not match any fuzzy rules. While offering a potentially powerful inference mechanism, in the current literature, typical representation of fuzzy rules in FRI assumes that all attributes in the rules are of equal significance in deriving the consequents. This is a strong assumption in practical applications, thereby, often leading to less accurate interpolated results. To address this challenging problem, this paper employs feature selection (FS) techniques to adjudge the relative significance of individual attributes and therefore, to differentiate the contributions of the rule antecedents and their impact upon FRI. This is feasible because FS provides a readily adaptable mechanism for evaluating and ranking attributes, being capable of selecting more informative features. Without requiring any acquisition of real observations, based on the originally given sparse rule base, the individual scores are computed using a set of training samples that are artificially created from the rule base through an innovative reverse engineering procedure. The attribute scores are integrated within the popular scale and move transformation-based FRI algorithm (while other FRI approaches may be similarly extended following the same idea), forming a novel method for attribute ranking-supported fuzzy interpolative reasoning. The efficacy and robustness of the proposed approach is verified through systematic experimental examinations in comparison with the original FRI technique over a range of benchmark classification problems while utilizing different FS methods. A specific and important outcome that is supported by attribute ranking, only two (i.e., the least number of) nearest adjacent rules are required to perform accurate interpolative reasoning, avoiding the need of searching for and computing with multiple rules beyond the immediate neighborhood of a given observation.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-01-15
Hai-Jun Rong; Plamen P. Angelov; Xiaowei Gu; Jian-Ming Bai

Evolving fuzzy systems (EFSs) are now well developed and widely used, thanks to their ability to self-adapt both their structures and parameters online. Since the concept was first introduced two decades ago, many different types of EFSs have been successfully implemented. However, there are only very few works considering the stability of the EFSs, and these studies were limited to certain types of membership functions with specifically predefined parameters, which largely increases the complexity of the learning process. At the same time, stability analysis is of paramount importance for control applications and provides the theoretical guarantees for the convergence of the learning algorithms. In this paper, we introduce the stability proof of a class of EFSs based on data clouds, which are grounded at the AnYa type fuzzy systems and the recently introduced empirical data analytics (EDA) methodological framework. By employing data clouds, the class of EFSs of AnYa type considered in this paper avoids the traditional way of defining membership functions for each input variable in an explicit manner and its learning process is entirely data driven. The stability of the considered EFS of AnYa type is proven through the Lyapunov theory, and the proof of stability shows that the average identification error converges to a small neighborhood of zero. Although, the stability proof presented in this paper is specially elaborated for the considered EFS, it is also applicable to general EFSs. The proposed method is illustrated with Box–Jenkins gas furnace problem, one nonlinear system identification problem, Mackey–Glass time series prediction problem, eight real-world benchmark regression problems as well as a high-frequency trading prediction problem. Compared with other EFSs, the numerical examples show that the considered EFS in this paper provides guaranteed stability as well as a better approximation accuracy.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-01-11
Tiantian He; Keith C. C. Chan

Many real-world datasets can be represented as attributed graphs that contain vertices, each of which is associated with a set of attribute values. Discovering clusters, or communities, which are structural patterns in these graphs, are one of the most important tasks in graph analysis. To perform the task, a number of algorithms have been proposed. Some of them detect clusters of particular topological properties, whereas some others discover them mainly based on attribute information. Also, most of the algorithms discover disjoint clusters only. As a result, they may not be able to detect more meaningful clusters hidden in the attributed graph. To do so more effectively, we propose an algorithm, called FSPGA, to discover fuzzy structural patterns for graph analytics. FSPGA performs the task of cluster discovery as a fuzzy-constrained optimization problem, which takes into consideration both the graph topology and attribute values. FSPGA has been tested with both synthetic and real-world graph datasets and is found to be efficient and effective at detecting clusters in attributed graphs. FSPGA is a promising fuzzy algorithm for structural pattern detection in attributed graphs.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-01-30
Chen Peng; Min Wu; Xiangpeng Xie; Yu-Long Wang

This paper investigates the event-triggered predictive control problem for networked nonlinear systems with imperfect premise matching. First, a model of networked nonlinear system is well constructed, which has integrated the event-triggered communication scheme (ETCS) and the predictive control together, in which, an ETCS is introduced to alleviate the communication burden by reducing the number of transmitted packets; and a fuzzy predictive controller is designed to predict future states and control signals between two successfully transmitted instants. Therefore, the data dropout induced by the networks can be actively compensated. Second, by using a common Lyapunov theory, a stability criterion and two stabilization criteria are deduced to ensure the asymptotical stability of the studied system and find the controller gains, respectively. Different from the traditional parallel distributed compensation method, the synchronous premise variables between the T–S fuzzy system and the fuzzy event-triggered predictive controller (FETPC) are no longer needed again. Since the imperfect premise matching condition is well considered in the derivation of the main results, the design flexibility and low cost of the FETPC implementation can be expected. Finally, the validity of the method proposed in this paper is demonstrated by a nonlinear mass-spring example.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-02-06
Hongyue Guo; Witold Pedrycz; Xiaodong Liu

In time series forecasting, a challenging and important task is to realize long-term forecasting that is both accurate and transparent. In this study, we propose a long-term prediction approach by transforming the original numerical data into some meaningful and interpretable entities following the principle of justifiable granularity. The obtained sequences exhibiting sound semantics may have different lengths, which bring some difficulties when carrying out predictions. To equalize these temporal sequences, we propose to adjust their lengths by involving the dynamic time warping (DTW) distance. Two theorems are included to ensure the correctness of the proposed equalization approach. Finally, we exploit hidden Markov models (HMM) to derive the relations existing in the granular time series. A series of experiments using publicly available data are conducted to assess the performance of the proposed prediction method. The comparative analysis demonstrates the performance of the prediction delivered by the proposed model.

更新日期：2018-10-03
• IEEE Trans. Fuzzy Syst. (IF 8.415) Pub Date : 2018-02-05
Jinghao Li; Qingling Zhang; Xing-Gang Yan; Sarah K. Spurgeon

This paper investigates observer-based stabilization for nonlinear descriptor systems using a fuzzy integral sliding mode control approach. Observer-based integral sliding mode control strategies for the Takagi–Sugeno (T–S) fuzzy descriptor systems are developed. A two-step design approach is first developed to obtain the observer gains and coefficients in the switching function using linear matrix inequalities (LMIs), and the results are used to facilitate the development of a single-step design approach, which is seen to be convenient but introduces some conservatism in the design. The potential application to a class of mechanical systems is also considered. Since the descriptor system representation of mechanical systems is adopted, it is shown that in contrast to the existing fuzzy sliding mode control methods based on the normal system representation, the resulting T-S fuzzy system does not contain different input matrices for each local subsystem and the required number of fuzzy rules is consequently markedly reduced. Finally, the balancing problem of a pendulum on a car is numerically simulated to demonstrate the effectiveness of the proposed method.

更新日期：2018-10-03
Some contents have been Reproduced with permission of the American Chemical Society.
Some contents have been Reproduced by permission of The Royal Society of Chemistry.