• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-02-12
Vikas Singh; Raghav Dev; Narendra Kumar Dhar; Pooja Agrawal; Nishchal K. Verma

This paper proposes a novel adaptive Type-2 fuzzy filter for removing salt and pepper noise from the images. The filter removes noise in two steps. In the first step, the pixels are categorized as good or bad based on their primary membership function (MF) values in the respective filter window. In this paper, two approaches have been proposed for finding threshold between good or bad pixels by designing primary MFs. a) MFs with distinct Means and same Variance and b) MFs with distinct Means and distinct Variances. The primary MFs of the Type-2 fuzzy set is chosen as Gaussian membership functions (GMFs). Whereas, in the second step, the pixels categorized as bad are denoised. For denoising, a novel Type-1 fuzzy approach based on a weighted mean of good pixels is presented in the paper. The proposed filter is validated for several standard images with the noise level as low as 20% to as high as 99%. The results show that the proposed filter performs better in terms of peak signal-noise-ratio (PSNR) values compared to other state-of-the-art algorithms.

更新日期：2018-02-13
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-02-08
Bo Li; Yuanguo Zhu; Yufei Sun; Aw Grace; 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 is large enough. Otherwise, it can only be regarded as an uncertain variable when the historical data is 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：2018-02-09
• IEEE Trans. Fuzzy Syst. (IF 7.671) 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 non-membership functions of a newly developed interval type-2 intuitionistic fuzzy logic system (IT2IFLS) of a Takagi-Sugeno-Kang (TSK) fuzzy inference system. The hybrid algorithms consisting of decoupled extended Kalman filter (DEKF) and gradient descent (GD) are used to tune the parameters of the IT2IFLS 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 between the proposed hybrid learning model of IT2IFLS, a TSK-type-1 intuitionistic fuzzy logic system (IFLS-TSK) and a TSK-type interval type-2 fuzzy logic system (IT2FLS-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 IT2IFLS outperforms its type-1 variants, IT2FLS and most of the existing models in the literature. Moreover, the minimal run time of the proposed hybrid learning model for IT2IFLS also puts this model forward as a good candidate for application in real time systems.

更新日期：2018-02-09
• IEEE Trans. Fuzzy Syst. (IF 7.671) 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 carry 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：2018-02-07
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-02-05
Jinghao Li; Qingling Zhang; Xing-Gang Yan; Sarah 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 T-S fuzzy descriptor systems are developed. A two step design is first developed to obtain the observer gains and coefficients in the switching function using linear matrix inequalities, 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：2018-02-06
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-11-29
Jun Cheng; Ju H. Park; Lixian Zhang; Yanzheng Zhu

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.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-11-29
Kai Yao; Jian Zhou

An insurance risk process usually describes the risk of an insurance company via many criteria, such as ruin index, ruin time, and deficit. So far, the insurance risk process involving random factors has been extensively investigated. As a complement, considering the human uncertainty in running an insurance company, this paper studies an insurance risk process involving human uncertainty. The inverse uncertainty distribution of the uncertain insurance risk process is obtained, and the uncertainty distribution of the ruin time is also derived. Some numerical experiments are performed to illustrate the results.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-01
Zhixiong Zhong; Chih-Min Lin; Zhenhua Shao; Min Xu

This paper addresses event-triggered data transmission in a class of large-scale networked nonlinear systems with transmission delays and nonlinear interconnections. Each nonlinear subsystem in the considered large-scale system is represented by a Takagi–Sugeno model, and exchanges its information through a digital channel. We propose an event-triggering mechanism, which determines when the premise variables and system states should be transmitted to the controller. Our goal is to design a decentralized event-triggered state-feedback fuzzy controller, such that the resulting closed-loop fuzzy control system is asymptotically stable while the measured information is transmitted to the controller as little as possible. By using the input delay and perturbed system approaches, the closed-loop sampled-data fuzzy system with event-triggered control is first reformulated into a continuous-time system with time-varying delay and extra disturbance. Then, based on the new model, we introduce a Lyapunov–Krasovskii functional with virtue of Wirtinger's inequality, where not all of the Lyapunov matrices are required to be positive definite. The codesign result is derived to obtain simultaneously the controller gains, sampled period, network delay, and event-triggered parameter in terms of a set of linear matrix inequalities. Finally, two simulation examples are provided to validate the advantage of the proposed method.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-01
Jinpeng Yu; Peng Shi; Wenjie Dong; Chong Lin

Adaptive fuzzy control via command filtering is proposed for uncertain strict-feedback nonlinear systems with unknown nonsymmetric dead-zone input signals in this paper. The command filtering is utilized to cope with the inherent explosion of the complexity problem of the classical backstepping method, and the error compensation mechanism is introduced to overcome the drawback of the dynamics surface approach. In addition, by utilizing the bound information of dead-zone slopes, a new adaptive fuzzy method that does not need to establish the inverse of the dead zone is presented for the unknown nonlinear systems. Compared with existing results, the advantages of the developed scheme are that the compensating signals are designed to eliminate the filtering errors and only one adaptive parameter is required, which will make the proposed control scheme more effective for practical systems. An example of position tracking control for the electromechanical system is given to demonstrate the usefulness and potential of the new design scheme.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-08
Chengdong Li; Junlong Gao; Jianqiang Yi; Guiqing Zhang

The single-input-rule-modules (SIRMs) connected fuzzy inference method can efficiently solve the fuzzy rule explosion phenomenon, which usually occurs in the multivariable modeling and/or control applications. However, the performance of the SIRMs connected fuzzy inference system (SIRM-FIS) is limited due to its simple input–output mapping. In this paper, to further enhance the performance of SIRM-FIS, a functionally weighted SIRM-FIS (FWSIRM-FIS), which adopts multivariable functional weights to measure the important degrees of the SIRMs, is presented. Then, in order to show the fundamental differences of the SIRMs methods, properties of the traditional SIRM-FIS, the type-2 SIRM-FIS (T2SIRM-FIS), the functional SIRM-FIS (FSIRM-FIS), the SIRMs model with single-variable functional weights (SIRM-FW), and FWSIRM-FIS are explored. These properties demonstrate that the proposed FWSIRM-FIS has more general and complex input–output mapping than the existing SIRMs methods. Such properties theoretically guarantee that better performance can be achieved by FWSIRM-FIS. Furthermore, based on the least-squares method, a novel data-driven optimization method is presented for the parameter learning of FWSIRM-FIS. It can also be used to optimize the parameters of SIRM-FIS, T2SIRM-FIS, FSIRM-FIS, and SIRM-FW. Due to the properties of the least-squares method, the proposed parameter learning algorithm can overcome the drawbacks of the gradients-based parameter learning methods and obtain both smallest training errors and smallest parameters. Finally, to show the effectiveness and superiority of FWSIRM-FIS and the proposed optimization method, six examples and detailed comparisons are given. Simulation results show that FWSIRM-FIS can obtain better performance than the other SIRMs methods, and, compared with some well-known methods, FWSIRM-FIS can achieve similar or better performance but has much less parameters and faster training speed.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-08
Jianchao Fan; Jun Wang

This paper presents a two-phase fuzzy clustering algorithm based on neurodynamic optimization with its application for polarimetric synthetic aperture radar (PolSAR) remote sensing image segmentation. The two-phase clustering algorithm starts with the linear-assignment initialization phase with the least similar cluster representatives to remedy the inconsistency of clustering results from random initialization and is, then, followed with multiple-kernel fuzzy C-means clustering. By incorporating multiple kernels in the clustering framework, various features are incorporated cohesively. A winner-takes-all neural network is employed to acquire the highest kernel weights and associated cluster centers and membership matrices, which enables better characterization and adaptability in each individual cluster. Simulation results for UCI benchmark datasets and PolSAR remote sensing image segmentation are reported to substantiate the effectiveness and the superiority of the proposed clustering algorithm.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-08
Dušan Guller

We provide the foundations of automated deduction in the propositional Gödel logic. The propositional Gödel logic is one of the simplest infinitely valued fuzzy logics, which generalizes classical propositional logic. We propose an extension of the Davis–Putnam–Logemann–Loveland ( DPLL ) procedure to this logic and prove its refutational soundness and finite completeness. Using the DPLL procedure, we solve the deduction problem ${T\models \phi }$ ( $\boldsymbol{T}$ is a finite theory and $\boldsymbol{\phi }$ a formula), which covers the finite SAT problem for a theory and the VAL problem for a formula, obviously. This paper serves, on the one side, as a technical basis for the design of a SAT solver; on the other side, gives some preliminary theoretical results concerning the logical and computational foundations of fuzzy inference, which is our main aim.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-08
Javier Andreu-Perez; Fan Cao; Hani Hagras; Guang-Zhong Yang

This paper presents a self-adaptive autonomous online learning through a general type-2 fuzzy system (GT2 FS) for the motor imagery (MI) decoding of a brain-machine interface (BMI) and navigation of a bipedal humanoid robot in a real experiment, using electroencephalography (EEG) brain recordings only. GT2 FSs are applied to BMI for the first time in this study. We also account for several constraints commonly associated with BMI in real practice: 1) the maximum number of EEG channels is limited and fixed; 2) no possibility of performing repeated user training sessions; and 3) desirable use of unsupervised and low-complexity feature extraction methods. The novel online learning method presented in this paper consists of a self-adaptive GT2 FS that can autonomously self-adapt both its parameters and structure via creation, fusion, and scaling of the fuzzy system rules in an online BMI experiment with a real robot. The structure identification is based on an online GT2 Gath–Geva algorithm where every MI decoding class can be represented by multiple fuzzy rules (models), which are learnt in a continous (trial-by-trial) non-iterative basis. The effectiveness of the proposed method is demonstrated in a detailed BMI experiment, in which 15 untrained users were able to accurately interface with a humanoid robot, in a single session, using signals from six EEG electrodes only.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-13
Shuang Feng; C. L. Philip Chen

A fuzzy restricted Boltzmann machine (FRBM) is extended from a restricted Boltzmann machine (RBM) by replacing all the real-valued parameters with fuzzy numbers. A new FRBM that employs the crisp possibilistic mean value of a fuzzy number to defuzzify the fuzzy free energy function is presented. This approach is much clearer and easier to obtain the expression of the defuzzified free energy function and its approximation than the centroid method. Several theorems that discuss the error bounds of the approximation to ensure the rationality and validity are also investigated. Learning algorithms are given for the designed FRBM with symmetric triangular fuzzy numbers (STFNs), asymmetric triangular fuzzy numbers, and Gaussian fuzzy numbers. By appropriately choosing the parameters, a theorem is concluded that all FRBMs with symmetric fuzzy numbers will have identical learning algorithm to that of FRBMs with STFNs. This is illustrated by a case of FRBM with Gaussian fuzzy numbers. Two experiments including the MNIST handwriting recognition and the Bars-and-Stripes benchmark are carried out. The results show that the proposed FRBMs significantly outperform RBMs in learning accuracy and generalization ability, especially when encountering unlearned samples and recovering incomplete images.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-16
Fanbiao Li; Peng Shi; Cheng-Chew Lim; Ligang Wu

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.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-16
Sunjie Zhang; Zidong Wang; Derui Ding; Guoliang Wei; Fuad E. Alsaadi; Tasawar Hayat

This paper deals with the nonfragile $H_\infty$ control problem for a class of discrete-time Takagi–Sugeno fuzzy systems with both randomly occurring gain variations (ROGVs) and channel fadings. The system measurement is subject to fading channels described by Rice fading model where the channel coefficients are random variables taking values within given intervals. The gain matrices of the output feedback controllers are subject to random fluctuations referred to as the ROGVs. The purpose of the addressed problem is to design a parameter-dependent nonfragile output-feedback controller such that, in the presence of both ROGVs and channel fadings, the closed-loop system is exponentially mean-square stable while achieving the guaranteed $H_\infty$ disturbance attenuation level. A gain-scheduling approach is developed to tackle the addressed problem where the designed controller gains are dependent on certain parameters of practical significance (e.g., packet dropout rate). Through stochastic analysis and Lyapunov functional approach, sufficient conditions are derived for the existence of the desired output feedback controller ensuring both the exponential mean-square stability and the prescribed $H_\infty$ performance. The explicit expression of the feedback controller is also characterized by using a semidefinite programming method. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed design method.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-30
Jun-Wei Wang; Huai-Ning Wu

This paper deals with the problem of exponential stabilization for nonlinear parabolic distributed parameter systems using the Takagi–Sugeno (T–S) fuzzy partial differential equation (PDE) model, where a finite number of actuators are active only at some specified points of the spatial domain (these actuators are referred to as pointwise actuators). Three cases of state feedback are respectively considered in this study as follows: full state feedback, piecewise state feedback, and collocated pointwise state feedback. It is initially assumed that a T–S fuzzy PDE model obtained via the sector nonlinearity approach is employed to accurately represent the semilinear parabolic PDE system. Based on the obtained T–S fuzzy PDE model, Lyapunov-based design methodologies of fuzzy feedback control laws are subsequently derived for the above three state feedback cases by using the vector-valued Wirtinger's inequality to guarantee locally exponential pointwise stabilization of the semilinear PDE system, and presented in terms of standard linear matrix inequalities (LMIs). Moreover, the favorable property offered by sharing all the same premises in the T–S fuzzy PDE models and fuzzy controllers is not applicable for the case of collocated pointwise state feedback. A parameterized LMI is introduced for this case to enhance the stabilization ability of the fuzzy controller. Finally, the merit and effectiveness of the proposed design methods are demonstrated by numerical simulation results of two examples.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-02
Armando Segatori; Francesco Marcelloni; Witold Pedrycz

Fuzzy decision trees (FDTs) have shown to be an effective solution in the framework of fuzzy classification. The approaches proposed so far to FDT learning, however, have generally neglected time and space requirements. In this paper, we propose a distributed FDT learning scheme shaped according to the MapReduce programming model for generating both binary and multiway FDTs from big data. The scheme relies on a novel distributed fuzzy discretizer that generates a strong fuzzy partition for each continuous attribute based on fuzzy information entropy. The fuzzy partitions are, therefore, used as an input to the FDT learning algorithm, which employs fuzzy information gain for selecting the attributes at the decision nodes. We have implemented the FDT learning scheme on the Apache Spark framework. We have used ten real-world publicly available big datasets for evaluating the behavior of the scheme along three dimensions: 1) performance in terms of classification accuracy, model complexity, and execution time; 2) scalability varying the number of computing units; and 3) ability to efficiently accommodate an increasing dataset size. We have demonstrated that the proposed scheme turns out to be suitable for managing big datasets even with a modest commodity hardware support. Finally, we have used the distributed decision tree learning algorithm implemented in the MLLib library and the Chi-FRBCS-BigData algorithm, a MapReduce distributed fuzzy rule-based classification system, for comparative analysis.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-30
Jian Wu; Francisco Chiclana; Huchang Liao

Intuitionistic fuzzy preference relations (IFPRs) are used to deal with hesitation, while interval-valued fuzzy preference relations (IVFPRs) are for uncertainty in multicriteria decision making (MCDM). This paper aims to explore the isomorphic multiplicative transitivity for IFPRs and IVFPRs, which builds the substantial relationship between hesitation and uncertainty in MCDM. To do that, the definition of the multiplicative transitivity property of IFPRs is established by combining the multiplication of intuitionistic fuzzy sets and Tanino's multiplicative transitivity property of fuzzy preference relations. It is proved to be isomorphic to the multiplicative transitivity of IVFPRs derived via Zadeh's extension principle. The use of the multiplicative transitivity isomorphism is twofold: 1) to discover the substantial relationship between IFPRs and IVFPRs, which will bridge the gap between hesitation and uncertainty in MCDM problems; and 2) to strengthen the soundness of the multiplicative transitivity property of IFPRs and IVFPRs by supporting each other with two different reliable sources, respectively. Furthermore, based on the existing isomorphism, the concept of multiplicative consistency for IFPRs is defined through a strict mathematical process, and it is proved to satisfy the following several desirable properties: weak transitivity, max–max transitivity, and center-division transitivity. A multiplicative consistency-based multiobjective programming (MOP) model is investigated to derive the priority vector from an IFPR. This model has the advantage of not losing information, as the priority vector representation coincides with that of the input information, which was not the case with the existing methods, where crisp priority vectors were derived as a consequence of the modeling transitivity just for the intuitionistic membership function and not for the intuitionistic nonmembership function. Finally, a numerical example concerning green supply selection is given to validate the efficiency and practicality of the proposed multiplicative consistency MOP model.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-30
Vuppuluri Sumati; C. Patvardhan

This paper presents an interval type-2 mutual subsethood fuzzy neural inference system (IT2MSFuNIS). A mutual subsethood measure between two interval type-2 fuzzy sets (IT2 FS) has been derived and has been used in determining the similarity between the IT2 FS inputs and IT2 FS antecedents. The consequent weights are taken to be interval sets. The inputs to the system are fuzzified into IT2 FSs with Gaussian primary membership function having fixed center and uncertain variance. Aggregation of type-2 mutual subsethood based activation spreads is performed using product operator. The output is obtained using simplified type-reduction followed by defuzzification. The system learns using memetic procedure involving differential evolution for global search and gradient descent for local exploitation in solution space. The mathematical modeling and empirical studies of IT2MSFuNIS bring forth its efficacy in problems pertaining to function approximation, time-series prediction, control, and classification. Comparisons with other type-1 and type-2 neuro-fuzzy systems verify that IT2MSFuNIS compares excellently with other models with a performance better than most of them both in terms of total number of trainable parameters and result accuracy. Empirical studies indicate the intelligent decision making capability of the proposed model. The main contribution of this paper lies in the identification of mutual subsethood to find out the correlation between IT2 FSs and to find out its applicability in diverse application domains. The improved performance of the proposed method can be attributed to the better contrast handling capacity of mutual subsethood method and uncertainty handling capacity of IT2 FSs. The integration of mutual subsethood with interval type-2 fuzzy logic puts forth a novel model with various merits as demonstrated amply with the help of well-known problems reported in the literature.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-05
Thomas Laurain; Jimmy Lauber; Reinaldo Martinez Palhares

Many of the recent advances on control and estimation of systems described by Takagi–Sugeno (TS) fuzzy models are based on matrix inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this matrix inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the matrix inversion by multiple sums and the second methodology is based on an estimation of the matrix inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-04
Qinghua Hu; Lingjun Zhang; Yucan Zhou; Witold Pedrycz

In complex pattern recognition tasks, objects are typically characterized by means of multimodality attributes, including categorical, numerical, text, image, audio, and even videos. In these cases, data are usually high dimensional, structurally complex, and granular. Those attributes exhibit some redundancy and irrelevant information. The evaluation, selection, and combination of multimodality attributes pose great challenges to traditional classification algorithms. Multikernel learning handles multimodality attributes by using different kernels to extract information coming from different attributes. However, it cannot consider the aspects fuzziness in fuzzy classification. Fuzzy rough sets emerge as a powerful vehicle to handle fuzzy and uncertain attribute reduction. In this paper, we design a framework of multimodality attribute reduction based on multikernel fuzzy rough sets. First, a combination of kernels based on set theory is defined to extract fuzzy similarity for fuzzy classification with multimodality attributes. Then, a model of multikernel fuzzy rough sets is constructed. Finally, we design an efficient attribute reduction algorithm for large scale multimodality fuzzy classification based on the proposed model. Experimental results demonstrate the effectiveness of the proposed model and the corresponding algorithm.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-05
Shao-Jun Yang

In this paper, some results of the fuzzy relation inequalities with addition–min composition are given. First, the uniqueness of minimal solutions of this system is discussed. Then, the relation between this system and the corresponding equations’ system is introduced. The definition of the critical set is presented, and an algorithm of the critical system is obtained. Finally, an algorithm for the fuzzy relation inequalities is presented.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-05
Hongyi Li; Jiahui Wang; Ligang Wu; Hak-Keung Lam; Yabin Gao

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.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-09
Rami Al-Hmouz; Witold Pedrycz; Abdullah Saeed Balamash; Ali Morfeq

In this study, we present a methodology of building a hierarchical framework of system modeling by engaging concepts and design methodology of granular computing. We demonstrate that it arises as a result of designing and using locally constructed models to develop a model of a global nature. Two main categories of development of hierarchical models are proposed and discussed. In the first one, given a collection of local models, designed is a granular output space and the ensuing hierarchical model produces information granules of the corresponding type depending upon the depth of the hierarchy of the overall hierarchical structure. The crux of the second category of modeling is about selecting one of the original models and elevating its level of information granularity so that it becomes representative of the entire family of local models. The formation of the most “promising” granular model identified in this way involves mechanisms of allocation of information granularity. The focus of the study is on information granules represented as intervals and fuzzy sets (which in case of type-2 information granules lead to so-called granular intervals and interval-valued fuzzy sets) while the detailed models come as rule-based architectures and neural networks. A series of experiments is presented along with a comparative analysis.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-10
Tina Verma; Amit Kumar

In the last few years, a lot of researchers have proposed different methods, to solve the mathematical programming problem of matrix games with Atanassov's intuitionistic fuzzy payoffs. In this paper, the flaws of the existing methods for solving matrix games with Atanassov's intuitionistic fuzzy payoffs (matrix games in which payoffs are represented by Atanassov's intuitionistic fuzzy numbers) are pointed out. Also, to resolve these flaws, new methods (named as Ambika methods) are proposed to obtain the optimal strategies as well as minimum expected gain of Player I and maximum expected loss of Player II for matrix games with Atanassov's intuitionistic fuzzy payoffs. To illustrate proposed Ambika methods, some existing numerical problems of matrix games with Atanassov's intuitionistic fuzzy payoffs are solved by proposed Ambika methods.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-17

Inspired by the real needs of group decision problems, aggregation of ordered weighted averaging (OWA) operators is studied and discussed. Our results can be applied for data acting on any real interval, such as the standard scales $[0,1]$ and $[0,\infty [$ , bipolar scales $[-1,1]$ and $\mathbb {R}=]-\infty, \infty [$ , etc. A direct aggregation is shown to be rather restrictive, allowing the convex combinations to be considered only, except the case of dimension n = 2. More general is the approach based on the aggregation of related cumulative weighting vectors. The piecewise linearity of OWA operators allows us to consider bilinear forms of aggregation of related weighting vectors. Several interesting examples yielding the link between the aggregation of OWA operators and the related ANDness and ORness measures are also included. Some possible applications and generalizations of our results are also discussed.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-17
Edwin Lughofer; Mahardhika Pratama

In this paper, we propose three criteria for efficient sample selection in case of data stream regression problems within an online active learning context. The selection becomes important whenever the target values, which guide the update of the regressors as well as the implicit model structures, are costly or time-consuming to measure and also in case when very fast models updates are required to cope with stream mining real-time demands. Reducing the selected samples as much as possible while keeping the predictive accuracy of the models on a high level is, thus, a central challenge. This should be ideally achieved in unsupervised and single-pass manner. Our selection criteria rely on three aspects: 1) the extrapolation degree combined with the model's nonlinearity degree , which is measured in terms of a new specific homogeneity criterion among adjacent local approximators; 2) the uncertainty in model outputs, which can be measured in terms of confidence intervals using so-called adaptive local error bars — we integrate a weighted localization of an incremental noise level estimator and propose formulas for online merging of local error bars; 3) the uncertainty in model parameters, which is estimated by the so-called A-optimality criterion, which relies on the Fisher information matrix. The selection criteria are developed in combination with evolving generalized Takagi–Sugeno (TS) fuzzy models (containing rules in arbitrarily rotated position), as it could be shown in previous publications that these outperform conventional evolving TS models (containing axis-parallel rules). The results based on three high-dimensional real-world streaming problems show that a model update based on only 10%–20% selected samples can still achieve similar accumulated model errors over time to the case when performing a full model update on all samples. This can be achieved with a negligible sensitivity on the size of the active learning latency buffer. Random sampling with the same percentages of samples selected, however, achieved much higher error rates. Hence, the intelligence in our sample selection concept leads to an economic balance between model accuracy and measurement as well computational costs for model updates.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-26
Mehran Mazandarani; Naser Pariz; Ali Vahidian Kamyad

In this paper, using the concept of horizontal membership functions, a new definition of fuzzy derivative called granular derivative is proposed based on granular difference. Moreover, a new definition of fuzzy integral called granular integral is defined, and its relation with the granular derivative is given. A new definition of a metric—granular metric—on the space of type-1 fuzzy numbers, and a concept of continuous fuzzy functions are also presented. Restrictions associated to previous approaches—Hukuhara differentiability, strongly generalized Hukuhara differentiability, generalized Hukuhara differentiability, generalized differentiability, Zadeh's extension principle, and fuzzy differential inclusions—dealing with fuzzy differential equations (FDEs) are expressed. It is shown that the proposed approach does not have the drawbacks of the previous approaches. It is also demonstrated how this approach enables researchers to solve FDEs more conveniently than ever before. Moreover, we showed that this approach does not necessitate that the diameter of the fuzzy function be monotonic. It is also proved that the result of each of the four basic operations on fuzzy numbers introduced based on the proposed approach leads to a fuzzy number. Moreover, the condition for the existence of the granular derivative of a fuzzy function is provided by a theorem. Additionally, by two examples, it is shown that the existence of the granular derivative of a fuzzy function does not imply the existence of the generalized Hukuhara differentiability of the fuzzy function, and vice versa. The terms doubling property and unnatural behavior in modeling phenomenon are also introduced. Furthermore, using some examples, the paper proceeds to elaborate on the efficiency and effectiveness of the proposed approach. Moreover, as an application of the proposed approach, the response of Boeing 747 to impulsive elevator input is obtained in the presence of uncertain initial conditions and parameters.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-26
Konstantinos D. Koutroumbas; Spyridoula D. Xenaki; Athanasios A. Rontogiannis

In this paper, a convergence proof for the recently proposed cost function optimization sparse possibilistic c-means (SPCM) algorithm is provided. Specifically, it is shown that the algorithm will converge to one of the local minima of its associated cost function. It is also shown that similar convergence results can be derived for the well-known possibilistic c-means (PCM) algorithm proposed by Krishnapuram and Keller, 1996, if we view it as a special case of SPCM. Note that the convergence results for PCM are stronger than those established in previous works.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-26
Yu-Ting Liu; Nikhil R. Pal; Amar R. Marathe; Chin-Teng Lin

This study proposes an architecture based on a weighted fuzzy Dempster–Shafer framework (WFDSF), which can adjust weights associated with inconsistent evidence obtained by different classification approaches, to realize a fusion system for integrating multimodal information. The Dempster–Shafer theory (D-S theory) of evidence enables us to integrate heterogeneous information from multiple sources to obtain collaborative inferences for a given problem. To conquer various uncertainties associated with the collected information, our system assigns beliefs and plausibilities to possible hypotheses of each decision maker and uses a combination rule to fuse multimodal information. For information fusion, an important step in D-S aggregation is to find an appropriate basic probability assignment scheme for allocating support to each possible hypothesis/class, which remains an arduous and unsolved problem. Here, we propose a mathematical structure to aggregate weighted evidence extracted from two different types of approaches: fuzzy Naïve Bayes and nearest mean classification rule. Further, an intuitionistic belief assignment is employed to address uncertainties between hypotheses/classes. Finally, 12 benchmark problems from the UCI machine learning repository for classification are employed to validate the proposed WFDSF-based scheme. In addition, an application of WFDSF to a practical brain–computer interface problem involving multimodal data fusion is demonstrated in this study. The experimental results show that the WFDSF is superior to several existing methods.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-02-08
Zhaojun Xing; Wei Xiong; Hailin Liu

In the literature on Atanassov intuitionistic fuzzy sets, several methods have been proposed in order to obtain a ranking on intuitionistic fuzzy values. However, some problems may arise when working with these methods, such as the inadmissibility problem, the nonrobustness problem, the indifference problem, etc. Based on the concept of the Euclidean distance, we propose a novel approach for ranking intuitionistic fuzzy values, which addresses these problems. With the aid of its geometrical representation, we rank the intuitionistic fuzzy values in accordance with the following basic principle: The closer the intuitionistic fuzzy value is to the most favorable intuitionistic fuzzy value, the higher the ranking of the intuitionistic fuzzy value is. Moreover, we extend this approach by taking into account human cognitive bias, which reflects a decision maker's attitude toward positive or negative consequences in decision problems involving uncertainty. Finally, we generalize our approach by introducing the Minkowski distance, and show that the generalized approach also addresses the problems encountered by the existing methods.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-08
Han Sol Kim; Jin Bae Park; Young Hoon Joo

This paper presents an output-feedback exponential stabilization condition of sampled-data polynomial fuzzy control systems under variable sampling rates. Compared with previous work, the proposed method is less conservative because of the newly developed time-dependent fuzzy Lyapunov–Krasovskii functional that is based on the conventional fuzzy Lyapunov function. Moreover, the controller is allowed to contain polynomial gain matrices, thereby improving the control performance and design flexibility. This is realized by assuming the difference between the continuous- and discrete-time state vectors as time-varying norm-bounded uncertainties, which are manipulated using a robust control technique. A new sufficient condition is introduced to cast the stability condition containing the integral term as the sum-of-square conditions. Finally, the effectiveness of the proposed method is validated by simulations.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-08
Yong Su; Hua-Wen Liu; Witold Pedrycz

It is known that bisymmetry generalizes the simultaneous commutativity and associativity in the framework of the unit interval. In this work, we will completely characterize two classes of bisymmetric aggregation operators: one with a neutral element and the other with the vertical and horizontal sections of the idempotent elements being smooth on a finite chain, but not necessarily smooth and commutative. Thus, the previous results, based on the smoothness that is known as a very restrictive condition, are improved. For example, there is only one smooth Archimedean t-norm on a finite chain. In this paper, the discrete bisymmetric aggregation operators are explored without the limit of the smoothness. As a by-product, it is deduced that for smooth aggregation operators on a finite chain, the bisymmetry is equivalent to the commutativity and associativity, which improves the conclusion obtained by Mas et al. that associativity and bisymmetry are equivalent for commutative smooth aggregation operators on a finite chain.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-14
Likui Wang; Hak-Keung Lam

This brief paper investigates the local stabilization for continues-time Takagi–Sugeno fuzzy systems with constant time delay. In order to deal with the time delay, we design a Lyapunov–Krasovskii functional that is dependent on the membership function. Based on the Lyapunov–Krasovskii functional and the analysis of the time derivative of the membership function, less conservative results can be obtained; however, the Lyapunov–Krasovskii functional is designed so complicated that the Lyapunov level set is hard to be measured directly. Alternatively, two sets are obtained to estimate the local stabilization. One set is for the time-varying initial conditions and the other is for the time-invariant initial conditions. The relationship between the two sets are also discussed. In the end, two examples are given to illustrate the effectiveness of the proposed approach.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-01-09
Alireza Nasiri; Sing Kiong Nguang; Akshya Swain; Dhafer J. Almakhles

This paper proposes an $H_{\infty }$ robust state-feedback controller design for uncertain Takagi–Sugeno fuzzy systems using a nonmonotonic Lyapunov function. In the nonmonotonic approach, the monotonicity requirement of the Lyapunov function is relaxed by allowing it to increase locally. Based on the nonmonotonic Lyapunov function approach, sufficient conditions for the existence of a robust state-feedback $H_{\infty }$ controller that guarantees stability and a prescribed $H_{\infty }$ performance are given in terms of linear matrix inequalities. The proposed design technique is shown to be less conservative than the existing $k$ -samples variations of the Lyapunov function. The effectiveness of the proposed approach is further illustrated via numerical examples.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-12-08
Jia-Cai Liu; Deng-Feng Li

There are some mistakes in the computation results of the real example in the article by Li, “TOPSIS-based nonlinear-programming methodology for multi-attribute decision making with interval-valued intuitionistic fuzzy sets” [ IEEE Trans. Fuzzy Syst. , vol. 18, no. 2, pp. 299–311, 2010], and this article provides corrections to that paper.

更新日期：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) 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 inter-event 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：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-02-01
Fa-xiang Zhang; Jing Hua; Yimin Li

In this paper, a design method of indirect adaptive fuzzy controller is proposed for a class of 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：2018-02-02
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-30
Chen Peng; Min Wu; Xiangpeng Xie; Yulong Wang

This paper investigates the event-triggered predictive control (ETPC) problem for networked nonlinear systems with imperfect premise matching. Firstly, 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, a) an ETCS is introduced to alleviate the communication burden by reducing the number of transmitted packets; b) an 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. Secondly, 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 (PDC) 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 method proposed in this paper is demonstrated by a nonlinear mass-spring example.

更新日期：2018-01-31
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-30
Jian Han; Huaguang Zhang; Yingchun Wang; Kun Zhang

This paper addresses the problems of fault estimation (FE) and fault-tolerant control (FTC) for switched fuzzy stochastic systems with actuator fault and sensor fault. A novel observer is proposed to estimate the system states, actuator and sensor faults, simultaneously. The proposed observer can be treated as an extension of the traditional proportional-integral (PI) observer. The estimation information is utilized to design the fault-tolerant controller. Based on the piecewise Lyapunov function and the average dwell time, a set of linear matrix inequalities (LMIs) can be achieved, which ensure that the closed-loop system is mean-square exponentially stable with a weighted $H_\infty$ performance level. At last, two simulation examples are provided to illustrate the effectiveness of the proposed approach.

更新日期：2018-01-31
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-26
Peijia Ren; Bin Zhu; Zeshui Xu

To reduce the water conservancy projects’ negative effects on the ecological environment, in this paper, we propose a method to assess the impacts of hydropower stations on the environment in the processes of the flood discharge and energy dissipation. The method utilizes the hesitant fuzzy linguistic information to describe the problem's uncertainty and fuzziness, portrays the satisfaction degree with the increasing marginal utility, and applies the hyperplane to establish a mathematical programming model. Then, we discuss the undetermined parameter in the model, and then provide a decision-making procedure for solving the considered problem. Furthermore, an experiment is designed to verify the availability and reasonability of the proposed method by comparing it with an existing one. Finally, we apply our method to assess the impacts of giant hydropower stations’ flood discharge and energy dissipation on the environment in Sichuan China.

更新日期：2018-01-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) 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 are not transgressed their constrained sets. The effectiveness of the proposed control approach can be verified by setting a simulation example.

更新日期：2018-01-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-25
Bin Hu; Zhi-Hong Guan; Xinghuo Yu; Qingming Luo

This paper studies a class of heterogeneous delayed impulsive neural networks with memristors and their collective evolution for multisynchronization.} The multisynchronization represents a diversified collective behavior that is inspired by multitasking as well as observations of heterogeneity and hybridity arising from system models. {In view of memristor, the memristor-based impulsive neural network is first represented by an impulsive differential inclusion.} According to the memristive and impulsive mechanism, a fuzzy logic rule is introduced, and then a new fuzzy hybrid impulsive and switching control method is presented correspondingly. It is shown that using the proposed fuzzy hybrid control scheme, multisynchronization of interconnected memristor-based impulsive neural networks can be guaranteed with a positive exponential convergence rate. {The heterogeneity and hybridity in system models thus can be indicated by the obtained error thresholds that contribute to the multisynchronization.} Numerical examples are presented and compared to demonstrate the effectiveness of the developed theoretical results.

更新日期：2018-01-26
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-23
Loukia Karanikola; Isambo Karali

Vague information has been emerged as a main issue in Semantic Web community. Vagueness is traditionally represented by fuzzy set theory. Besides vagueness, Semantic Web queries often have to deal with information incompleteness, aka uncertainty. This kind of information can be represented through Dempster-Shafer theory, that also enables distributed information fusion. Vagueness along with information incompleteness are often referred to under the common term imprecise information. Imprecise information should be represented and manipulated under a common framework. We propose such a framework by defining a fuzzy Description Logic extended with Dempster-Shafer theory. Furthermore, we regard our method as a DL extension and we implemented it by a meta-ontology that captures Dempster-Shafer Fuzzy statements.

更新日期：2018-01-24
• IEEE Trans. Fuzzy Syst. (IF 7.671) 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 while false or redundant anchors get removed. The time complexity of 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：2018-01-24
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-23
Tao Lei; Xiaohong Jia; Yanning Zhang; Lifeng He; Hongying Meng; Asoke K. Nandi

As fuzzy c-means clustering (FCM) algorithm is sensitive to noise, local spatial information is often introduced to an objective function to improve the robustness of the FCM algorithm for image segmentation. However, the introduction of local spatial information normally leads to a high computational complexity, arising out of an iterative calculation of the distance between the spatial neighbors of pixels and clustering centers. To address this issue, an improved FCM algorithm based on morphological reconstruction and membership filtering (FRFCM) that is significantly faster and more robust than FCM, is proposed in this paper. Firstly, the local spatial information of images is incorporated into our FRFCM by introducing morphological reconstruction operation to guarantee noise-immunity and image detail-preservation. Secondly, the modification of a pixel's membership, based on the distance between the spatial neighbors of the pixel and clustering centers, is replaced by local membership filtering that depends only on the spatial neighbors of the pixel's membership. Compared to state-of-the-art algorithms, the proposed FRFCM algorithm is simpler and significantly faster since it is unnecessary to compute the distance between the neighbors of pixels and clustering centers. In addition, it is efficient for noisy image segmentation because spatial filters are able to improve pixels' membership efficiently. Experiments performed on synthetic and real-world images demonstrate that the proposed algorithm not only achieves better results, but also requires less time than state-of-the-art algorithms for image segmentation.

更新日期：2018-01-24
• IEEE Trans. Fuzzy Syst. (IF 7.671) 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 non-stationary 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 (pClass). 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：2018-01-24
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-15
Miklos Ferenc Hatwagner; Engin Yesil; Furkan Dodurka; Elpiniki I. Papageorgiou; Leon Urbas; Laszlo T. Koczy

In this study, a new two-stage learning based reduction approach for Fuzzy Cognitive Maps (FCM) is introduced in order to reduce the number of concepts. FCM is a graphical modeling technique that follows a reasoning approach similar to the human reasoning and decision-making process. The FCM model incorporates the available knowledge and expertise in the form of concepts and in the direction and strength of the interactions among concepts. One of the modeling problems of FCMs is that over-sized FCM models suffer from interpretability problems. An over-sized FCM may contain concepts that are semantically similar and affects the other concepts in a similar way. This new study introduces a two-stage model reduction approach, and both static and dynamic analysis are considered without losing essential information. In the first stage the number of concepts is reduced by merging similar concepts into clusters, while in the second stage the transformation function parameters of concepts are optimized. In order to show the benefit of using the proposed reduction approach, two sets of studies are conducted. First, a huge set of synthetic FCMs are generated, and the results of these statistical analyses are presented via various tables and figures. Subsequently, suggestions to the decision makers are given. Second, experimental studies are also presented to show the decision parameters and procedure for the proposed approach. The results show that after using the concept reduction approach presented in this study, the interpretability of FCM increases with an acceptable amount of information loss in the output concepts.

更新日期：2018-01-17
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-15
Haijun Rong; Plamen P Angelov; Xiaowei Gu; Jianming 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 firstly 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 pre-defined 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 analysis (EDA) methodological framework. By employing data clouds, the class of EFSs of AnYa type considered in this work 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：2018-01-17
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-15
Fang Liu; Yu-Hao Wu; Witold Pedrycz

In order to deal with a complex decision making problem, a group of experts are commonly invited to express their opinions and reach a final decision. For the purpose of building consensus among the group, it is requisite to include iterative mechanisms of brain storming. The particle swarm optimization (PSO) method can be used to model the interactive process. In this paper, we propose a modified consensus model of group decision making augmented by an allocation of information granularity. Under a level of information granularity, it is found that the consistency indexes of randomly created multiplicative reciprocal matrices in the analytic hierarchy process (AHP) may be bigger than unity. To alleviate this limitation, a modified objective function is proposed and it is optimized by using the modified PSO method. The information granularity is allocated by considering the reciprocity of preference relations. Some comparative studies are carried out to illustrate the proposed consensus model by using numerical examples. The observations reveal that a more consistent decision can be achieved by using the proposed approach.

更新日期：2018-01-17
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-15
Changchun Hua; Kuo Li; Xinping Guan

This paper focuses on the problem of decentralized event-based dynamic output feedback adaptive fuzzy control for a class of interconnected stochastic nonlinear systems. In order to relax the Lipschitz condition for the nonlinearity, a novel dynamic gain observer is constructed to estimate the unmeasured state variables. The funnel-like control technique is proposed to ensure that the output of each subsystem satisfies the prescribed performance requirement. To save energy in signal transmission, the controller and its triggered mechanism is co-designed based on backstepping method. By applying the approximation theory of fuzzy logic systems, an unknown continuous function is approximated, and the difficulty caused by unmodeled dynamics is removed with the aid of changing supply function idea. By applying the Lyapunov stability theory, it is proved that all the signals of the whole closed-loop system with the designed controller are bounded in probability. Finally, simulation results are given to verify the effectiveness of the theoretical results.

更新日期：2018-01-17
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-12
LeSheng Jin; Martin Kalina; Radko Mesiar; Surajit Borkotokey

Choquet Integral is a powerful aggregation function especially in merging finite real inputs. However in real life, many inputs exist in continuum, e.g., the Riemann Integrable functions. The standard Choquet Integral formulas can not accommodate such inputs. This study proposes a new expression which enables merging Riemann Integrable inputs using a discrete Choquet integral. Relevant properties arising therein are discussed. A few application domains are identified which include time dependent multicriteria decision aid and dynamic fuzzy cooperative games etc.

更新日期：2018-01-13
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-12
Andrea Zemankova; Stephen Kelly; Khurshid Ahmad

Bonferroni mean aggregates the interaction between all pairs of inputs from some n-dimensional input vector. Therefore it is able to capture the dependency structure between the inputs. Weighted version of the Bonferroni mean then assumes that each input has a possibly different weight. Such an approach poses several constraints that decrease the modelling flexibility of the dependency structure on the input space. In this paper we present an overview of the different approaches to weighted Bonferroni mean and introduce the Bonferroni mean with weighted interaction where interactions between inputs are weighted rather than the inputs themselves. We show several important properties of the Bonferroni mean with weighted interaction and its connection to concepts studied before. Finally, using the described approach we design a system for emergency management that is able to raise an alarm in the case where certain criteria are met.

更新日期：2018-01-13
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-12
Konstantinos D. Koutroumbas

The contribution of this paper is twofold. First, it introduces a generalized framework where sparsity is imposed to a well-known class of cost-function optimization possibilistic algorithms. In addition, under mild conditions, the algorithms in this framework have the ability to determine the number of the true clusters, starting from an overestimation of it. Second, it proposes a new algorithm that is proved to belong to the above framework, which is able to cope with linearly-shaped clusters in the two-dimensional space. The algorithm employs (finite) line segments as cluster representatives and the distance of a data point from a cluster is defined as its distance from the corresponding representative line segment. In contrast to several relative algorithms, the proposed algorithm is able to identify intersecting linear clusters as well as to discriminate between collinear clusters. Finally, experimental results that assess the performance of the proposed algorithm are provided.

更新日期：2018-01-13
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-11
Qianfang Liao; Da Sun

Interaction measure determines decentralized and sparse control configurations for 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 i). A data-driven IT2TSF modeling method is introduced; ii). Explicit formulas to execute the two measures based on IT2TSF models are given; iii). Two interaction indexes are defined from RNGA to select sparse control configuration; iv). The calculations to derive sensitivities of the two measures with respect to parametric variations in the IT2TSF models are developed; v). 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：2018-01-12
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-11

This paper proposes a semi-parametric autoregressive integrated moving average model for those real world applications whose observed data are reported by fuzzy numbers. To this end, a hybrid method including non-parametric kernel-based method, least absolute deviations and cross-validation method is suggested which allows estimating parameters of the model including the autoregressive order $p$ , optimal value of the smoothing parameter $h$ and fuzzy smooth function of the innovations, simultaneously. A correlation concept is also developed for fuzzy time series data and its main properties are investigated. Some common goodness-of-fit criteria are employed to examine performance of the proposed fuzzy semi-parametric time series model. A potential application of the proposed method is represented through a simulated fuzzy time series data. To illustrate utility of this approach, it is applied to a set of real life house price data in fuzzy environment. The results indicate that the proposed method is potentially effective for predicting fuzzy time series data in real applications.

更新日期：2018-01-12
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-11
Tiantian He; Keith C. C. Chan

Many real-world data 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 is 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 based mainly on attribute information. Also, most 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 clusters discovery as a fuzzy constrained optimization problem which takes into consideration both graph topology and attribute values. FSPGA has been tested with both synthetic and real-world graph data sets 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：2018-01-12
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-01-11
Xiangpeng Xie; Dong Yue; Ju H. Park; Hongyi Li

This paper deals with more relaxed designs of discrete-time Takagi--Sugeno fuzzy-model-based observers via two effective technical measures. Different from previous methods of this field, two effective technical measures are developed for obtaining more relaxed results, i.e., 1) A novel ranking-based switching mechanism is proposed by introducing a set of weighted variables so as to make use of the size differences information among normalized fuzzy weighting functions more freely. 2) A new slack variable method is proposed via the introduction of some extended representations for homogenous polynomials, and those major and minor relationships among all normalized fuzzy weighting functions are mapped to sole augmented multi-indexed matrix for each homogeneous polynomial. Therefore, two positive results are provided in this paper, i.e., less conservative fuzzy observers can be given as a result of the above effective measures whilst a part of the online computational cost can be transferred to the offline implementation. Finally, two numerical examples are applied to illustrate the effectiveness of the proposed approach.

更新日期：2018-01-12
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2016-10-13
Zhixiong Zhong; Rong-Jong Wai; Zhenhua Shao; Min Xu

This paper investigates the problem of reachable set estimation and decentralized controller design for large-scale nonlinear systems, where time-varying delays and nonlinearities appear in interconnections connected to other subsystems. The Takagi-Sugeno model is used to describe each nonlinear subsystem. The aim of this paper is to design a decentralized state-feedback fuzzy controller such that the reachable set of the resulting closed-loop system with input constraint is bounded by an intersection of ellipsoids. First, a model transformation is proposed to reformulate the closed-loop system as several feedback interconnections with extra inputs and outputs. Then, based on a combined application of the Lyapunov-Krasovskii functional and the scaled small-gain theorem, the input-output approach is developed for the reachable set estimation and synthesis. Several conditions for the existence of a decentralized state-feedback fuzzy controller that ensures an ellipsoidal bound of reachable sets for the closed-loop system with input constraint are derived in terms of linear matrix inequalities. Finally, two numerical examples are given to validate the effectiveness of the proposed strategy.

更新日期：2018-01-10
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.