• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-21
Baoping Jiang; Hamid Reza Karimi; Yonggui Kao; C Gao

This paper concerns with the problem of robust fuzzy sliding mode control for continuous-time Takagi-Sugeno fuzzy systems with semi-Markovian switching and nonlinear disturbances. The attentions are focused on designing a novel fuzzy integral sliding surface without assumption that the input matrices are the same with full column rank and then developing a fuzzy sliding mode controller for stochastic stability purpose. Based on Lyapunov theory, a set of newly developed linear matrix inequality conditions are established for stochastic stability of the sliding mode dynamics with generally uncertain transition rates, and then extended to the case where the input matrix are plant-rule independent as discussed in most existing literatures. Further, finite-time reachability of the sliding surface is also guaranteed by the proposed fuzzy sliding mode control laws. Finally, a practical example is provided to demonstrate the effectiveness of the established method numerically.

更新日期：2018-05-22
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-21
Qingyuan Zhang; Rui Kang; Meilin Wen

Measuring system reliability by a reasonable metric is a basic problem in reliability engineering. Since the real systems are usually uncertain random systems which is affected by both aleatory and epistemic uncertainties, the existed reliability metrics may not work well. This paper aims to develop a general reliability metric, called belief reliability metric, to cope with the problem. In this paper, the belief reliability is defined as the chance that a system state is within a feasible domain. Mathematically, the metric can degenerate to either probability theory-based reliability, which mainly copes with aleatory uncertainty, or uncertainty theory-based reliability, which mainly considers the effect of epistemic uncertainty. Based on the proposed metric, some commonly used belief reliability indexes, such as belief reliability distribution, mean time to failure and belief reliable life, are introduced. We also develop some system belief reliability formulas for different systems configurations. To further illustrate the formulas, a simple case study is finally performed in this paper.

更新日期：2018-05-22
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-18
Boris Yatsalo; Luis Martinez

Ordering fuzzy quantities is a key and challenging problem in fuzzy sets theory that has attracted the interest of many researchers. Despite the multiple indices introduced for this purpose and due to the fact that fuzzy quantities do not have a natural order, there is still a chance to provide a new approach for ranking this type of quantities from the acceptability and foundation points of view. This paper aims at developing a new approach for ranking fuzzy numbers, Fuzzy Rank Acceptability Analysis (FRAA), that not only implements a ranking of the fuzzy numbers but also provides a degree of confidence for all ranks. Additionally, the FRAA can be efficiently implemented by using different fuzzy preference relations including both transitive and intransitive ones. Properties of FRAA ranking, their dependence on the fuzzy preference relations and correspondence with the basic axioms for ranking fuzzy numbers are analyzed. Eventually, a comparison of the FRAA ranks with ranks from other ranking methods is done together with a discussion of the advantages of FRAA ranking.

更新日期：2018-05-19
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-18
Chunbing Bao; Dengsheng Wu; Jianping Li

Risk measures play significant roles in determining the magnitude of risks. The traditional risk measures consider only the consequence (C) and the probability (P) and ignore the support of the knowledge behind to estimate C and P. Several researchers have suggested adding knowledge as a third dimension in the risk measures. However, the issues of how to embed the dimension of knowledge in the risk measures to output an explicit expression of the risk measure and how to measure the strength of knowledge remain unresolved. This paper proposes a new risk measure incorporating the dimension of knowledge, apart from C and P. It is shown that the proposed risk measure has the form of traditional risk measures when the risk assessor has full knowledge. In addition, a fuzzy multi-criteria decision-making (MCDM) method is employed to assess the strength of knowledge. In the fuzzy MCDM method, an entropy optimization problem is solved to obtain fuzzy measures, which are critical for determining the score of the strength of knowledge. Last, the proposed method is applied to a project risk assessment, showing the feasibility of the method.

更新日期：2018-05-19
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-17
Reda Boukezzoula; Sylvie Galichet; Laurent Foulloy

This paper presents a new and a more general formulation of the min and max operations for gradual intervals, initially proposed in [1] for the special case of triangular fuzzy intervals. Gradual intervals generalize the conventional interval representation by increasing its specificity, thereby making it possible to represent the imprecision and the uncertainty via the notion of gradualness. In this context, a new interpretation of fuzzy intervals through the notion of gradual intervals is developed. The originality of the proposed methodology lies in the extension of inter-interval relations to the gradual case according to Midpoint-Radius representation.

更新日期：2018-05-18
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-15
Yi Zeng; Hak-Keung Lam; Ligang Wu

This paper is concerned with the model reduction problem of discrete-time interval type-2 Takagi-Sugeno (T-S) fuzzy systems which represent the discrete-time nonlinear systems subject to uncertainty. With the use of interval type-2 fuzzy sets, the uncertainty of the discrete-time nonlinear system can be captured by the lower and upper membership functions. For a given high-order discrete-time interval type-2 T-S fuzzy system, the purpose is to find a lower dimensional system to approximate the original system. To achieve the approximation performance, an H$\infin$ norm is used to suppress the error between the original system and its simplified system. By introducing a membership-functions-dependent technique and applying a convex linearization method, a membership-functions-dependent condition, which takes the information of membership functions into account, is obtained to reduce the dimensions of system matrices and the number of fuzzy rules of the system. All the obtained theorems are represented as in the form of linear matrix inequalities (LMIs). Finally, simulation results are demonstrated to show the effectiveness of the derived results.

更新日期：2018-05-16
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-15
Feng Liu; Jie Lu; Guangquan Zhang

Unsupervised domain adaptation (UDA) aims to recognize newly emerged patterns in target domains, which may be unlabeled, by leveraging knowledge from patterns learnt from source domains. However, existing UDA models and algorithms still suffer from heterogeneous domains, known as the heterogeneous unsupervised domain adaptation (HeUDA) issue. To address this issue, this paper presents a novel HeUDA model via n-dimensional fuzzy geometry and fuzzy equivalence relations, called F-HeUDA. The n-dimensional fuzzy geometry is used to propose a metric to measure the similarity between features on one domain. Then, based on this metric, shared fuzzy equivalence relations (SFER) is proposed. The SFER can allow two domains to use the same - to get the same number of clustering categories. Through these clustering categories, knowledge from the heterogeneous source domain can be transferred to the unlabeled target domain. Different to existing HeUDA models, the proposed F-HeUDA model does not need that two domains must have the same number of instances. As a result, the proposed model has a better ability to handle the issue of small datasets. Experiments distributed across four real datasets were conducted to validate the proposed model. This testing regime demonstrates that the proposed model outperforms the state-of-the-art models, especially when the target domain has very few instances.

更新日期：2018-05-16
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-15
Zahra Moslehi; Mahsa Taheri; Abdolreza Mirzaei; Mehran Safayani

In this paper, a new unsupervised metric learning algorithm with real world application in clustering is proposed. To have a desirable clustering, it is needed to improve the separability among different classes of data. A common manner in accomplishing this objective is to take the advantages of metric learning in clustering and vice versa. Clustering provides an estimation of class labels and metric learning maximizes the separability among these different estimated classes of data. This procedure is performed in an iterative fashion, alternating between clustering and metric learning. Here, a new method is proposed, called Discriminative Fuzzy C-Means (Dis-FCM), in which fuzzy c-means and metric learning are integrated into one joint formulation. Unlike the traditional approaches which simply alternate between clustering and metric learning, Dis-FCM applies both of them simultaneously. Here, fuzzy c-means provides the data which are "similar" or "dissimilar" as two fuzzy relations. This can avoid the problem of fast convergence, which is common in the previous of the algorithm. Moreover, Dis-FCM is able to handle not only numerical data, but also categorical data, which are not found in the traditional methods. The experimental results indicate its superiority over other state-of-the-art algorithms in terms of extrinsic and intrinsic clustering measures.

更新日期：2018-05-16
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-11
Liang Bai; Jiye Liang; Yike Guo

Fuzzy cluster ensemble is an important research content of ensemble learning, which is used to aggregate several fuzzy base clusterings to generate a single output clustering with improved robustness and quality. However, since clustering is unsupervised, where the "accuracy" does not have a clear meaning, it is difficult for existing ensemble methods to integrate multiple fuzzy k-means clusterings to find arbitrarily shaped clusters. To overcome the deficiency, we propose a new ensemble clusterer (algorithm) of multiple fuzzy k-means clusterings based on a local hypothesis. In the new algorithm, we study the extraction of local-credible memberships from a base clustering, the production of multiple base clusterings with different local-credible spaces, and the construction of cluster relation based on indirect overlap of local-credible spaces. The proposed ensemble clusterer not only inherits the scalability of fuzzy k-means but also overcomes its limitation that it can not find arbitrarily shaped clusters. We compare the proposed algorithm with other cluster ensemble algorithms on several synthetical and real data sets. The experimental results illustrate the effectiveness and efficiency of the proposed algorithm.

更新日期：2018-05-12
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-11
Yan Yu; Hak-Keung Lam; Kit Yan Chan

This paper investigates the output feedback tracking control for fuzzy-model-based control (FMB) system when the control input is saturated, where the FMB is developed based on a T-S fuzzy model and a fuzzy controller. The controller is employed to close the feedback loop and generate the system to trace the trajectory of the states of a stable reference model subject to H $\infin$ performance. To enhance the fuzzy controller design flexibility, the number of rules and premise membership functions can be adjusted. Stability analysis for the FMB control system is performed based on Lyapunov stability theory. To address the control input saturation problem, linear sectors are created by local linear upper and lower bounds to include the possible control area. Hence the nonlinear saturation problem can be tackled by the stability analysis of linear sectors. Membership-functions-dependent (MFD) technique is used to bring the information and address the nonlinearity of embedded membership functions into the stability analysis. The numerical simulation example demonstrates the effectiveness of proposed approach and discusses the effect of H $\infin$ performance and control input saturation rate according to the tracking result.

更新日期：2018-05-12
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-10

In this paper, a class of signed-distance measures was proposed for interval-valued fuzzy numbers based on some specific bivariate functions called kernels and -values of interval-valued fuzzy numbers. The main properties of the proposed signed-distance measure such as robustness were also studied in the space of interval-valued fuzzy numbers. Then, the proposed signed distance was applied to rank a set of interval-valued fuzzy numbers using an axiomatic approach. The proposed method was compared with several existing methods and its feasibility and effectiveness were cleared via some numerical and theoretical comparisons. The results indicated that the proposed method was feasible for ranking all kind of LR-interval-valued fuzzy numbers and it could overcome some drawbacks of the existing methods based on some reasonable axioms expected for a ranking criteria in the space of interval-valued fuzzy numbers. Finally, the proposed method was applied to a case study related to multi-criteria group decision-making.

更新日期：2018-05-11
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-07
Jinquan Xu; Yutao Du; Ye-Hwa Chen; Hong Guo; Xiaofeng Ding

A fuzzy-based optimal approach to robust control design is proposed for interconnected uncertain system with mismatching condition, which was not available earlier. We consider an interconnected system containing uncertainty, which may include initial conditions, unknown system parameters, and input disturbance. The uncertainty bound lies within a prescribed fuzzy set. The system does not satisfy the matching condition. The robust control design in this paper consists of control scheme design and control gain optimization. A new robust control scheme is first proposed, whose structure is deterministic and not if-then fuzzy rule-based. The control gain design problem is then formulated as a constrained optimization problem by fuzzy description of the uncertainty bound, which minimizes the fuzzy system performance and the control effort. We show that the global solution to this optimization problem always exists and is unique. The closed-form solution and closed-form minimum cost are presented. The resulting control is able to render the system performance in twofold. First, it guarantees uniform boundedness and uniform ultimate boundedness regardless of the actual value of uncertainty. Second, it minimizes a fuzzy-based performance index. The novelty of this research is a new and carefully orchestrated effort in blending several creative methods and tools, including simultaneous state transformation and control design, dual deterministic and fuzzy features of the performance index, and raised control order, into an integrated framework, which results in a tractable design problem.

更新日期：2018-05-08
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-07
Liuyang Song; Huaqing Wang; Peng Chen

A step-by-step fuzzy diagnostic method based on frequency domain symptom extraction and trivalent logic fuzzy diagnosis theory (TLFD), which is established by combining the trivalent logic inference theory with the possibility and fuzzy theories, is proposed herein. The features for diagnosing a number of abnormal states are extracted sequentially from the measured signals using statistical tests in the frequency domain. The symptom parameters (SPs) that can sensitively reflect the symptoms of the abnormal states are then selected to provide effective information for the discrimination of each state, and the membership function of each state is generated based on the possibility theory using the probability functions of the SPs. The step-by-step fuzzy diagnoses are performed based on the TLFD. This method can be extensively used to diagnose anomalies in various equipment. In this study, the diagnosis of structure faults of a rotating machine is cited as an example to demonstrate the effectiveness and universality of this method.

更新日期：2018-05-08
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-07
Jinquan Xu; Yutao Du; Ye-Hwa Chen; Hong Guo

We consider the control design problem for a class of constrained uncertain systems in this paper. The uncertainty in the system, including unknown system parameters and external disturbance, is nonlinear and time-varying. The bound of the uncertainty is described via a fuzzy set. The states of the system are constrained to be bounded. We propose a one-to-one state transformation to convert the bounded state constrained system into the unconstrained system. A new robust control scheme is then proposed for the transformed system, which is in deterministic form and not fuzzy if-then rule-based. By fuzzy description of the uncertainty bound, the optimal design of the control gain is proposed, which minimizes a fuzzy performance index associated with both the fuzzy system performance and the control effort. The analytic solution to the optimization problem is demonstrated to always exist and be unique. The resulting control can guarantee uniform boundedness and uniform ultimate boundedness of the uncertain system, while minimizing the fuzzy-based performance index. In addition, the state constraint can be always guaranteed.

更新日期：2018-05-08
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-03
Zhen-Song Chen; Kwai-Sang Chin; Luis Martinez; Kwok-Leung Tsui

Linguistic computational techniques based on hesitant fuzzy linguistic term set (HFLTS) have been swiftly advanced on various fronts during the past five years. However, one of the key issues in the existing theoretical developments is that modeling possibility distribution-based semantics involves a relatively strict constraint that linguistic terms are uniformly distributed across an HFLTS. Releasing the constraint of uniform HFLTS through which individual semantics could be customized is challenging yet intriguing for participants interested in this topic. Comparative linguistic terms (CLEs) generated from context-free grammar facilitate flexible and accurate linguistic elicitation, and in consideration of computational simplicity they are transformed into HFLTSs which are machine manipulatable. It is imperative that the precision of customized individual semantics can be significantly improved in respect of different CLEs. This study proposes a novel possibility computation structure for HFLTS possibility distributions based on the linguistic terms similarity measure. The uniquely established linguistic terms in each and every CLE are initially treated as referential items for comparison. Then, possibilities of linguistic terms in a transformed HFLTS can be calculated as their similarity degrees to the predetermined referential item. Subsequently, the Interweaving method, in which a consistent Inner Interweaving Matrix needs to be constructed, is adopted to adapt Attitudinal Character to attain appealing degrees characterized in the unit interval. The generated attitudinal HFLTS possibility distributions provide a solution to the problem of modeling individually the semantic implications of CLEs. Several illustrative examples and comparative analyses further demonstrate that individual semantics endowed with Attitudinal Character model efficiently individual differences in cognitive styles.

更新日期：2018-05-04
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-03
Liang Sun; Wei He; Sun Changyin

A six-degrees-of-freedom integrated adaptive fuzzy nonlinear control method is presented in this paper for uncertain spacecraft proximity systems subject to unknown model uncertainties and complex kinematic couplings. Adaptive fuzzy logic systems are developed to approximate the unknown nonlinear functions, and an adaptive fuzzy backstepping relative pose controller is designed. To overcome the drawback of "curse of dimensionality" in adaptive fuzzy systems for multiple variable systems, all of parameters in membership functions are updated to reduce the amount of fuzzy rules and computational burden. It is proven via Lyapunov theory that the proposed adaptive fuzzy nonlinear controller ensures the boundedness of all signals in overall system, and the relative motion information ultimately converges to adjustable small neighborhoods of zero. A computer experiment with numerical example is carried out to demonstrate the performance of the proposed control approach.

更新日期：2018-05-04
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-02
Hao Shen; Feng Li; Zheng-Guang Wu; Ju H. Park; Victor Sreeram

This paper researches the fuzzy-model-based non-fragile control problem for nonlinear discrete-time singularly perturbed systems with Markov jumping parameters. To remove the restriction of sojourn-time in widely used discrete-time Markov jump model, i.e. the sojourn-time is subject to a geometric distribution which leads that the transition probabilities is memoryless, the semi-Markov jump model in which the ${memory}$ property of the transition probabilities is considered, is adopted to describe the stochastic jump parameters in the nonlinear singularly perturbed systems. Based on the T-S fuzzy model approach and semi-Markov Kernel concept, several criteria ensuring $\delta$ -error mean square stability of the underlying closed-loop system are established. With the help of those criteria, the design procedures of a resilient controller which can well deal with the fragility problem in the implementation of the proposed fuzzy-model-based controller is presented and a technique is developed to estimate the larger permissible maximum value of singularly perturbed parameter for discrete-time nonlinear semi-Markov jump singularly perturbed systems. Finally, the validity of the established theoretical results is illustrated by a numerical example and a modified tunnel diode circuit.

更新日期：2018-05-03
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-02
Javier A. Livio; Rania Hodhod

In the coffee industry, "cupping" is the process of sensorial evaluation of coffee beans, also known as Sample Evaluation. This process is done for three major reasons: 1. to determine the actual sensory differences between coffee samples; 2. to describe the flavors of the samples; and 3. to determine preference of product. In totality, cupping targets the measurement of the coffee's quality which is expressed with a final numerical score. When cupping, the expert judge writes down the individual components' scores and ranks their intensities for reference. Fuzzy logic has been employed for sensory evaluation of chhana podo (a baked dairy product), also for mango pulp and litchi juice. Moreover, a similar work exists only to train the Honduran Coffee Cuppers. This paper introduces a fuzzy expert system, AI Cupper offering an intuitive way for representing the judge's knowledge by linguistically modeling his perception of the coffee attributes through sensorial evaluation, it is capable of training cuppers when evaluating coffees from several countries and even has the capacity to learn as cupping data flows through it. The system was tested and showed more than 95% of matching results compared with the experts' results.

更新日期：2018-05-03
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-05-02
Yanyong Huang; Tianrui Li; Chuan Luo; Hamido Fujita; Shi-Jinn Horng

Information fusion is capable of fusing and transforming multiple data derived from different sources to provide a unified representation for centralized knowledge mining that facilitates effective decision-making, classification and prediction, etc. Multi-source interval-valued data, characterizing the uncertainty phenomenons in the data in the form of intervals in different sources, are the most common symbolic data which widely exist in many real-world applications. This paper concentrates on efficient fusing of multi-source interval-valued data with the dynamic updating of data sources which involves the addition of new sources and the deletion of obsolete sources. We propose a novel data fusion method based on fuzzy information granulation, which translates multi-source interval-valued data into trapezoidal fuzzy granules. Given this effectively fusing capability, we develop incremental mechanisms and algorithms for fusing multi-source interval-valued data with dynamic variation of data sources. Finally, extensive experiments are carried out to verify the effectiveness of the proposed algorithms when comparing with other six different fusion algorithms. Experimental results show that the proposed fusion method outperforms the related approaches. Furthermore, the proposed incremental fusion algorithms can reduce the computing overhead in comparison with the static fusion algorithm when adding and deleting multiple data sources.

更新日期：2018-05-03
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-30
Shanchao Yang; Jing Liu

Fuzzy cognitive maps (FCMs) have been successfully used to model and predict stationary time series. However, it still remains challenging to deal with large-scale non-stationary time series which have trend and vary rapidly with time. In this paper, we propose a time series prediction model based on the hybrid combination of high-order FCMs with the redundant wavelet transform to handle large-scale non-stationary time series. The model is termed as Wavelet-HFCM. The redundant Haar wavelet transform is applied to decompose original non-stationary time series into multivariate time series, then the high-order FCM is used to model and predict multivariate time series. In learning high-order FCM to represent large-scale multivariate time series, a fast high-order high-order FCM learning method is designed on the basis of ridge regression to reduce the learning time. Finally, summing multivariate time series up yields the predicted time series at each time step. Compared with existing classical methods, the experimental results on eight benchmark datasets show the effectiveness of our proposal, indicating that our prediction model can be applied to various prediction tasks.

更新日期：2018-05-01
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-23

Considering some aggregation functions, we define $\textbf{B}$ - A-weighting vectors. Then, a definition for OWA operators is given based on $\textbf{B}$ - A-weighting vectors. Moreover, we show that our proposed definition for OWA operators over complete lattices is a generalization of the given definition by I. Lizasoain and C. Moreno, 2013. Finally, a special case is studied.

更新日期：2018-04-24
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-23
Pingping Chen; Yingchen Yan; Geni Xu; Ruiqing none Zhao

The recent growth of specialized promotion groups has encouraged many firms to shift from self-operated promotion to third-party promotion, including offline-outlet and online platform promotion. Compared with self-operated promotion, firms adopting third-party promotion can often generate more demand but incur screening costs stemming from the third party's uncertain ability to generate demand. Furthermore, firms applying offline-outlet promotion can benefit from the additional demand created by service effort at physical outlets while simultaneously being affected by another uncertain factor, namely, the effort level. By capturing these fundamental differences, we develop a specific multi-stage decision-making model to answer a key question: which strategy should firms adopt, self-operated, online-platform or offline-outlet promotion. We find that a firm's preferences shift from self-operated promotion to offline-outlet promotion and then to online-platform promotion as production quantity increases. Furthermore, decreases in promotional prices make firms more willing to adopt self-operated and online-platform promotion but less willing to adopt offline-outlet promotion. Moreover, we present an interesting insight: the promotion quantity allocated to a low-type third party under online-platform promotion is downward distorted to avoid mimicking the high type, whereas under offline-outlet promotion, the promotion quantity is upward distorted due to the impact of service effort and its incentive mechanism.

更新日期：2018-04-24
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-23
Wei Chen; Dandan Li; Yong-Jun Liu

This paper deals with a multi-period portfolio selection problem in an uncertain investment environment, in which the returns of securities are assumed to be uncertain variables and determined by experts' subjective evaluation. Based on uncertain theory, we present a novel multi-period multi-objective mean-variance-skewness model by considering multiple realistic investment constraints, such as transaction cost, bounds on holdings, and cardinality etc. For solution, we first apply a weighted max-min fuzzy goal programming approach to convert the proposed multi-objective programming model into a single-objective one. After that, we design a novel hybrid of imperialist competitive algorithm (ICA) and firefly algorithm (FA), termed ICA-FA to solve it. Finally, we provide a numerical example to demonstrate the effectiveness of the proposed model and corresponding algorithm.

更新日期：2018-04-24
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-12
Peide Liu; Peng Wang

The theory of q-rung orthopair fuzzy sets (q-ROFSs) proposed by Yager can more effectively describe fuzzy information in the real-world. Because q-ROFSs contain a parameter q and can adjust the range of expressed fuzzy information, they are more superior to intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). Archimedean T-norm and T-conorm (ATT) is an important tool to generate operational rules, so many general operational rules can be provided by ATT based on the q-rung orthopair fuzzy numbers (q-ROFNs). Meanwhile, the Bonferroni mean (BM) operator has the prominent advantage that it can consider the interrelationships between the different attributes. Therefore, it is an important and meaningful innovation to extend the BM operator to the q-ROFNs based on the ATT. In this paper, we firstly discuss and give some q-rung orthopair fuzzy operational rules by using ATT. Further we extend BM operator to the q-ROFNs, and propose the q-Rung Orthopair fuzzy Archimedean BM (q-ROFABM) operator and the q-Rung Orthopair fuzzy weighted Archimedean BM (q-ROFWABM) operator and study their desirable properties. Then, a new multiple-attribute decision-making (MADM) method is developed based on q-ROFWABM operator and its process is presented in detail. Finally, we take advantage of the practical example to verify its effectiveness and superiority by comparing with other existing methods.

更新日期：2018-04-13
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-12
Shanling Dong; Zheng-Guang Wu; Peng Shi; Hamid Reza Karimi; Hongye Su

This paper deals with the problem of dissipativity-based asynchronous fault detection for Takagi-Sugeno fuzzy Markov jump systems with network data dropouts. It is assumed that data dropouts happen intermittently from the plant to the fault detection filter, which is described by Bernoulli process. The hidden Markov model is employed to describe the asynchronous phenomenon between the plant and filter. Based on Lyapunov theory, a sufficient condition is developed to guarantee that the fault detection system is stochastically stable with strictly dissipative performance. By choosing an appropriate Lyapunov function with the slack matrix technique and Finsler's Lemma, two approaches are proposed to compute filter gains by solving linear matrix inequalities. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed design methods.

更新日期：2018-04-13
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-12
Haitao Yu; Changjun Jiang; Randong Xiao; Hangou Liu; Weifeng Lv

Predicting the passenger flow of public transport in a newly developed area of a city is very urgent for designing a precise and efficient public transport network. This paper proposes a new prediction model by exploring the relationship between the passenger flow of a station and its surrounding area's factors. First, in order to obtain more accurate factors affecting the passenger flow, the city is divided into multiple regions with similar internal traffic properties and moderate spatial size using the data of urban road network and buildings. Second, to effectively solve the problem of fuzziness of the station's attraction scope, the concept of the membership degree and fuzzy processing method is proposed. Finally, the station's passenger flow prediction model is launched based on Xgboost. The experimental results on three districts in Beijing show that our method outperforms all baselines significantly which improves the accuracy by more than 20%.

更新日期：2018-04-13
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-12
Xiaofeng Xu; Jun Hao; Lean Yu; Yirui Deng

Obtaining a multi-resource allocation scheme for multi-task influenced by uncertain factors is a critical problem in collaborative logistics network. This paper presents an optimal allocation model of fuzzy resources for multi-stage random logistics tasks based on the six-point trapezoidal fuzzy number and the membership function. Besides, considering task demands and resource constraints, a new cost-time-quality multi-objective programming of N-N task-resource assignment is introduced, which can be divided into minimize total logistics cost and execution time, maximize total service quality. Furthermore, by setting the different simulation scenarios, the results show that if the decision maker has a higher risk preference and pursues the optimization of single or multi-objective, the higher degree membership and satisfaction function values can be gotten with a larger compensation coefficient. The allocation scheme of task-resource assignment generated by proposed model has a high global level of utilization efficiency, which can effectively utilize fuzzy resources in collaborative logistics network, and avoid resource shortage caused by the excessive occupation of local resources.

更新日期：2018-04-13
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-12
Huai-Ning Wu; Shuang Feng

This paper addresses a mixed fuzzy/boundary control problem of a class of nonlinear coupled systems described by ordinary differential equation (ODE) and boundary-disturbed uncertain beam equation. A mixed fuzzy/boundary control scheme is first proposed, consisting of an ODE-state feedback fuzzy controller for the ODE system and an anti-disturbance robust boundary controller for the boundary-disturbed uncertain beam. The boundary controller includes a linear feedback controller for the beam stabilization via boundary measurements, a nonlinear compensator with adaptive bounding and a disturbance observer based compensator for canceling the effects of the uncertain nonlinearity and the boundary disturbance of the beam, respectively. The mixed control design is developed in terms of space dependent bilinear matrix inequalities (SDBMIs) to guarantee the closed-loop input-to-state practical stability. Meanwhile the closed-loop well-posedness analysis is also given. Furthermore, a two-step procedure is introduced to solve the SDBMI feasibility problem by the existing linear matrix inequality optimization techniques. Finally, a simulation study on a flexible spacecraft is given to illustrate the effectiveness of the proposed method.

更新日期：2018-04-13
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-10
Qiang Xiao; Tingwen Huang; Zhigang Zeng

A class of T-S fuzzy memristor-based inertial neural networks (FMINNs) is studied on time scales. The second-order derivative of the state variable in the network denotes the inertial term. At first, one timescale-type FMINNs is, for the first time, formulated on the basis of T-S fuzzy rules. By a variable transformation, the original network is transformed into some first-order differential equations. Then some passivity criteria for the FMINNs are presented based on the characteristic function approach, linear matrix inequality (LMI) techniques and the calculus of time scales. Furthermore, two classes of control protocols, i.e., memristor- and fuzzy-related control protocols are designed, respectively, to solve the passification problem for the considered FMINNs. The optimization problem of the passivity performance is also involved. Finally, some simulation examples are given to show the effectiveness and validity of the obtained results, and an application is also given in pseudorandom number generation.

更新日期：2018-04-11
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-10
Ke Gong; Yong Wang; Maozeng Xu; Zhi Xiao

With the advent of big data era, data become bigger than ever. Recently, as a fundamental task of pattern recognition, predict and data mining, feature selection has aroused wide public concern. However, extant methods on feature selection have an O(|C| $^{2}$ |U| $^{y}$ ) time complexity, which is the bottleneck preventing people from exploring knowledge in large-scale or high dimensional data sets. In this paper, based on bijective soft sets, we propose a new rationale for feature selection, which can help to break the bottleneck. Subsequently, this paper proposes an $O(\left|U\right|)$ feature selection method, whose computational time increases linearly only with the number of instances. To validate the proposed method, we conduct extensive experiments on UCI data sets, in which large-scale and high-dimensional data sets containing four million instances and over three million features are included. The results reveal that the proposed method is an efficient and effective and outperforms traditional methods in runtime, which can save massive computing resources. Moreover, the proposed method can be applied to feature selection for large-scale and gigantic-dimensional data sets, which are hard to be processed with traditional methods.

更新日期：2018-04-11
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-04-09
Ta Zhou; Hisao Ishibuchi; ShiTong Wang

In this paper, we propose a blockwise combination of interpretable Takagi-Sugeno-Kang (TSK) fuzzy classifiers to simultaneously achieve high accuracy and concise interpretability. As a special hierarchical fuzzy classifier, the proposed classifier is built in a stacked block-by-block way. Each base building block consists of multiple zero-order TSK fuzzy classifiers, which are simultaneously trained in an analytical manner by using negative correlation learning to enhance the generalization ability of the base building block. For utilizing the stacked generalization principle, a random projection of the outputs from the current base building block is presented to the next base building block together with the current training sample in order to enhance the generalization ability of our hierarchical fuzzy classifier. The point of such a special hierarchical structure is that all base building blocks can be trained in the same input-output space with the current training sample and the randomly projected output from the previous building block. In the input layer, the target output for the current training sample is used instead of the randomly projected output from the previous building block. Each TSK fuzzy classifier in base building blocks consists of interpretable TSK fuzzy rules, which are generated by randomly selecting input features and randomly assigning an antecedent fuzzy subset from a fixed fuzzy partition to each of the selected input features. Merits of the proposed classifier are demonstrated through comparative studies on benchmark datasets.

更新日期：2018-04-10
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-03-30
M. Wang; Jianbin Qiu; Gang Gary Feng

In this paper, we will investigate the problem of finite frequency memory fixed-order output feedback controller design for Takagi-Sugeno (T-S) fuzzy affine systems. It is assumed that the disturbances reside in a finite frequency range, i.e., the low, middle, or high frequency range. The objective is to design a memory piecewise affine controller by using past output measurements to guarantee the asymptotic stability of the resulting closed-loop system with prescribed finite frequency H-infinity performance. Via the system state-input augmentation, a novel descriptor system approach is proposed to facilitate the controller design. All the design conditions are formulated in the form of linear matrix inequalities (LMIs). It is also proven that the H1 performance can be improved with the memory control strategy. Finally, simulation studies are presented to show the effectiveness of the proposed design method.

更新日期：2018-03-31
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2018-03-30
Shuai Sui; Shaocheng Tong; C. L. Philip Chen

This paper solves the finite time decentralized control problem for uncertain nonlinear large-scale systems in nonstrict-feedback form. The considered controlled plants are different from the previous results of finite time control systems, which are the nonstrict-feedback large-scale systems with the unknown functions consisting of all states, interactions and immeasurable states. Fuzzy logic systems and a filter-based state observer are utilized to model the uncertain systems and deal with the immeasurable states, respectively. By combining the backstepping recursive design with Lyapunov function theory, a finite time adaptive fuzzy decentralized control approach is raised. It is testified that the developed control strategy can guarantee the closed-loop signals are bounded, and the outputs of systems have satisfactory tracking performance in a finite time. A quadruple-tank process system is given to testify the effectiveness and applicability of the proposed approach.

更新日期：2018-03-31
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-02-08
Zongcheng Liu; Xinmin Dong; Wujie Xie; Yong Chen; Hongbo Li

An adaptive fuzzy control approach is proposed for nonaffine pure-feedback systems with nonaffine functions being semibounded and possibly indifferentiable. A semibounded and continuous condition for nonaffine function is presented to guarantee the controllability of system. To overcome the difficulty from this mild condition, a compact set is introduced, and the nonaffine nonlinear functions are modeled in a new way based on this compact set, which is proved to be invariant set eventually. By using the dynamic surface control (DSC) technique, the problem of explosion of complexity inherent in backstepping method is avoided in the proposed adaptive fuzzy control scheme. Robust compensators are used to minify the influence of uncertainties and disturbances. Furthermore, it is proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-02-09
Kai Yao

The observations of some samples from the population of a probability density function with unknown parameters are usually imprecise due to various reasons. By employing uncertain variables to model these imprecise observations, this paper proposes an interdiscipline called the uncertain statistical inference, which is composed of statistical inference and uncertainty theory. It presents three types of statistic inference problems with imprecise observations that are the point estimation, the hypothesis test, and the interval estimation. Then, it proposes a method of moments and a method of likelihood function (maximum likelihood estimation) for the first problem, and a method of likelihood ratio function for the other two problems.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-02-16
Hengyang Wu; Yuxin Deng

Modal logics and behavioral equivalences play an important role in the specification and verification of concurrent systems. In this paper, we first present a new notion of bisimulation for nondeterministic fuzzy transition systems, which is distribution based and coarser than state-based bisimulation appeared in the literature. Then, we define a distribution-based bisimilarity metric as the least fixed point of a suitable monotonic function on a complete lattice, which is a behavioral distance and is a more robust way of formalizing behavioral similarity between states than bisimulations. We also propose an on-the-fly algorithm for computing the bisimilarity metric. Moreover, we present a fuzzy modal logic and provide a sound and complete characterization of the bisimilarity metric. Interestingly, this characterization holds for a class of fuzzy modal logics. In addition, we show the nonexpansiveness of a typical parallel composition operator with respect to the bisimilarity metric, which makes compositional verification possible.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-02-22
Dejian Yu; Zeshui Xu; Yuhsuan Kao; Chin-Teng Lin

The IEEE Transactions on Fuzzy Systems (TFS) is a reputable international journal in the research domain of computer science and engineering. This study surveys the TFS publications between 1994 and 2015 which are indexed in Web of Sciences. The purpose is to present a comprehensive overview of the main influencing factors that affect the journal and identify the theme and citation structures of TFS. First of all, the publication and general citation structure of the journal as well as the most cited articles are analyzed. Then, the TFS authorship and coauthorship are well investigated, the maps of author cocitation network and representative subnetwork of the TFS coauthorship are presented. Next, this study gives a global overview of TFS publications. The most influential and productive countries/territories as well as the temporal analysis of the leading countries/territories are presented. Finally, the cocitation network for exploring the ground-breaking research is generated and the main cocitation clusters of TFS publications are discovered.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-21
Pedro A. Baziuk; Jorge E. Núñez Mc Leod; Selva S. Rivera

In this paper, we introduce a new Human Reliability Analysis method based on a Human Abilities Theory Model (HRA-HAT). This approach simultaneously addresses cross-cutting aspects of the main issues and criticisms of human reliability models: 1) model's theoretical bases (including taxonomy and concept specificity); 2) definition and use of performance shaping factors; and 3) HRA quantification. HAT is used to support method parameters selection and the consequent data collection procedure. The resulting methodology works on the basis of three main stages: 1) Fuzzy Cognitive Task Analysis; 2) Fuzzy Operator Analysis; and 3) Fuzzy Human Error Probability estimation based on Human Abilities Theory model. “Operator Analysis” is a new stage of HRA that reduces uncertainty about individuals’ actual behavior in specific situations by focusing on this essential component of sociotechnical systems. To exemplify method implementation procedures, an illustrative example is analyzed. Finally, methodology sensibility and uncertainty are explored in order to prompt HRA-HAT validation. Since this methodology was conceived as an approach applicable to several fields, it is expected to be revised and adapted for further practical applications.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-23
Huai-Ning Wu; Zi-Peng Wang

In this paper, an observer-based $H_{\infty }$ sampled-data fuzzy control problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems. With the aid of the modal decomposition technique, a nonlinear ordinary differential equation (ODE) model is initially derived to describe the dominant (slow) dynamics of the PDE system. Subsequently, the resulting nonlinear ODE model is accurately represented by the Takagi–Sugeno (T–S) fuzzy model. Then, based on the T–S fuzzy model, a finite-dimensional observer-based sampled-data fuzzy control design with $H_\infty$ performance is developed for the PDE system via employing a novel time-dependent functional. The outcome of the observer-based $H_{\infty }$ sampled-data fuzzy control problem can be formulated as a bilinear matrix inequality optimization problem. Moreover, an iterative optimization algorithm based on the linear matrix inequalities is given to obtain a suboptimal $H_\infty$ sampled-data fuzzy controller. Finally, simulation results on the Fisher equation and a temperature cooling fin of high-speed aerospace vehicle illustrate that the proposed design method is effective.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-22
Guanyu Lai; Zhi Liu; C. L. Philip Chen; Yun Zhang; Xin Chen

The problem of direct adaptive compensation for infinite number of time-varying actuator failures/faults is of both theoretical and practical importance in the fuzzy tracking control of uncertain nonlinear systems. However, due to the technical difficulties, so far, very limited result is available in addressing such an issue, which thus motivates us to propose a new fuzzy control methodology in this paper. The proposed scheme is established from the techniques of projection adaptation design, a new piecewise Lyapunov function analysis, and an optimized fuzzy adaptation. It is shown that all the closed-loop signals are bounded and the steady-state tracking error converges to a residual around zero, irrespective of a possibility that there are infinite number of time-varying actuator failures. Simulations are provided to illustrate the effectiveness and applicability of the proposed scheme.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-22
Daniel Paternain; María Jesús Campión; Radko Mesiar; Irina Perfilieva; Humberto Bustince

In this paper, we investigate a mechanism for fusing a set of inputs (values) in such a way that the procedure does not create new information during the process. In order to do so, we introduce internal fusion functions, a family of fusion functions in which the output always corresponds to some of the given inputs. We perform an in-depth theoretical study of internal fusion functions and, furthermore, we propose three different construction methods, which are based on 1) an arbitrary fusion function and a partition of the domain; 2) a linear order; and 3) a minimization mechanism using penalty functions. Finally, we illustrate this paper with the application of internal fusion functions in two image processing algorithms where a set of images must be fused, namely multifocus image and denoised image fusion, as well as in an example of multiclass problem, where we fuse a set of score matrices obtained by several classification algorithms.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-27
Yanling Wei; Jianbin Qiu; Hamid Reza Karimi

This paper studies the piecewise-affine memory $\mathscr {H}_{\infty }$ filtering problem for nonlinear systems with time-varying delay in a delay-dependent framework. The nonlinear plant is characterized by a continuous-time Takagi–Sugeno fuzzy-affine model with parametric uncertainties. The purpose is to develop a new approach for filter synthesis procedure with less conservatism. Specifically, by constructing a novel Lyapunov–Krasovskii functional, together with a Wirtinger-based integral inequality, reciprocally convex inequality and S-procedure, an improved criterion is first attained for analyzing the $\mathscr {H}_{\infty }$ performance of the filtering error system, and then via some linearization techniques, the piecewise-affine memory filter synthesis is carried out. It is shown that the existence of desired filter gains can be explicitly determined by the solution of a convex optimization problem. Finally, simulation studies are presented to reveal the effectiveness and less conservatism of the developed approaches. It is anticipated that the proposed scheme can be further extended to the analysis and synthesis of continuous-time fuzzy-affine dynamic systems with integrated communication delays in the networked circumstance.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-22

This paper considers the classical semiparametric partially linear model with exact inputs and interval-valued fuzzy outputs. For this purpose, the most commonly used classical two-phase procedure is extended to estimate an interval-valued fuzzy smooth function using nonparametric kernel methods at phase 1 and a least absolute deviation method at phase 2 to estimate the interval-valued fuzzy coefficients. A potential application of the proposed method is presented by a simulated data in hydrology study and an applied example. The proposed interval-valued semiparametric partially linear model is also examined to compare with the interval-valued fuzzy linear regression model via some extended goodness-of-fit criteria into the space of interval-valued fuzzy numbers.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-22
Hongyi Li; Jiahui Wang; Haiping Du; Hamid Reza Karimi

This paper investigates the problem of adaptive integral sliding mode control for general Takagi–Sugeno fuzzy systems with matched uncertainties and its applications. Different control input matrices are allowed in fuzzy systems. The matched uncertainty is modeled in a unified form, which can be handled by the adaptive methodology. A fuzzy integral-type sliding surface is utilized and the parameter matrices can be determined according to user's requirement. Based on the designed sliding surface, a new sliding mode controller is proposed, and the structure of the controller depends on the difference between the disturbance input matrices and the control input matrices. It is shown that under the proposed sliding mode controller, the resulting closed-loop system can achieve the uniformly ultimate boundedness. Furthermore, simulation examples are presented to show the merit and applicability of the proposed fuzzy sliding mode control method.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-22
Pawel Zdanowicz; Dobrila Petrovic

Rule-based fuzzy cognitive maps (RBFCMs) have been developed for modeling nonmonotonic, uncertain, cause-effect systems. However, the standard reasoning and impact accumulation mechanisms developed for RBFCMs assume that the level of variation that a fuzzy set represents is directly linked with the shape of the fuzzy set. It poses a big restriction on how the corresponding fuzzy sets have to be constructed. In this paper, we propose a new reasoning and impact accumulation mechanisms which take into consideration standard semantics of fuzzy sets, where their uncertainty is measured by fuzziness. New type of complex fuzzy relationships and reasoning on them is introduced to model a joint impact of several causal nodes on one effect node. With these new mechanisms, RBFCMs become much more flexible, provide more means to capture complexity of real-world systems, and are less computational demanding than standard mechanisms. The advantages of the new RBFCMs are demonstrated using different examples and compared with standard mechanisms.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-22
Maria J. Asiain; Humberto Bustince; Radko Mesiar; Anna Kolesárová; Zdenko Takáč

Admissible orders have brought the structure of chains in the framework of interval-valued fuzzy sets. However, a deeper study of functions monotone with respect to admissible orders is still missing in the literature. In this work, we consider the construction of negations and strong negations on intervals with respect to admissible orders, in particular, for the Xu and Yager and lexicographical orders, as well as for those based on $K_\alpha$ operators. We introduce and discuss an approach to the construction of strong negations on intervals with respect to $K_{\alpha,\beta }$ orders based on an arbitrary couple of strong negations defined over the standard real interval $[0,1]$ . The introduced strong negations have a deep impact on all fields exploiting fuzzy methods dealing with intervals, allowing to introduce complements, dual aggregations, implications, entropies, etc.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-22
Shaocheng Tong; Kangkang Sun; Shuai Sui

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

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-23
Ding Zhai; Liwei An; Jiuxiang Dong; Qingling Zhang

This paper deals with the problem of adaptive tracking control for a class of switched uncertain nonlinear systems under arbitrary switching. First, combing fuzzy approximation and dynamic surface control (DSC), a switched adaptive state-feedback control scheme is proposed based on directly tuning the estimation of the switching ideal weight vectors in fuzzy logic systems. Switched adaptive laws and switched first-order filters in DSC are designed at each step in the backstepping to reduce the conservativeness caused by adoption of common adaptive laws and filters for each subsystem. By constructing a novel common Lyapunov function, the boundedness of the closed-loop system is ensured, while the tracking error converges to a small neighborhood of the origin. Next, based on the estimation of ideal weight vectors, the proposed adaptive control scheme is extended to the output-feedback case where a switched fuzzy observer is first proposed to estimate the unmeasured states. The main advantage of the developed adaptive control schemes is that the changes of plant can be considered explicitly due to switching, which contributes to less conservativeness of the designed controllers. Finally, two simulation results illustrate the effectiveness of the proposed schemes.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-23
Wenjuan Gong; Fabio Cuzzolin

In example-based human pose estimation, the configuration of an evolving object is sought given visual evidence, having to rely uniquely on a set of sample images. We assume here that, at each time instant of a training session, a number of feature measurements is extracted from the available images, while ground truth is provided in the form of the true object pose. In this scenario, a sensible approach consists in learning maps from features to poses, using the information provided by the training set. In particular, multivalued mappings linking feature values to set of training poses can be constructed. To this purpose we propose a belief modeling regression (BMR) approach in which a probability measure on any individual feature space maps to a convex set of probabilities on the set of training poses, in a form of a belief function. Given a test image, its feature measurements translate into a collection of belief functions on the set of training poses which, when combined, yield there an entire family of probability distributions. From the latter either a single central pose estimate or a set of extremal ones can be computed, together with a measure of how reliable the estimate is. Contrarily to other competing models, in BMR the sparsity of the training samples can be taken into account to model the level of uncertainty associated with these estimates. We illustrate BMR's performance in an application to human pose recovery, showing how it outperforms our implementation of both relevant vector machine and Gaussian process regression. Finally, we discuss motivation and advantages of the proposed approach with respect to its most direct competitors.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-23
Jing Gu; Licheng Jiao; Shuyuan Yang; Fang Liu

This paper introduces the popular sparse representation method into the classical fuzzy c-means clustering algorithm, and presents a novel fuzzy clustering algorithm, called fuzzy double c-means based on sparse self-representation (FDCM_SSR). The major characteristic of FDCM_SSR is that it can simultaneously address two datasets with different dimensions, and has two kinds of corresponding cluster centers. The first one is the basic feature set that represents the basic physical property of each sample itself. The second one is learned from the basic feature set by solving a spare self-representation model, referred to as discriminant feature set, which reflects the global structure of the sample set. The spare self-representation model employs dataset itself as dictionary of sparse representation. It has good category distinguishing ability, noise robustness, and data-adaptiveness, which enhance the clustering and generalization performance of FDCM_SSR. Experiments on different datasets and images show that FDCM_SSR is more competitive than other state-of-the-art fuzzy clustering algorithms.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-23
Antoon Bronselaer; Robin De Mol; Guy De Tré

In this paper, a novel framework for data quality measurement is proposed by adopting a measure-theoretic treatment of the problem. Instead of considering a specific setting in which quality must be assessed, our approach departs more formally from the concept of measurement. The basic assumption of the framework is that the highest possible quality can be described by means of a set of predicates. Quality of data is then measured by evaluating those predicates and by combining their evaluations. This combination is based on a capacity function (i.e., a fuzzy measure) that models for each combination of predicates the capacity with respect to the quality of the data. It is shown that expression of quality on an ordinal scale entails a high degree of interpretation and a compact representation of the measurement function. Within this purely ordinal framework for measurement, it is shown that reasoning about quality beyond the ordinal level naturally originates from the uncertainty about predicate evaluation. It is discussed how the proposed framework is positioned with respect to other approaches with particular attention to aggregation of measurements. The practical usability of the framework is discussed for several well known dimensions of data quality and demonstrated in a use-case study about clinical trials.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-24
Jun Wang; Huan Liu; Xiaohua Qian; Yizhang Jiang; Zhaohong Deng; Shitong Wang

The success of fuzzy clustering heavily relies on the features of the input data. Based on the fact that deep architectures are able to more accurately characterize the data representations in a layer-by-layer manner, this paper proposes a novel feature mapping technique called cascaded hidden-space (CHS) feature mapping and investigates its combination with classical fuzzy c-means (FCM) and fuzzy c-regressions (FCR). Since the parameters between the layers of CHS feature mapping are randomly generated and need not be tuned layer-by-layer, CHS is easily implemented with less training data. By performing classical FCM in CHS, a novel fuzzy clustering framework called CHS-FCM is developed; several of its variants are presented using different dimension-reduction methods in a CHS-FCM clustering framework. The combination of CHS-FCM with nonlinear switch regressions is called CHS-FCR, and it performs FCR in CHS. The proposed CHS-FCR provides better results than FCR for nonlinear process modeling. Both CHS-FCM and CHS-FCR exhibit low memory consumption and require less training data. The experimental results verify the superiority of the proposed methods over classical fuzzy clustering methods.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-24
Wen-Ran Zhang

A cellular transformation of bipolar fuzzy sets to quantum intelligence (QI) machinery is presented based on an axiomatic formulation of equilibrium-based business intelligence (EBBI) and information conservational quantum-fuzzy cryptography (ICQFC). It is proven that any active bipolar cognitive map can be normalized to a bipolar quantum-fuzzy cognitive map—the logical equivalent of an information conservational bipolar quantum-fuzzy logic gate for equilibrium-based quantum cellular rebalancing. Such rebalancing leads to EBBI and ICQFC—an unexpected combination with unexpected synergy. Applicability of one EBBI algorithm and two ICQFC algorithms are illustrated. Information theoretic security and scalability of ICQFC are proved as a computational intelligence testbed for postquantum cryptography. It is argued that, while the illogical aspect of quantum mechanics prevents quantum computing from lending itself as an analytical paradigm, EBBI and ICQFC constitute a cellular transformation of bipolar fuzzy sets to high precision QI machinery—an equilibrium-based analytical paradigm for ubiquitous quantum modeling and quantum-digital compatible computing. A QI architecture is drafted. A QI transfer protocol is illustrated with ICQFC for EBBI. QI is, thus, distinguished by its ubiquitous, analytical, transferable, and quantum-digital compatible properties. It is asserted that QI as the most generic genre of intelligence underpins artificial and biological intelligence with mathematical, philosophical, and scientific distinctions. It is expected that through QI the research field of fuzzy sets and systems is destined to advance to the forefront of modern science including but not limited to brain science and quantum information science.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-27
Zhenghai Ai; Zeshui Xu

Intuitionistic fuzzy set (A-IFS) introduced by Atanassov, a generalized form of fuzzy sets, is a useful tool to deal with vagueness and ambiguity. Each element of an A-IFS is called an intuitionistic fuzzy value, based on which the intuitionistic fuzzy calculus (IFC) has been proposed recently. However, the existing study only discusses the one-variable IFC, in order to enrich the theory of the IFC; in this paper, we put forward the intuitionistic fuzzy multiple definite integrals (IFMDI). We first define some concepts related to the IFMDI, based on which we reveal the relationships between the IFMDI and the intuitionistic fuzzy definite integrals. After that we investigate the basic properties of the IFMDI in detail, and finally, we apply the knowledge of abstract algebra to construct some isomorphic mappings, based on which, we interpret the reason why there are some parallel properties between the additive IFMDI and the multiplicative IFMDI.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-28
Desh Raj; Aditya Gupta; Bhuvnesh Garg; Kenil Tanna; Frank Chung-Hoon Rhee

Due to the numerous applications that utilize different types of fuzzy membership functions (MFs), it may sometimes be difficult to choose an appropriate MF for a particular application. In this paper, we establish preliminary guidelines to direct this selection by proposing a three-stage method. In the “forward” stage, different MFs, such as crisp MFs, type-1 (T1) fuzzy MFs, and type-2 (T2) fuzzy MFs, are generated from multidimensional data sets. Next, in the “reverse” stage, data is generated back from these MFs by considering different bin sizes. In doing so, various data sets may be generated for different applications which require fuzzy data. Finally, for the “similarity analysis” stage, we propose an iterative algorithm that makes use of the results of Wilcoxon signed rank (WSR) and Wilcoxon rank sum (WRS) tests to compare the original data and the generated data. From the results of these tests, recommendations concerning the suitability of MFs for a specific application may be suggested by observing the accuracy of representation and the requirements of the application. With this analysis, the objective is to gain insight on when T2 fuzzy sets may be considered to outperform T1 fuzzy sets, and vice versa. Several examples are provided using synthetic and real data to validate the iterative algorithm for data sets in various dimensions.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-28
Hao Sun; Han Zhao; Kang Huang; Mingming Qiu; Shengchao Zhen; Ye-Hwa Chen

In this paper, we propose a fuzzy approach for optimal robust control design of an automotive electronic throttle (ET) system. Compared with the conventional ET control systems, we establish the fuzzy dynamical model of the ET system with parameter uncertainties, nonlinearities, and external disturbances, which may be nonlinear, (possibly fast) time varying. These uncertainties are assumed to be bounded, and the knowledge of the bound only lies within a prescribed fuzzy set. A robust control that is deterministic and is not the usual if–then rules-based control is presented to guarantee the controlled system to achieve the deterministic performance: uniform boundedness and uniform ultimate boundedness. Furthermore, a fuzzy-based system performance index including average fuzzy system performance and control cost is proposed based on the fuzzy information. The optimal design problem associated with the control can then be solved by minimizing the fuzzy-based performance index. With this optimal robust control, the performance of the fuzzy ET system is both deterministically guaranteed and fuzzily optimized.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-28
Andrea Mesiarová-Zemánková

Uninorms with continuous underlying t-norm and t-conorm are discussed and properties of the set of discontinuity points of such a uninorm are shown. This set is proved to be a subset of the graph of a special symmetric, u-surjective, nonincreasing set-valued function, which gives us a necessary condition for a uninorm to have continuous underlying functions. A sufficient condition for a uninorm to have continuous underlying operations is also given. Several examples are included.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-28
Liviu-Cristian Duţu; Gilles Mauris; Philippe Bolon

The problem of learning fuzzy rule bases is analyzed from the perspective of finding a favorable balance between the accuracy of the system, the speed required to learn the rules, and, finally, the interpretability of the rule bases obtained. Therefore, we introduce a complete design procedure to learn and then optimize the system rule base, called the precise and fast fuzzy modeling approach. Under this paradigm, fuzzy rules are generated from numerical data using a parameterizable greedy-based learning method called selection-reduction , whose accuracy–speed efficiency is confirmed through empirical results and comparisons with reference methods. Qualitative justification for this method is provided based on the coaction between fuzzy logic and the intrinsic properties of greedy algorithms. To complete the precise and fast fuzzy modeling strategy, we finally present a rule-base optimization technique driven by a novel rule redundancy index, which takes into account the concepts of the distance between rules and the influence of a rule over the dataset. Experimental results show that the proposed index can be used to obtain compact rule bases, which remain very accurate, thus increasing system interpretability.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-28
I-Fang Chung; Yi-Cheng Chen; Nikhil R. Pal

Features that have good predictive power for classes or output variables are useful features and hence most feature selection methods try to find them. However, since there may be high correlation or nonlinear dependence between such good features, we may obtain a comparable performance even when we use only a few of those good features. Thus, a feature selection method should select useful features with controlled redundancy. In this paper, we propose a novel learning method that imposes a penalty on the use of dependent/correlated features during system identification along with feature selection. This feature selection scheme can choose good features, discard indifferent, and derogatory features, and can control the level of redundancy in the set of selected features. This is probably the first attempt to feature selection with redundancy control using a fuzzy rule based framework. We have demonstrated the effectiveness of this method by utilizing a tenfold cross-validation setup on a synthetic dataset as well as on several commonly used datasets for classification problems. We have also compared our results with some state-of-the-art methods.

更新日期：2018-03-30
• IEEE Trans. Fuzzy Syst. (IF 7.671) Pub Date : 2017-03-28