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Fuzzy Systems, IEEE Transactions on

Issue 2 • Date April 2006

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  • Table of contents

    Page(s): c1
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  • IEEE Transactions on Fuzzy Systems publication information

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  • Some properties of fuzzy random renewal processes

    Page(s): 173 - 179
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (271 KB) |  | HTML iconHTML  

    Fuzzy random variable is a measure function from a probability space to a collection of fuzzy variables. Based on the fuzzy random theory, this paper addresses some properties of fuzzy random renewal processes generated by a sequence of independent and identically distributed (iid) fuzzy random interarrival times. The relationship between the expected value of the fuzzy random renewal variable and the distribution functions of the alpha-pessimistic values and alpha-optimistic values of the interarrival times is discussed. Furthermore, the fuzzy random style of renewal equation is provided. Finally, fuzzy random Blackwell's renewal theorem and Smith's key renewal theorem are also given View full abstract»

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  • Distributivity and conditional distributivity of a uninorm and a continuous t-conorm

    Page(s): 180 - 190
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (387 KB) |  | HTML iconHTML  

    The open problem recalled by Klement in the Linz2000 closing session, related to distributivity and conditional distributivity of a uninorm and a continuous t-conorm, is solved for the most usual known classes of uninorms. From the obtained results, it is deduced that distributivity and conditional distributivity are equivalent for these cases. It is remarkable that solutions appear involving not only strict t-conorms but also ordinal sums of the maximum with a strict t-conorm. Conversely, the distributivity of a t-conorm over a uninorm is also studied leading only to already known solutions. Moreover, the dual case of distributivity and conditional distributivity involving uninorms and continuous t-norms is also solved, proving again the equivalence of both kinds of distributivities View full abstract»

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  • Fuzzy probabilistic approximation spaces and their information measures

    Page(s): 191 - 201
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (375 KB) |  | HTML iconHTML  

    Rough set theory has proven to be an efficient tool for modeling and reasoning with uncertainty information. By introducing probability into fuzzy approximation space, a theory about fuzzy probabilistic approximation spaces is proposed in this paper, which combines three types of uncertainty: probability, fuzziness, and roughness into a rough set model. We introduce Shannon's entropy to measure information quantity implied in a Pawlak's approximation space, and then present a novel representation of Shannon's entropy with a relation matrix. Based on the modified formulas, some generalizations of the entropy are proposed to calculate the information in a fuzzy approximation space and a fuzzy probabilistic approximation space, respectively. As a result, uniform representations of approximation spaces and their information measures are formed with this work View full abstract»

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  • Observability and decentralized control of fuzzy discrete-event systems

    Page(s): 202 - 216
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (468 KB) |  | HTML iconHTML  

    Fuzzy discrete-event systems as a generalization of (crisp) discrete-event systems have been introduced in order that it is possible to effectively represent uncertainty, imprecision, and vagueness arising from the dynamic of systems. A fuzzy discrete-event system has been modeled by a fuzzy automaton; its behavior is described in terms of the fuzzy language generated by the automaton. In this paper, we are concerned with the supervisory control problem for fuzzy discrete-event systems with partial observation. Observability, normality, and co-observability of crisp languages are extended to fuzzy languages. It is shown that the observability, together with controllability, of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor. When a decentralized solution is desired, it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co-observable. Moreover, the infimal controllable and observable fuzzy superlanguage, and the supremal controllable and normal fuzzy sublanguage are also discussed. Simple examples are provided to illustrate the theoretical development View full abstract»

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  • An educational tool for fuzzy control

    Page(s): 217 - 221
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (432 KB) |  | HTML iconHTML  

    This paper presents an educational library to be used with the MATLAB/Simulink package from the Mathworks company for the design of fuzzy controllers. This free library, named FlouLib, has its foundations in a clear representation of the fuzzy interfaces (fuzzification, inference, defuzzification). First, Mamdani-type conventional fuzzy logic controllers are presented, including when rulebases are chained. Then, from the modal equivalence principle, advanced Takagi-Sugeno fuzzy controllers are introduced especially those relying on input-output linearization techniques. Examples, all available in FlouLib demos, are used to show the potentialities of FlouLib for control engineering curricula. View full abstract»

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  • A new approach to fuzzy modeling of nonlinear dynamic systems with noise: relevance vector learning mechanism

    Page(s): 222 - 231
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (861 KB) |  | HTML iconHTML  

    This paper presents a new fuzzy inference system for modeling of nonlinear dynamic systems based on input and output data with measurement noise. The proposed fuzzy system has a number of fuzzy rules and parameter values of membership functions which are automatically generated using the extended relevance vector machine (RVM). The RVM has a probabilistic Bayesian learning framework and has good generalization capability. The RVM consists of the sum of product of weight and kernel function which projects input space into high dimensional feature space. The structure of proposed fuzzy system is same as that of the Takagi-Sugeno fuzzy model. However, in the proposed method, the number of fuzzy rules can be reduced under the process of optimizing a marginal likelihood by adjusting parameter values of kernel functions using the gradient ascent method. After a fuzzy system is determined, coefficients in consequent part are found by the least square method. Examples illustrate effectiveness of the proposed new fuzzy inference system View full abstract»

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  • Robust tracking control of an electrically driven robot: adaptive fuzzy logic approach

    Page(s): 232 - 247
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (599 KB) |  | HTML iconHTML  

    This paper is concerned with the robust tracking control of an electrically driven robot with the model uncertainties in the robot dynamics and the motor dynamics. The motors driving the joints of the robot are assumed to be equipped with only the joint position and the current measurement devices. Adaptive fuzzy logic and adaptive backstepping method are employed to provide the solution to the control problem. The suggested method does not require the measurement of the velocity nor the acceleration. Simulation results from a two-link electrically driven robot show the satisfactory performance of the proposed control scheme even in the presence of internal model uncertainties in both the robot and motor dynamics and external disturbances View full abstract»

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  • A min-max approach to fuzzy clustering, estimation, and identification

    Page(s): 248 - 262
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1698 KB) |  | HTML iconHTML  

    This study, for any unknown physical process y=f(x1,...,xn), is concerned with the: 1) fuzzy partition of n-dimensional input space X=X1timesmiddotmiddotmiddottimesXn into K different clusters, 2) estimating the process behavior ycirc=f(xcirc) for a given input xcirc=(xcirc1,middotmiddotmiddot,xcircn )isinX, and 3) fuzzy approximation of the process, with uncertain input-output identification data {(x(k)plusmndeltaxk ),(y(k)plusmnvk)}k=1,..., using a Sugeno type fuzzy inference system. A unified min-max approach (that attempts to minimize the worst-case effect of data uncertainties and modeling errors on estimation performance), is suggested to provide robustness against data uncertainties and modeling errors. The proposed method of min-max fuzzy parameters estimation does not make any assumption and does not require a priori knowledge of upper bounds, statistics, and distribution of data uncertainties and modeling errors. To show the feasibility of the approach, simulation studies and a real-world application of physical fitness classification based on the fuzzy interpretation of physiological parameters, have been provided View full abstract»

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  • An adaptive control for video transmission over bluetooth

    Page(s): 263 - 274
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    This paper is concerned with transmission of a moving picture expert group (MPEG) video stream over a Bluetooth channel, using an adaptive neuro-fuzzy technique. MPEG variable bit rate (VBR) video sources over a network generally experience long delay and unacceptable data loss, due to high variations in bit rate. Furthermore, transmission rate could be unpredictable in a Bluetooth network due to interferences by other wireless devices or general Bluetooth channel noises. Subsequently, it is almost impossible to transmit VBR data sources over Bluetooth without excessive delay or data loss. In this work, an adaptive scheme is introduced so that the controller may adjust itself to the current state of the system under control. This paper utilizes a traffic-shaping buffer to prevent excessive back-to-back transmissions of MPEG VBR data sources. A novel adaptive neuro-fuzzy scheme regulates the output rate of the buffer to ensure that the video stream from the host conforms to the traffic conditions of the Bluetooth channel during the transmission period. The computer simulation results show that the use of the neuro-fuzzy controller reduces excessive delay and data loss at the host-controller-interface, as compared with a conventional VBR video transmission and a rule-based fuzzy controller (RBF1) in Bluetooth View full abstract»

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  • Experimental studies in nonlinear discrete-time adaptive prediction and control

    Page(s): 275 - 286
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    This paper presents implementation results using recently introduced discrete-time adaptive prediction and control techniques using online function approximators. We consider a process control experiment as our test bed, and develop a discrete-time adaptive predictor for liquid volume and a discrete-time adaptive controller for reference volume tracking. We use Takagi-Sugeno (TS) fuzzy systems as our function approximators, and for both prediction and control we investigate the use of a least-squares update of the fuzzy system's parameters View full abstract»

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  • Ranking type-2 fuzzy numbers

    Page(s): 287 - 294
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (335 KB) |  | HTML iconHTML  

    Type-2 fuzzy sets are a generalization of the ordinary fuzzy sets in which each type-2 fuzzy set is characterized by a fuzzy membership function. In this paper, we consider the problem of ranking a set of type-2 fuzzy numbers. We adopt a statistical viewpoint and interpret each type-2 fuzzy number as an ensemble of ordinary fuzzy numbers. This enables us to define a type-2 fuzzy rank and a type-2 rank uncertainty for each intuitionistic fuzzy number. We show the reasonableness of the results obtained by examining several test cases View full abstract»

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  • Convergent results about the use of fuzzy simulation in fuzzy optimization problems

    Page(s): 295 - 304
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    We discuss the convergence of fuzzy simulation as it is employed in fuzzy optimization problems. Several convergence concepts for sequences of fuzzy variables are defined such as convergence in optimistic value. A new approach to approximating essentially bounded fuzzy variables with continuous possibility distributions is introduced. Applying the proposed approximation method to our previous work, we prove three convergence theorems about the use of fuzzy simulation in computing the credibility of a fuzzy event, finding the optimistic value of a return function, and calculating the expected value of a fuzzy variable View full abstract»

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  • Recursive pointwise design for nonlinear systems

    Page(s): 305 - 313
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (690 KB) |  | HTML iconHTML  

    This paper presents a recursive pointwise design (RPD) method for a class of nonlinear systems represented by x(t)=f(x(t))+g(x(t))u(t). A main feature of the RPD method is to recursively design a stable controller by using pointwise information of a system. The design philosophy is that f(x(t)) and g(x(t)) can be approximated as constant vectors in very small local state spaces. Based on the design philosophy, we numerically determine constant control inputs in very small local state spaces by solving linear matrix inequalities (LMIs) derived in this paper. The designed controller switches to another constant control input when the states move to another local state space. Although the design philosophy is simple and natural, the controller does not always guarantee the stability of the original nonlinear system x(t)=f(x(t))+g(x(t))u(t). Therefore, this paper gives ideas of compensating the approximation caused by the design philosophy. After addressing outline of the pointwise design, we provide design conditions that exactly guarantee the stability of the original system. The controller design conditions require to give the maximum and minimum values of elements in the functions f(x(t)) and g(x(t)) in each local state - space. Therefore, we also present design conditions for unknown cases of the maximum and minimum values. Furthermore, we construct an effective design procedure using the pointwise design. A feature of the design procedure is to subdivide only infeasible regions and to solve LMIs again only for the subdivided infeasible regions. The recursive procedure saves effort to design a controller. A design example demonstrates the utility of the RPD method View full abstract»

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  • A robust design criterion for interpretable fuzzy models with uncertain data

    Page(s): 314 - 328
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    We believe that nonlinear fuzzy filtering techniques may be turned out to give better robustness performance than the existing linear methods of estimation (H2 and H filtering techniques), because of the fact that not only linear parameters (consequents), but also the nonlinear parameters (membership functions) attempt to identify the uncertain behavior of the unknown system. However, the fuzzy identification methods must be robust to data uncertainties and modeling errors to ensure that the fuzzy approximation of unknown system's behavior is optimal in some sense. This study presents a deterministic approach to the robust design of fuzzy models in the presence of unknown but finite uncertainties in the identification data. We consider online identification of an interpretable fuzzy model, based on the robust solution of a regularized least-squares fuzzy parameters estimation problem. The aim is to resolve the difficulties associated with the robust fuzzy identification method due to lack of a priori knowledge about upper bounds on the data uncertainties. The study derives an optimal level of regularization that should be provided to ensure the robustness of fuzzy identification strategy by achieving an upper bound on the value of energy gain from data uncertainties and modeling errors to the estimation errors. A time-domain feedback analysis of the proposed identification approach is carried out with emphasis on stability, robustness, and steady-state issues. The simulation studies are provided to show the superiority of the proposed fuzzy estimation over the classical estimation methods. View full abstract»

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  • Perception-based granular probabilities in risk modeling and decision making

    Page(s): 329 - 339
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    Our focus is on the issue of decision making in risky situations. We discuss the need for using decision functions to aid in capturing the decision maker's preference among these types of uncertain alternatives. The use of fuzzy rule based formulations to model these functions is investigated. We discuss the role of perception based granular probability distributions as a means of modeling the uncertainty profiles of the alternatives. Various properties of this method of describing uncertainty are provided. Tools for evaluating rule based decision functions in the face of perception based uncertainty profiles are presented. Consideration is given to the situation in which our uncertainty profiles are expressed in terms of a cumulative distribution function. We introduce the idea of a perception based granular cumulative distribution and describe its representation in terms of a fuzzy rule-based model View full abstract»

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  • Fuzzy interpolative reasoning via scale and move transformations

    Page(s): 340 - 359
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    Interpolative reasoning does not only help reduce the complexity of fuzzy models but also makes inference in sparse rule-based systems possible. This paper presents an interpolative reasoning method by means of scale and move transformations. It can be used to interpolate fuzzy rules involving complex polygon, Gaussian or other bell-shaped fuzzy membership functions. The method works by first constructing a new inference rule via manipulating two given adjacent rules, and then by using scale and move transformations to convert the intermediate inference results into the final derived conclusions. This method has three advantages thanks to the proposed transformations: 1) it can handle interpolation of multiple antecedent variables with simple computation; 2) it guarantees the uniqueness as well as normality and convexity of the resulting interpolated fuzzy sets; and 3) it suggests a variety of definitions for representative values, providing a degree of freedom to meet different requirements. Comparative experimental studies are provided to demonstrate the potential of this method View full abstract»

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  • Special issue on granular computing

    Page(s): 360
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  • IEEE Computational Intelligence Society Information

    Page(s): c3
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  • IEEE Transactions on Fuzzy Systems Information for authors

    Page(s): c4
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Aims & Scope

The IEEE Transactions on Fuzzy Systems (TFS) is published quarterly. TFS will consider papers that deal with the theory, design or an application of fuzzy systems ranging from hardware to software.

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Meet Our Editors

Editor-in-Chief
Chin-Teng Lin
National Chiao-Tung University