This paper proposes a new concept of thick gradual sets (TGSs), which is based on the notions of thick sets (TSs) and gradual sets (GSs). A TS is an uncertain set, which is represented by a pair of crisp sets (CSs). These CSs represent the upper and lower bounds of the TS. Therefore, a TS can be considered as an interval of CSs. A GS is a CS, which is parameterized by a degree of pertinence and aims to increase the specificity of CSs. Furthermore, a TGS is an interval of GSs, i.e., a pair of lower and upper GSs. In situations when the constraint of monotonicity (consistency) is guaranteed, a GS becomes a type-1 fuzzy set (T1FS) and a TGS can be regarded as a thick fuzzy set (TFS). Moreover, a TFS, which is composed of lower and upper T1FS bounds, can be interpreted as a type-2 fuzzy set (T2FS). According to the TGS representation, this new approach offers an original concept for interpreting, manipulating, and computing some uncertain quantities that cannot be represented by GSs, T1FSs, and/or T2FSs. The potential applications of the TGS concept has been validated using application examples in the frameworks of solving fuzzy systems of equations and uncertain fuzzy regression and through a real-world application where the trajectory of an underwater robot is uncertain and cannot be precisely known because of disturbances induced by the environment. The proposed approach makes it possible to compute the uncertain zone explored by the underwater robot.

This paper presents a new and a more general formulation of the min and max operations for gradual intervals, initially proposed 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.

Recently, gradual numbers have been introduced as a means of extending standard interval computation methods to fuzzy and gradual intervals. However, it is well known that the practical use of standard interval arithmetic operators, just like their fuzzy extension, gives results that are more imprecise than necessary and, in some cases, even counterintuitive. In this paper, we combine the concepts of gradual numbers and Kaucher arithmetic on extended intervals to define extended gradual interval arithmetic, where subtraction and division operators are, respectively, the inverse operators of the addition and the multiplication. They are applied to the inversion of a linear regressive model and to a control problem that is based on the inversion of a linear model.

This paper aims at expressing MIN and MAX operations when triangular fuzzy intervals are taken as inputs, that is when Zadeh's extension principle is considered. First presented approach consists in representing fuzzy intervals by means of their profiles. In this context, a computation algorithm can be easily derived for implementing the MIN and MAX operations. Another methodology based on interval relations is then proposed for determining a general analytical expression of the MIN and MAX operations. The potential use of these expressions in the framework of uncertain aggregation operators is illustrated with the two-additive Choquet integral.

This paper aims at designing and analyzing an inverse controller for stable inversible (minimum phase) fuzzy interval linear and/or multilinear systems. The controller is designed from the fuzzy interval ranges of the system parameters using an /spl alpha/-cut methodology. Indeed, for a given /spl alpha/-cut of the fuzzy system parameters representing an uncertainty level, the control objective can be viewed as maintaining the system output within a tolerance envelope, around the exact trajectory, specified by the degree of preference /spl alpha/ on the fuzzy trajectory. The stability is ensured in the way that the controller restricts the system output divergence within the tolerance envelope. The validity of the proposed method is illustrated by simulation examples.

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.

This part aims at designing a fuzzy inverse controller for fuzzy linear interval systems. The controller is designed from the fuzzy interval ranges of the system parameters. Indeed, for a given degree of confidence on the fuzzy system parameters, the control objective can be viewed as maintaining the system output within a tolerance envelope, around the exact trajectory, specified by a degree of preference on the fuzzy trajectory. The validity of the proposed method is illustrated by simulation examples.

This two part paper proposes a methodology of designing and analyzing an inverse controller for stable fuzzy interval linear systems according to fuzzy interval arithmetic. The first part aims at revisiting the solving of first order fuzzy linear equations. The general solution is expressed in a compact form which is directly used for deriving the condition of the solution existence. The suggested method is inspired from the a-cut principle where the fuzzy interval arithmetic is defined in terms of well-established interval arithmetic operations on closed intervals of real numbers. The so-built solution is useful for the inverse controller synthesis dealt with in part II of this paper. The validity of the proposed method is illustrated by a simulation example.

The aim of this paper is to examine the feedback linearization technique for unknown non affine-in-control systems. As the nonlinear plant is assumed to be unknown, an adaptive Takagi-Sugeno fuzzy system is used to represent it. Based on the error between the nonlinear plant and the adapted fuzzy model, the parameters of the latter are updated according to Lyapunov synthesis. Then, at each sampling time, the linearizing controller is obtained by inversion of the fuzzy model. The closed-loop control structure stability is guaranteed using Lyapunov analysis. An illustrative simulation example is given to demonstrate the feasibility of the proposed method.

This paper investigates the possible applications of dynamical fuzzy systems to control nonlinear plants with asymptotically stable zero dynamics using a fuzzy nonlinear internal model control strategy. The developed strategy consists in including a dynamical Takagi-Sugeno fuzzy model of the plant within the control structure. In this way, the controller design simply results in a fuzzy model inversion. In this framework, the originality of the presented work lies in the use of a dynamical fuzzy model and its inversion. In order to be able to implement the control structure, two crucial points have to be addressed in the considered fuzzy context, on the one hand the model representation and identification, on the other, the model inversion. As the fuzzy system can be viewed as a collection of elementary subsystems, its inversion is approached here in a local way, i.e., on the elementary subsystems capable to provide an inverse solution. In this case, the inversion of the global fuzzy system is thus tackled by inversion of some of its components. By doing so, exact inversion is obtained and offset-free performances are ensured. In order to guarantee a desired regulation behavior and robustness of stability of the control system, the fuzzy controller is connected in series with a robustness filter. The potential of the proposed method is demonstrated with simulation examples.

This paper is concerned with the use of fuzzy inputs in fuzzy logic controllers. A precise representation of fuzzy logic controllers by means of mappings is used to introduce different ways for dealing with fuzzy inputs. Two types of fuzzy inputs are presented and their potential use in fuzzy control is discussed. The proposed concepts are applied to control a first order process with a PI controller. This simple process is chosen to clearly illustrate the behavior of the closed-loop system using fuzzy inputs for fuzzy reference and fuzzy measurement. Finally, a nonlinear process is used to illustrate the effects of fuzzy inputs on a more complex system. Although it is sometimes speculated that fuzzy inputs may improve the behavior of fuzzy controllers, experiments developed in this paper show this point is not straightforward and that the relevance of fuzzy inputs should be questioned in closed-loop fuzzy control.

Examines the control problem of discrete-time feedback linearizable nonlinear systems for which there are no available analytic models. Based on the ability of fuzzy systems to approximate any nonlinear mapping, the unknown nonlinear system is represented by a Takagi-Sugeno fuzzy model which is identified using input-output data. Then, a fuzzy feedback linearizing controller, based on fuzzy model inversion, is used to linearize the system. The key concept is the combination of this fuzzy feedback linearizing controller with a simple linear controller resulting in a robust feedback control structure. The equivalence between the feedback linearization technique and the internal model control methodology is then established. Finally, simulation results are given to demonstrate the feasibility of the proposed method.

This paper presents an automatic output generation based on XML description of intelligent instruments. This description uses the service based approach called INOMs. The XML representation of intelligent instruments enables three different outputs: user information output in HTML format, supervisor information output, and source code output for a selected field bus network target. The intelligent instrument model is briefly described and the area of interest consists in the automatic code generation. A basic example is presented in order to illustrate the different steps and to show the simplicity of the operational implementation.

This paper presents a modeling of intelligent sensors based on a representation of the sensor by services it uses or it proposes, and by its user operating modes (USOMs). This modeling is used for the definition of the reactive layer of distributed agent based intelligent sensors. Our area of interest is the agent-level layer in which the concept of IIC (intelligent instrument cluster) is defined. An application that uses fuzzy-based intelligent sensors is presented in order to illustrate the concepts.

The concept of industrial performance has been a major issue for manufacturing companies for a long time. In the last few years, the important changes of the industrial context have led to new performance expression requirements. After having overviewed the chronological evolution of performance expression, current developments are stated and new directions are discussed, especially the temporal dynamics of performance.

Deals with H/sub /spl infin// control for discrete-time nonlinear systems using an input-output linearization concept. Based on the ability of fuzzy systems to approximate any nonlinear mapping, the unknown nonlinear system is represented by a Takagi-Sugeno fuzzy model. The control problem is then tackled using a feedback linearization of the fuzzy nonlinear system. However, this feedback linearization can not guarantee robustness in the presence of uncertainties and disturbances. In order to solve this problem, an additive H/sub /spl infin// control component is added to the linearizing controller to attenuate uncertainty and disturbance influence on the control performances. In the paper, the H/sub /spl infin// control component is designed in terms of a modified Riccati inequality. Finally, an illustrative example is included to demonstrate the feasibility of the proposed method.

Performance indicators are introduced in manufacturing companies in order to improve the reactivity of production activity control by providing performance evaluations reflecting the analysis of the state of processes with regard to pre-set objectives. After having recalled the formal model of performance indicators, the focus is on the semantics of the performance evaluation, which is an important point in order to take control decisions. This semantics depends in fact on the mathematical comparison operators (between the state of the process and the assigned objective) used to evaluate the performance. In this view, possibility and necessity measures are studied. They are also used to define the uncertainty of the performance evaluation.

The problem of learning control is addressed for a class of nonlinear systems for which there is no available analytic model. Based on the ability of fuzzy systems to approximate any nonlinear function, a global architecture is proposed where the unknown input-output linearizing controller is replaced by a fuzzy system whose rule conclusions are learned on line. A direct learning algorithm is implemented in which the parameter evolution is guided simultaneously by the tracking error and a prediction error of the fuzzy system output. During the learning phase, additive components, such as bounding control and sliding mode control are introduced to guarantee system's stability and parameter convergence. Stability of the closed loop system is proved according to Lyapunov theory. Simulation results for the inverted pendulum are included to demonstrate the method applicability.

A reconstruction methodology is proposed for dealing with size reduction in fuzzy rulebases. Elimination of redundant fuzzy rules is always at the root of size reduction. As a matter of fact, it is thus important to be aware of the different kinds of redundancy that may appear in fuzzy rulebases. Two types of redundancy are distinguished, i.e. interpolation redundancy and overlap redundancy. On the contrary to usual methods that are only able to deal with overlap redundancy, the presented method is efficient for both redundancy types. Furthermore, the proposed reconstruction principle induces the obtention of readable linguistic rules. The method performance is illustrated by means of two examples.

This paper presents the concept of fuzzy component networks. First, we introduce fuzzy components such as fuzzy sensors, fuzzy actuators, and fuzzy inference components. Then, we describe the implementation of such components into a generic component, called a fuzzy cell. Depending on its configuration, a fuzzy cell is able to perform the functions of one or several fuzzy components. Each fuzzy cell is implemented by means of the Intel 80C196 microcontroller and is connected to a field bus. Fuzzy cells are characterized by their ability to handle and exchange fuzzy symbolic information. Their configuration is performed via the field bus using the language prototype of integrated language for symbolic sensors and actuators (PLICAS) that was specially designed for this purpose. A PLICAS compiler is integrated inside each cell, thus conferring interoperability properties to the cell. Two applications are presented: 1) a fuzzy controller whose fuzzification, inference, end defuzzification interfaces are distributed into three fuzzy cells connected by the fieldbus; and 2) the fusion of information provided by two ultrasonic fuzzy sensors for the detection of obstacles.

It has been proved that fuzzy controllers are capable of approximating any real continuous control function on a compact set to arbitrary accuracy. In particular, any given linear control can be achieved with a fuzzy controller for a given accuracy. The aim of this paper is to show how to automatically build this fuzzy controller. The proposed design methodology is detailed for the synthesis of a Sugeno or Mamdani type fuzzy controller precisely equivalent to a given PI controller. The main idea is to equate the output of the fuzzy controller with the output of the PI controller at some particular input values, called modal values. The rule base and the distribution of the membership functions can thus be deduced. The analytic expression of the output of the generated fuzzy controller is then established. For Sugeno-type fuzzy controllers, precise equivalence is directly obtained. For Mamdani-type fuzzy controllers, the defuzzification strategy and the inference operators have to be correctly chosen to provide linear interpolation between modal values. The usual inference operators satisfying the linearity requirement when using the center of gravity defuzzification method are proposed.>

This paper introduces sensors employing a fuzzy numeric to symbolic interface. The fundamental design considerations for this kind of fuzzy symbolic sensor, or fuzzy sensor, are formally presented. Then, the use of these components for fuzzy control is discussed and illustrated.

This paper deals with the conception of a rule based experimental system for the robotization of metal cutting using a 5 kW CO2continuous laser. The image of the melted metal pulsed out of the kerf during the cut has been processed on the fly by a special purpose vision system in order to estimate the cut quality. The reasons for the design of a rule based decision system are analysed. Then, the methods used for the construction of the rules and the global architecture of the system are presented. Finally, an example of the system at work, representing its on the fly behaviour, will be provided.

Least square error methods are employed to improve the precision of a robot world coordinate system model. A solution which reduces the large scale errors of the robot is presented. This method is then applied to the task of vision directed workpiece reorientation.