fuzzy systems with overlapping gaussian concepts approximation properties in sobolev norms in this paper the approximating capabilities of fuzzy systems with overlapping gaussian concepts are considered the target function is assumed to be sampled either on a regular gird or according to a uniform probability density by exploiting a connection with radial basis functions approximators a new method for the computation of the system coefficients is provided showing that it guarantees uniform approximation of the derivatives of the target function

approximation theorem of the fuzzy transform in fuzzy reasoning and its application to the scheduling problem in this paper the theoretical foundation of fuzzy reasoning is analyzed and the idea that the fuzzy transform given in the fuzzy reasoning method should be continuous with respect to a certain fuzzy distance is proposed also the fuzzy transforms given in the two fuzzy reasoning methods the mamdani method and the iii method are proved to be continuous based on the continuity of the fuzzy transform the approximation theorem of the continuous fuzzy number transform is proven then on the basis of the approximation theorem a simple fuzzy number transform is constructed in order to implement the fuzzy reasoning based on multiple rules at last the fuzzy reasoning based on multiple rules implemented by a simple fuzzy number transform is applied to machine scheduling problems and numerical computational results of different scale scheduling problems with the objective of minimizing the total number of tardy jobs show that it is more effective than usual heuristics based on rules and in the computational time it has the obvious advantage over the reasoning by fuzzy rules directly

approximation accuracy analysis of fuzzy systems as function approximators this paper establishes the approximation error bounds for various classes of fuzzy systems i e fuzzy systems generated by different inferential and defuzzification methods based on these bounds the approximation accuracy of various classes of fuzzy systems is analyzed and compared it is seen that the class of fuzzy systems generated by the product inference and the center average defuzzifier has better approximation accuracy and properties than the class of fuzzy systems generated by the min inference and the center average defuzzifier and the class of fuzzy systems defuzzified by the mom defuzzifier in addition it is proved that fuzzy systems can represent any linear and multilinear function and explicit expressions of fuzzy systems generated by the mom defuzzified method are given

expert fuzzy controller abstract we describe a fuzzy controller based on our general purpose fuzzy expert system shell flops we take a decision theoretic view in designing an optimal fuzzy controller the variables in the decision problem are 1 the defuzzification rules 2 the fuzzification rules and 3 the fuzzy control rules the objective function is composed of fuzzy goals specified for each system output we differentiate between decision making under certainty risk or uncertainty depending whether or not random elements are present in the system an example is presented illustrating varying the defuzzification rules to improve system performance

fuzzy control of unknown multiple input multiple output plants abstract a self learning fuzzy logic system is given for control of unknown multiple input multiple output mimo plants some nomenclature and several data types are introduced to develop a general formulation for controller activity a random optimization algorithm is given to train the controller a plant model is not required for training instead training is guided by observations of plant responses to inputs

adaptive fuzzy logic control of feedback linearizable discrete time dynamical systems under persistence of excitation the objective of this paper is to achieve tracking control of a class of unknown feedback linearizable nonlinear dynamical systems using a discrete time fuzzy logic controller flc discrete time flc design is significant because almost all flcs are implemented on digital computers a repeatable design algorithm and a stability proof for an adaptive fuzzy logic controller is presented that uses basis functions based on the fuzzy system unlike most standard adaptive control approaches which generate basis vectors by computing a regression matrix a new approach to adapt the fuzzy system parameters is attempted with mild assumptions on the class of discrete time nonlinear systems using this adaptive fuzzy logic controller the uniform ultimate boundedness of the closed loop signals is shown under a persistency of excitation pe condition new passivity properties of fuzzy logic systems are described the result is a model free universal fuzzy controller that works for any system in the given class of systems

sugeno type controllers are universal controllers abstract we show that given any continuous real valued function on a compact set there is a sugeno type controller that will approximate this function to any degree of accuracy an application of this result to fuzzy control is presented which shows that this type of sugeno controller is a universal controller

universal fuzzy controllers based on generalized t s fuzzy models this paper investigates the universal fuzzy control problem based on generalized t s fuzzy models the universal approximation capability of the generalized t s fuzzy models is shown and an approach to robust controller design for general nonlinear systems based on this kind of generalized t s fuzzy models is developed the results of universal fuzzy controllers for two classes of nonlinear systems are then given and constructive procedures to obtain the universal fuzzy controllers are also provided an example is finally presented to show the effectiveness of our approach

autostructuration of fuzzy systems by rules sensitivity analysis abstract we present a destructive pruning method aiming at gradually finding the appropriate number of rules in the case of fuzzy models a particular attention has been paid to takagi sugeno fuzzy systems ts for the problem of functions approximation the proposed system can be seen as a generalization of the conventional ts system and allows to evaluate the importance of one particular rule in the inference process the advantage of our approach has been put in light on two well known benchmarks related to the field of chaotic time series forecasting we also study and compare possible local and global learning strategies for these systems in terms of readability and performance

interactions of hermitian and non hermitian hamiltonians the coupling of non hermitian symmetric hamiltonians to standard hermitian hamiltonians each of which individually has a real energy spectrum is explored by means of a number of soluble models it is found that in all cases the energy remains real for small values of the coupling constant but becomes complex if the coupling becomes stronger than some critical value for a quadratic non hermitian symmetric hamiltonian coupled to an arbitrary real hermitian symmetric hamiltonian the reality of the ground state energy for small enough coupling constant is established up to second order in perturbation theory

universal fuzzy controllers for a class of nonlinear systems in this paper we address the issues of universal fuzzy controllers we first present a universal function approximation theorem based on a fuzzy dynamic model then we show the results of universal fuzzy controllers for a large class of nonlinear systems

universal fuzzy controllers a collection b of fuzzy controllers is a universal fuzzy controller if and only if given any controllable process p it can also be controlled by some fuzzy controller in b this paper identifies a new type of universal fuzzy controller

theory of the fuzzy controller abstract we first introduce notation in an attempt to standardize the description of a basic fuzzy controller if r 1 r 2 r n are the real number inputs to the fuzzy controller and is its defuzzified output then f r 1 r n for some function f by the theory of the fuzzy controller we mean in this paper the study of the structure of f for elementary fuzzy controllers using this standardized notation we first survey the known results on the theory of the fuzzy controller and then discuss important future research topics in this area

universal approximation by hierarchical fuzzy systems abstract a serious problem limiting the applicability of standard fuzzy controllers is the rule explosion problem that is the number of rules increases exponentially with the number of input variables to the fuzzy controller a way to deal with this curse of dimensionality is to use the hierarchical fuzzy systems a hierarchical fuzzy system consists of a number of hierarchically connected low dimensional fuzzy systems it can be shown that the number of rules in the hierarchical fuzzy system increases linearly with the number of input variables in this paper we prove that the hierarchical fuzzy systems are universal approximators that is they can approximate any nonlinear function on a compact set to arbitrary accuracy our proof is constructive that is we first construct a hierarchical fuzzy system in a step by step manner then prove that the constructed fuzzy system satisfies an error bound and finally show that the error bound can be made arbitrarily small

controllable processes and the fuzzy controller abstract we show that any controllable process can be controlled by the scaled and averaged output of multiple elementary fuzzy controllers operating simultaneously

necessary conditions for some typical fuzzy systems as universal approximators abstract we investigate necessary conditions for general single input single output fuzzy systems and a class of typical multiple input single output fuzzy systems as universal approximators for continuous functions defined on compact domains with arbitrarily small uniform approximation error bounds considering the case where the only available data about the continuous function to be approximated are a finite set of its extrema we have established some necessary conditions for the fuzzy systems to be universal approximators of the function the conditions can be used practically to determine input fuzzy sets output fuzzy sets and fuzzy rules of the fuzzy systems furthermore these necessary conditions provide a basis for insightful analysis of the strengths as well as the limitations of the fuzzy systems the main strength is that only a small number of fuzzy rules may be needed to uniformly approximate continuous functions that have a complicated formulation but a relatively small number of extrema the limitation is that in order to approximate highly oscillatory continuous functions the number of fuzzy rules must be large 1997 elsevier science ltd

periodic solutions and chaos in a delay differential equation modelling haematopoesis simple mathematical models have been devised to describe the process of haematopoesis the formation and differentiation of blood cells within the human body l 21 haematopoesis is an example of a biological control system with an inherent delay in it this is due to the time required for primitive blood cells to mature such a delayed response is known to cause oscillatory behaviour in control systems and it has been found that similar oscillatory instabilities in blood cell counts are associated with diseases such as aplastic anaemia 2 this suggest that the study of such equations may be of biological importance mathematically they are of interest because they can exhibit complex aperiodic behaviour a model put forward for consideration by mackey glass 3 is

stability and stabilization of fuzzy large scale systems this paper investigates the stability and stabilization problems for the fuzzy large scale system in which the system is composed of a number of takagi sugeno fuzzy model subsystems with interconnections the stability criterion of the fuzzy large scale system without control is derived first instead of fuzzy parallel distributed compensation design linear state feedback control is used in the stabilization work each local control is obtained from riccati equation of the corresponding subsystem and the interconnection terms are used to determine the local feedback gain determination based on lyapunov criterion some conditions are derived under which the whole fuzzy large scale system is stabilized asymptotically a numerical example is given to illustrate the control design procedure and its effectiveness

decentralized pdc for large scale t s fuzzy systems this paper studies the decentralized stabilization problem for a large scale system the considered large scale system comprises of a number of subsystems and each subsystem is represented by a takagi sugeno t s fuzzy model the interconnection between any two subsystems may be nonlinear and satisfies some matching condition by the concept of parallel distributed compensation pdc the decentralized fuzzy control for each subsystem is synthesized in which the control gain depends on the strength of interconnections maximal number of the fired rules in each subsystem and the common positive matrix p sub i based on lyapunov criterion and riccati inequality some sufficient conditions are derived and the common p sub i is solved by linear matrix inequalities lmi so that the whole closed loop large scale fuzzy system with the synthesized fuzzy control is asymptotically stable finally a numerical example is given to illustrate the control synthesis and its effectiveness

stability and the fuzzy controller abstract this paper corrects a part of the main result theorem 1 in buckley fuzzy sets and systems 77 1996 167 173

can fuzzy neural nets approximate continuous fuzzy functions abstract we first argue that regular fuzzy neural nets based on standard fuzzy arithmetic and the extension principle cannot be universal approximators this negative result is surprising since regular neural nets are universal approximators we then argue that hybrid fuzzy neural nets not necessarily based on standard fuzzy arithmetic can be universal approximators