layer compactness in l fuzzy topological spaces and its applications the concept of layer compactness in l fuzzy topological spaces is defined and characterized in terms of nets and filters it is shown that the layer compactness is hereditary with respect to closed l fuzzy sets and is an invariant of continuous l valued zadeh function by the application of this concept the characterizations of chains layer compact lattices and algebraic lattices are given and the difference between n compactness and strong f compactness resp f compactness compactness is found out it is also proved that the three kinds of 1 paracompactness resp 2 paracompactness lindelof properties defined on the n compactness the strong f compactness and the f compactness respectively are equivalent in the class of all layer compact spaces

determining conductivity by boundary measurements ii interior results abstract in a recent paper the authors showed that an unknown real analytic conductivity gamma may be determined from static boundary measurements in this document they extend this analysis by demonstrating that a similar result holds for piecewise real analytic conductivities in addition for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements originator supplied keywords include inversion convergence algorithms estimates coefficients

the categorical topology approach to fuzzy topology and fuzzy convergence it is the purpose of this paper to have a look at fuzzy topology from the point of view of categorical topology we first look at interesting subcategories of fts and determine whether they are bireflective and or coreflective we also describe the set of all subcategories of fts which are at the same time bireflective and coreflective due to the fact that top is one of these subcategories of fts ffs itself can be neither cartesian closed nor extensional we therefore secondly construct a supercategory of bts which is a topological quasitopos the construction of this quasitopos is based on the theory of convergence in fts

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

approximation properties of piece wise parabolic functions fuzzy logic systems spline functions are widely used in the field of approximation theory and its applications in this article we propose the use of p functions which are spline functions of degree two as membership functions of the input variables at first we show by a constructive theory that multi input single output miso sugeno fuzzy logic systems with p input variables membership functions are universal approximators to every continuously differentiable function defined on a compact subset of r n moreover they are of first order approximation accuracy then we show that with appropriately chosen parameters of the p functions fuzzy logic systems with p input variables membership functions are universal approximators not only for the function itself but also for its first order derivative

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

approximation accuracy of some neuro fuzzy approaches many methods have been proposed in the literature for designing fuzzy systems from input output data the so called neuro fuzzy methods but very little was done to analyze the performance of the methods from a rigorous mathematical point of view in this paper we establish approximation bounds for two of these methods the table lookup scheme proposed by wang et al 1992 and the clustering method studied by wang 1993 1997 we derive detailed formulas of the error bounds between the nonlinear function to be approximated and the fuzzy systems designed using the methods based on input output data these error bounds show explicitly how the parameters in the two methods influence their approximation capability we also propose modified versions for the two methods such that the designed fuzzy systems are well defined over the whole input domain

generation of a probabilistic fuzzy rule base by learning from examples this study considers probabilistic fuzzy systems constructed using mamdani probabilistic fuzzy rules as a generalisation of deterministic fuzzy systems mamdani probabilistic fuzzy systems better model practical complex systems involving uncertainty because they combine the interpretability of fuzzy systems with the statistical properties of probabilistic systems using probabilistic fuzzy rules both probabilistic uncertainty and linguistic ambiguity are handled simultaneously with a single framework considering that the information available often consists of a training set of input output data pairs a general method for generating mamdani probabilistic fuzzy rule bases from numerical data pairs is presented a fuzzy reasoning method is used on the generated probabilistic fuzzy rule base to derive a map leading from the input space to the output space and a probabilistic fuzzy system is constructed we use this probabilistic fuzzy modelling method for nonlinear regression analysis the effectiveness of the proposed method is demonstrated by a comparison with similar regression techniques

a uniqueness theorem for an inverse boundary value problem in electrical prospection we show that a near constant conductivity of a two dimensional body can be uniquely determined by steady state direct current measurements at the boundary mathematically we show that the coefficient in the operator is uniquely determined by its dirichlet integrals

recovery of singularities for formally determined inverse problems in this paper we considered several formally determined problems in two dimensions there are no global identifiability results for these problems however we can recover an important feature of these functions namely their singularities more precisely we prove that one can determine the location and strength of singularities of anl compactly supported potential by knowing the associated scattering amplitude at a fixed energy also we prove that one can determine the location and strength of the singularities of the sound speed of a medium by making measurements just on the boundary of the medium

sufficient conditions on general fuzzy systems as function approximators abstract in a constructive way we have found sufficient conditions under which general fuzzy systems can uniformly approximate any real continuous function on a compact domain to any degree of accuracy more importantly we have revealed the underlying mechanism of such function approximation the fuzzy systems can uniformly approximate any polynomials which according to the weierstrass approximation theorem can uniformly approximate any continuous function on a compact domain these findings lead to the following practical results 1 explicit fuzzy rules of fuzzy systems can now be easily obtained according to functions to be approximated and 2 formulas are derived which can calculate the number of input fuzzy sets output fuzzy sets and fuzzy rules needed in order to satisfy any given approximation accuracy the number increases as required approximation error decreases and as approximation error approaches zero the number approaches these formulas also reveal that the number is minimal when the maximum number of intersection between adjacent input fuzzy sets is one practical implications of these results will be discussed especially in the context of fuzzy control and fuzzy modeling two examples are provided to demonstrate how to design fuzzy systems to approximate given functions with required approximation accuracy

ic l cotopological spaces the aim of this paper is to define and study ic l cotopological spaces a generalization of martin s weakly induced i topological spaces particularly weiss s induced spaces and lowen s topologically generated spaces under a moderate restriction to l we prove that icltop c the category of ic l cotopological spaces and continuous mappings is an isomorphism closed full proper subcategory of ltop c the category of l cotopological spaces and continuous mappings which is simultaneously bireflective and bicoreflective in ltop c and that an l cotopological space x d is an ic space if and only if its induced i l cotopological space x w l o p d is an ic space

intersection operation on union preserving mappings in completely distributive lattices in his classic paper 11 zadeh introduced the notion of a fuzzy set subsequently goguen 21 extended this to the more general notion of an l fuzzy set thereafter the completely distributive lattice 3 became a suitable framework to expound the theory of the l fuzzy set meanwhile much research has been carried out in the area of fuzzy topology cf 6 91 some recent articles 4 51 have considered the uniformities and metrizations on fuzzy sets and obtained rather profound results in these articles the importance of the investigation of the intersection operation on union preserving mappings in completely distributive lattices became apparent especially hutton s formula on the intersection operation 4 lemma 31 is useful in this paper by counterexample we shall show that this formula does not hold for all completely distributive lattices except the lattice 0 i moreover under an additional assumption a proof of this formula is given we shall also show some properties about the intersection operation which will be needed in our latter work on fuzzy uniformity and fuzzy metrization

some results on i l and r l abstract this paper gives a partial solution to problem 1 in wang and lu 1992 and a suggestion about how to construct a better fuzzy unit interval it defines a new kind of fuzzy real line and investigates a series of its properties

evolutionary fuzzy modeling this study is concerned with a general methodology of identification of fuzzy models unlike numeric models fuzzy models operate at a level of information granules fuzzy sets and this aspect brings up an important design requirement of transparency of the model we propose a three phase development framework by distinguishing between structural and parametric optimization processes the underlying topology of the model dwells on fuzzy neural networks architectures governed by fuzzy logic and equipped with parametric flexibility two general optimization mechanisms are explored the structural optimization is realized via genetic programming whereas for the ensuing detailed parametric optimization we proceed with gradient based learning the main advantages of this approach are discussed in detail the study is illustrated with the aid of a numeric example that provides a detailed insight into the performance of the fuzzy models and quantifies crucial design issues

h l completely regular l fuzzy sets and their applications first we introduce the concept of h completely regular l fuzzy set in l fts and give some characterizations of it then we propose the concept of h complete regularization of l fts and investigate some properties of this complete regularization we also establish the relations between h completely regular l fts completely regular l fts and weakly induced l fts based on these results we obtain several characterizations of h completely regular l fts

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

a special green s function for the biharmonic operator and its application to an inverse boundary value problem abstract a construction of the special green s function for the biharmonic operator is given this result is used to recover the operator a2 v x from its diricldet to neumann map 1 introduction let n 2 and put az e ix a z z ei z for z e c r with z z o since the inverse of the symbol of az is locally absolutely integrable and decays algebraically at infinity its inverse fourier transform defines a tempered distribution which is a fundamental solution of az and called a green faddeev function at z z for the laplace operator this terminology is seen in 1 this function plays an important role in studying several inverse problems for example inverse scattering problems see 1 2 inverse boundary value problems see 3 in short those problems are to determine the coefficients of an elliptic partial differential operator l in r n or a bounded domain f by the scattering datum at izl oo or the cauchy datum on a of the solutions of

weak topological categories in order to provide a categorical framework for fuzzy topology this paper proposes the concept of weak topological category a weaker form of topological category properties of weak topological categories are investigated and some examples of such category are provided moreover the relationship between a useful weak topological category ltop the category of l fuzzy topological spaces and continuous l valued zadeh functions and some of its subcategories is studied

approximation theory of fuzzy systems spl minus siso case in this paper the approximation properties of mimo fuzzy systems generated by the product inference are discussed we first give an analysis of fuzzy basic functions fbf s and present several properties of fbf s based on these properties of fbf s we obtain several basic approximation properties of fuzzy systems 1 basic approximation property which reveals the basic approximation mechanism of fuzzy systems 2 uniform approximation bounds which give the uniform approximation bounds between the desired control or decision functions and fuzzy systems 3 uniform convergent property which shows that fuzzy systems with defined approximation accuracy can always be obtained by dividing the input space into finer fuzzy regions and 4 universal approximation property which shows that fuzzy systems are universal approximators and extends some previous results on this aspect the similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds

remarks on products of l fuzzy topological spaces two essential theorems about fuzzy projection are improved and a negative answer to wang s question in 1987 on products of l fuzzy topological spaces is given

local connectedness in l topological spaces this paper studies local strong f1 connectedness and local q connectedness of l topological spaces it is shown that every l interval j l and its weak inducification j l are both local strong f1 connected and local q connected and that the local q connectedness of an l topological space is equivalent to that of its induced i l topological space

the wm method completed a flexible fuzzy system approach to data mining in this paper the so called wang mendel wm method for generating fuzzy rules from data is enhanced to make it a comprehensive and flexible fuzzy system approach to data description and prediction in the description part the core ideas of the wm method are used to develop three methods to extract fuzzy if then rules from data the first method shows how to extract rules for the user specified cases the second method generates all the rules that can be generated directly from the data and the third method extrapolates the rules generated by the second method over the entire domain of interest in the prediction part two fuzzy predictive models are constructed based on the fuzzy if then rules extracted by the methods of the description part the first model gives a continuous output and is suitable for predicting continuous variables and the second model gives a piecewise constant output and is suitable for predicting categorical variables we show that by comparing the prediction accuracy of the fuzzy predictive models with different numbers of fuzzy sets covering the input variables we can rank the importance of the input variables we also propose an algorithm to optimize the fuzzy predictive models and show how to use the models to solve pattern recognition problems throughout this paper we use a set of real data from a steel rolling plant to demonstrate the ideas and test the models