analysis and design of minimax optimal interpolators we consider a class of interpolation algorithms including the least squares optimal yen 1956 interpolator and we derive a closed form expression for the interpolation error for interpolators of this type the error depends on the eigenvalue distribution of a matrix that is specified for each set of sampling points the error expression can be used to prove that the yen interpolator is optimal the implementation of the yen algorithm suffers from numerical ill conditioning forcing the use of a regularized approximate solution we suggest a new approximate solution consisting of a sinc kernel interpolator with specially chosen weighting coefficients the newly designed sinc kernel interpolator is compared with the usual sinc interpolator using jacobian area weighting through numerical simulations we show that the sinc interpolator with jacobian weighting works well only when the sampling is nearly uniform the newly designed sinc kernel interpolator is shown to perform better than the sinc interpolator with jacobian weighting

on fuzzy integral inequalities and fuzzy expectation and s i ydl l b does not imply indeed let us consider the following example let x and y be inexact variables satisfying the conditions q 0 11 0 x w o7 1 if ogo 3 if obo 3 if w d 0 7 if w 0 7 it is easy to check that if 1 is lebesgue measure then

uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one point dirichlet data abstract we consider an inverse problem arising in laser induced thermotherapy a minimally invasive method for cancer treatment in which cancer tissues is destroyed by coagulation for the dosage planning quantitatively reliable numerical simulation are indispensable to this end the identification of the thermal growth kinetics of the coagulated zone is of crucial importance mathematically this problem is a nonlinear and nonlocal parabolic inverse heat source problem we show in this paper that the temperature dependent thermal growth parameter can be identified uniquely from a one point measurement

numerical inversions for a nonlinear source term in the heat equation by optimal perturbation algorithm this paper deals with an inverse problem of identifying a nonlinear source term g g u in the heat equation u t u x x a x g u by data compatibility analysis the forward problem is proved to have a unique positive solution with a maximum of m 0 with which an optimal perturbation algorithm is applied to determine the source function g u on u 0 m numerical inversions are carried out for g u with functional forms of polynomial trigonometric and index functions the inversion reconstruction sources basically coincide with the true source solution showing that the optimal perturbation algorithm is efficient to the inverse source problem here by the computations we find that the inversion results are better for polynomial sources than those of trigonometric and index sources the inversion algorithm seems to be very sharp if the solution s maximum m of the forward problem is relatively small otherwise the deviations in the source solutions become large especially near the endpoint of u m

nonlinearity of the fuzzy integral we prove that the fuzzy integral has some linearity properties only for small classes of fuzzy measures we also show that an extension of this concept to bounded functions as proposed by kandel 2 5 is not well defined in general

characterization of compact subsets of fuzzy sets a characterization of compact subsets is presented for the metric space of normal fuzzy convex fuzzy sets on the base space rn the metric for which is the supremum over the hausdorff distances between corresponding level sets it is shown that a closed subset is compact if and only if it is uniformly support bounded and the corresponding set of support functions is equileftcontinuous in the membership grade variable

reconstruction of tomographic images using analog projections and the digital radon transform abstract the digital radon transform drt can be adapted to reconstruct images from analog projection data this new technique is a variation of the conventional back projection method it requires no pre filtering of the projection data straightforward 1d linear interpolation and some simple sorting of projection samples the drt enables the use of a form of block data copy for the reconstruction which is fast in comparison to the usual methods of back projection to obtain reconstructed images of high quality further intrinsic interpolation is required the reconstructed image size has to be several times larger than the number of projection samples we describe an algorithm to convert analog projection data into a form suitable to apply the drt we compare the performance of the standard drt and a hybrid version of the drt to some conventional reconstruction algorithms

generalized fuzzy integrals part i fundamental concepts abstract in this paper we introduce a definition of fuzzy integral which is a generalization of both s fuzzy integral defined by m sugeno and n fuzzy integral due to zhao ruhuaiand discuss the fundamen tal properties of this kind of fuzzy integral

numerical methods for calculating the fuzzy integral abstract a general procedure for calculating the fuzzy integral fi is developed for monotonic and single maxima functions in the case of monotonic functions an iterative algorithm based on the standard iteration method sim is shown to converge to the fi independently of the initial value an alternative newton type procedure can be applied for both monotonic and single maxima functions provided that an appropriate initial approximation is used

monotonicity and uniqueness results in identifying an unknown coefficient in a nonlinear diffusion equation we consider the problem of identifying an unknown diffusion coefficient in a nonlinear diffusion equation from overspecified data measured on the boundary conditions ensuring compatibility of the data are derived and it is shown that the mapping which carries the diffusion coefficient into the data is isotonic this result is then used to derive a uniqueness result for the inverse problem and for an associated identification problem some results of numerical experiments are presented to illustrate the various results

toward a general theory of fuzzy variables abstract a general framework for a theory is presented that encompasses both statistical uncertainty which falls within the province of probability theory and nonstatistical uncertainty which relates to the concept of a fuzzy set and possibility theory l a zadeh j fuzzy sets 1 1978 3 28 the concept of a fuzzy integral is used to define the expected value of a random variable properties of the fuzzy expectation are stated and a mean value theorem for the fuzzy integral is proved comparisons between the fuzzy and the lebesgue integral are presented after a new concept of dependence is formulated various convergence concepts are defined and their relationships are studied by using a chebyshev like inequality for the fuzzy integral the possibility of using this theory in bayesian estimation with fuzzy prior information is explored

the eigenvalues of matrices that occur in certain interpolation problems the eigenvalues of the matrices that occur in certain finite dimensional interpolation problems are directly related to their well posedness and strongly depend on the distribution of the interpolation knots that is on the sampling set we study this dependency as a function of the sampling set itself and give accurate bounds for the eigenvalues of the interpolation matrices the bounds can be evaluated in as few as four arithmetic operations and therefore they greatly simplify the assessment of sampling sets regarding numerical stability the accuracy and usefulness of the bounds are illustrated with examples

generating fuzzy measures fuzzy measure and integration theory was introduced by sugeno 131 in order to deal with events affected by nonstatistical uncertainty further developments were concerned both with the analytical treatment of the concept of fuzzy measure and its links with the classical measure theory see e g 3 5 8 9 11 14 and the determination of a unique framework into which fuzziness and randomness can be set see 7 the main feature of the fuzzy measure in comparison with the classical one is the loss of additivity conditions while continuity and monotonicity axioms are assumed our present aim is to exhibit some constructive examples of fuzzy measures in terms of compositions of o additive measures and suitable real valued functions furthermore we show some properties that are peculiar to the related class of the fuzzy measures above

measurablility concepts for fuzzy mappings abstract in a series of recent works alternative measurability concepts for fuzzy mappings were introduced and studied in this paper we show that some of these concepts are equivalent or strongly inter related

metric spaces of fuzzy sets two classes of metrics are introduced for spaces of fuzzy sets their equivalence is discussed and basic properties established a characterisation of compact and locally compact subsets is given in terms of boundedness and p mean equileft continuity and the spaces shown to be locally compact complete and separable metric spaces

nonuniform fast fourier transforms using min max interpolation the fast fourier transform fft is used widely in signal processing for efficient computation of the ft of finite length signals over a set of uniformly spaced frequency locations however in many applications one requires nonuniform sampling in the frequency domain i e a nonuniform ft several papers have described fast approximations for the nonuniform ft based on interpolating an oversampled fft this paper presents an interpolation method for the nonuniform ft that is optimal in the min max sense of minimizing the worst case approximation error over all signals of unit norm the proposed method easily generalizes to multidimensional signals numerical results show that the min max approach provides substantially lower approximation errors than conventional interpolation methods the min max criterion is also useful for optimizing the parameters of interpolation kernels such as the kaiser bessel function

transformation theorems for fuzzy integrals on fuzzy sets abstract in this paper sugeno s fuzzy integrals studied in 5 8 9 are generalized some equivalent definitions of fuzzy integrals on fuzzy sets are given and several transformation theorems of such type of fuzzy integrals are proved these results reveal the relations between the fuzzy integrals on fuzzy sets and on classical sets

selection of observations in signal reconstruction in some signal reconstruction problems the observation equations can be used as a priori information for selecting the best combination of observations before acquiring them in the present correspondence the authors define a selection criterion and propose efficient methods for optimizing the criterion with respect to the combination of observations the examples illustrate the value of optimized sampling using the proposed methods

numerical solution of the inverse problem of determining an unknown source term in a two dimensional heat equation a numerical procedure for an inverse problem of determination of unknown source term in two dimensional parabolic equation is presented the approach of the proposed method is to approximate unknown function by a piecewise linear function whose coefficients are determined from the solution of minimisation problem based on the overspecified data some numerical examples are presented

regularity properties of non additive set functions abstract we investigate some regularity properties of non additive set functions a lebesgue decomposition theorem is proved for measures that are decomposable with regard to a triangular conorm

a method for solving an inverse biharmonic problem this paper deals with the problem of determining of an unknown coefficient in an inverse boundary value problem using a nonconstant overspecified data it has been shown that the solution to this inverse problem exists and is unique

source term identification for an axisymmetric inverse heat conduction problem we consider an inverse heat source problem of determining the heat source term from the final temperature history of a cylinder this problem is ill posed a simplified tikhonov regularization method is applied to formulate regularized solution which is stably convergent to the exact one with a logarithmic type error estimate

on the basic solutions to the generalized fuzzy integral equation abstract for the fuzzy measure space x a the structure of the basic solutions to the generalized fuzzy integral equation esh x x h x d is considered where h x is taken as a nonnegative measurable kernel function 0 is a constant denotes the logic multiplication minimum operator at first the existence of the constant basic solution to eq 1 is investigated and the solvable sufficient and necessary conditions to the eq 1 are characterized then the characteristic functional basic solution to eq 1 is shown in addition two convergent theorems corresponding to the sequences of approximate basic solutions each of which is constituted by the series with the logic addition maximum operator denoted by for the characteristic functions are obtained

topological properties of fuzzy numbers fuzzy numbers are defined and a metric is assigned to this class of fuzzy sets topological properties of the resulting metric space are studied the notion of q crisp fuzzy numbers is introduced and in particular it is shown that this class of fuzzy numbers is homeomorphic to the hilbert cube

mmse design of interpolation and downsampling fir filters in the context of periodic nonuniform sampling the generalized sampling theorem states that any analog signal whose spectrum is limited to 1 t can be exactly recovered from n sequences of samples taken at a rate 2 nt and all having a different sampling phase when n 2 the exact interpolation formula can be derived quite easily the ideal interpolation filters have infinite impulse responses iirs this paper addresses first the question of recovering from the two initial sequences any other sequence taken at the same rate 1 t and with a different sampling phase the design problem is dealt with for finite length filters and the criterion is the minimization of the mean squared interpolation error next the problem of computing from the two initial sequences a third one at a lower rate is addressed fir decimation filters are also designed for an mmse criterion these problems are illustrated for two typical covariance functions

nonideal sampling and interpolation from noisy observations in shift invariant spaces digital analysis and processing of signals inherently relies on the existence of methods for reconstructing a continuous time signal from a sequence of corrupted discrete time samples in this paper a general formulation of this problem is developed that treats the interpolation problem from ideal noisy samples and the deconvolution problem in which the signal is filtered prior to sampling in a unified way the signal reconstruction is performed in a shift invariant subspace spanned by the integer shifts of a generating function where the expansion coefficients are obtained by processing the noisy samples with a digital correction filter several alternative approaches to designing the correction filter are suggested which differ in their assumptions on the signal and noise the classical deconvolution solutions least squares tikhonov and wiener are adapted to our particular situation and new methods that are optimal in a minimax sense are also proposed the solutions often have a similar structure and can be computed simply and efficiently by digital filtering some concrete examples of reconstruction filters are presented as well as simple guidelines for selecting the free parameters e g regularization of the various algorithms

mean squared error sampling and reconstruction in the presence of noise one of the main goals of sampling theory is to represent a continuous time function by a discrete set of samples here we treat the class of sampling problems in which the underlying function can be specified by a finite set of samples our problem is to reconstruct the signal from nonideal noisy samples which are modeled as the inner products of the signal with a set of sampling vectors contaminated by noise to mitigate the effect of the noise and the mismatch between the sampling and reconstruction vectors the samples are linearly processed prior to reconstruction considering a statistical reconstruction framework we characterize the strategies that are mean squared error mse admissible meaning that they are not dominated in terms of mse by any other linear reconstruction we also present explicit designs of admissible reconstructions that dominate a given inadmissible method adapting several classical estimation approaches to our particular sampling problem we suggest concrete admissible reconstruction methods and compare their performance the results are then specialized to the case in which the samples are processed by a digital correction filter

fuzzy integrals and fuzzy measures with their values in complete lattices abstract real valued fuzzy measures and their associated fuzzy integrals were proposed by sugeno in this paper we consider fuzzy measures valued in complete lattices and their associated upper and lower fuzzy integrals moreover we define a class of functionals called fuzzy integrals in the setting of the complete lattices which are both brouwerian and dually brouwerian the upper and lower fuzzy integrals are fuzzy integrals while in that of the completely distributive complete lattices every fuzzy integral is both lower and upper fuzzy integral with respect to a fuzzy measure

a measure theoretical approach of the problem of computing production costs abstract the problem of determining the costs of generating goods in a production process productive economy is approached and it is shown that it can be represented as an equation with additive fuzzy measures as unknowns these kind of measures are proved to be representable by lebesgue integrals this fact is used in order to show that in some regularity conditions concerning the revenue rates of the capital invested in production the problem of determining a cost measure i e a function assigning to each product its producing cost can be a priori solved and have at least one solution moreover if the speed of variation of the capital s revenue rate with respect to the investments is limited by a sufficiently small upper bound then this solution is unique and it can be computed by an algorithmic procedure allowing an anticipative evaluation of the production costs the economic model presented in this work can be of use to study the efficiency of an economy and also to determine prices of produced goods

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

fuzzy metric and convergences based on the symmetric difference abstract in this paper by applying the lebesgue s measure on the symmetric difference of sets we introduce the notions of the symmetric difference metric d and p mean symmetric difference metric d p in order to measure the difference between fuzzy numbers the concept of the platform type of fuzzy number p fuzzy number is introduced and we show that d and d p are zero if and only if two fuzzy numbers are equal or have the same p fuzzy numbers further the relations between d and the uniform hausdorff metric d h cf diamond and kloeden 1989 d p and d p cf nola and ventre 1987 are discussed for the non p fuzzy numbers the equivalences of the metric convergences on d and d h d p and d p are provided

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

possibility and necessity integrals abstract in this paper we introduce seminormed and semiconormed fuzzy integrals associated with confidence measures these confidence measures have a field of sets as their domain and a complete lattice as their codomain in introducing these integrals the analogy with the classical introduction of lebesgue integrals is explored and exploited it is amongst other things shown that our integrals are the most general integrals that satisfy a number of natural basic properties in this way our dual classes of fuzzy integrals constitute a significant generalization of sugeno s fuzzy integrals a large number of important general properties of these integrals is studied furthermore and most importantly the combination of seminormed fuzzy integrals and possibility measures on the one hand and semiconormed fuzzy integrals and necessity measures on the other hand is extensively studied it is shown that these combinations are very natural and have properties which are analogous to the combination of lebesgue integrals and classical measures using these results the very basis is laid for a unifying measure and integral theoretic account of possibility and necessity theory in very much the same way as the theory of lebesgue integration provides a proper framework for a unifying and formal account of probability theory

stable determination of a semilinear term in a parabolic equation in 5 the flrst and third authors establish holder type stability estimates for the inverse problem consisting in the determination of a semilinear term of a parabolic equation from a single boundary measurement when the domain is a rectangle in the present paper we extend the results in 5 for a general smooth domain

unicity in an inverse problem for an unknown reaction term in a reaction diffusion equation in this paper we consider an inverse problem in which we seek to deter mine an unknown source or reaction term in a reaction diffusion equation from overspecified data measured on the boundary of the spatial region where the equation applies the analysis is based on the observation that the overspecified data depends monotonically on the unknown source term in the equation here we use this monotonicity to establish a type of unicity result for the inverse problem the attractiveness of the monotonicity methods illustrated here lies in their versatility surveying the rapidly expanding literature devoted to the topic of inverse problems one finds a considerable variety of ad hoc approaches methods which apply to a general class of problems seem to be few monotonicity methods however apply to a variety of inverse problems involving partial differential equations of parabolic or elliptic type this paper is organized as follows in section 1 we formulate the direct initial boundary value problem ibvp and state assumptions on the data and a priori assumptions on the unknown source term several properties of the solution to the direct problem are derived in section 2 the principal monotonicity estimates are established and in section 3 these are applied to the inverse problem to prove a type of unicity result for the solution to the inverse problem in particular it is a corollary of theorem 3 2 that in the class of analytic source terms the solution of the inverse problem is unique the problem of identifying an unknown source term in a heat equation 155

some properties of fuzzy integrable function space l 1 μ abstract we introduce definitions of fuzzy orlicz class l and fuzzy mean convergence we show that fuzzy mean convergence is equivalent to convergence in fuzzy measure and l l1 for any orlicz function this conclusion refines a result of d ralescu toward a general theory of fuzzy variable j math anal appl 86 1982 176 193 moreover a necessary and sufficient condition for l1 s is given it also improves a result of d ralescu and g adams the fuzzy integral j math anal appl 75 1980 562 570

the reconstruction of a band limited function and its fourier transform from a finite number of samples at arbitrary locations by singular value decomposition a method for the stable interpolation of a bandlimited function known at sample instants with arbitrary locations in the presence of noise is given singular value decomposition is used to provide a series expansion that in contrast to the method of sampling functions permits simple identification of vectors in the minimum norm space poorly represented in the sample values three methods miller regularization least squares estimation and maximum a posteriori estimation are given for obtaining regularized reconstructions when noise is present the singular value decomposition svd method is used to interrelate these methods examples illustrating the technique are given

probabilities and fuzzy events an operational approach abstract this paper tries to give a redesign of a well established research area of traditional fuzzy set theory the notion of a probability of a fuzzy event as well as related results are reexamined and new definitions for them are given which are based on the operational viewpoint of f set theory and on some concepts of operational statistics a critical survey of existing concepts will show some advantages of the operational approach

symmetry constrained 3 d interpolation of viral x ray crystallography data a three dimensional 3 d interpolation problem that is important in viral x ray crystallography is considered the problem requires new methods because the function is known to have icosahedral symmetry the data is corrupted by experimental errors and therefore lacks the symmetry the problem is 3 d the measurements are irregularly spaced and the number of measurements is large 10 sup 4 a least squares approach is taken using two sets of basis functions the functions implied by a minimum energy bandlimited exact interpolation problem and a complete orthonormal set of bandlimited functions a numerical example of the cowpea mosaic virus is described

interpolation and the discrete papoulis gerchberg algorithm analyze the performance of an iterative algorithm similar to the discrete papoulis gerchberg algorithm and which can be used to recover missing samples in finite length records of band limited data no assumptions are made regarding the distribution of the missing samples in contrast with the often studied extrapolation problem in which the known samples are grouped together indeed it is possible to regard the observed signal as a sampled version of the original one and to interpret the reconstruction result studied as a sampling result the authors show that the iterative algorithm converges if the density of the sampling set exceeds a certain minimum value which naturally increases with the bandwidth of the data they give upper and lower bounds for the error as a function of the number of iterations together with the signals for which the bounds are attained also they analyze the effect of a relaxation constant present in the algorithm on the spectral radius of the iteration matrix from this analysis they infer the optimum value of the relaxation constant they also point out among all sampling sets with the same density those for which the convergence rate of the recovery algorithm is maximum or minimum for low pass signals it turns out that the best convergence rates result when the distances among the missing samples are a multiple of a certain integer the worst convergence rates generally occur when the missing samples are contiguous

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

study on fuzzy optimization methods based on quasi linear fuzzy number and genetic algorithm fuzzy optimization is a well known optimization problem in artificial intelligence system control manufacturing and management establishing general and operable fuzzy optimization methods are important in both theory and application in this paper starting from the structure of fuzzy information and the mechanism of fuzzy optimization we propose the concept of quasi linear fuzzy number and discuss its approximation properties and the features on arithmetic operations further by distinguishing principal indices and secondary indices we establish the fuzzy optimization model based on synthesizing effect by combining the compound quantification strategy of fuzzy information and give a fuzzy optimization method based on principal operations and genetic algorithm fom bpo ga finally we consider the convergence of our algorithm using the theory of markov chains and analyze its performance through two concrete examples all these indicate that fom bpo ga can effectively merge decision preferences into the optimization process and it also possess better global convergence so it can be applied to many fuzzy optimization problems

possibility theory an integral theoretic approach this paper introduces possibility integrals as fuzzy integrals w r t possibility measures it is shown that this concept can be used to unify a lot of known results in possibility theory that up to now have been introduced on a more ad hoc basis the integral theoretic approach allows us amongst other things to introduce product and conditional possibility measures in very much the same way as product lebesgue measures and conditional probability measures are introduced furthermore to stress the fact that the concept of order relations is basic for possibility theory all the results are proved for a complete lattice as the evaluation set instead of the more familiar unit interval 0 1

analysis of error in reconstruction of two dimensional signals from irregularly spaced samples we consider the problem of estimating a band limited two dimensional 2 d signal based on a finite set of irregularly spaced samples we derive the minimum mean squared error estimator of the form of a sum of weighted interpolating functions that are identical in shape but are centered at the irregularly spaced sample points and show that this estimator is identical to the minimum energy band limited interpolator that has been previously obtained by others the relation between the mean squared error and the set of irregularly spaced sampling points is studied using the minimax principle the maximum of the mean squared error over a class of signals is minimized by proper choice of the set of sampling points three criteria for evaluating the performance of the sampling point set are derived from a candidate group of sets of irregularly spaced sampling points these criteria may be used to select that point set which is optimal for recovery over a class of signals

recovery of functions by interpolation and sampling 1 introductionthe idea of recovering an element of a normed space from a sequenceof values of linear functionals is one that has received much study recentlyand which has a number of applications in for example systems theoryand signal processing 3 11 in many situations one is given a finite set ofwxmeasurements from which to construct an approximation to some un known function that is one hopes that given a sequence of linearfunctionals f

a uniqueness theorem for determining conductivity from overspecified boundary data on cherche les coefficients inconnus k u dans l equation elliptique non lineaire k u u f x y x y ou u x y est soumise a des conditions aux limites de dirichlet et de neumann sur la frontiere de

the problem of completeness for p mean symmetric difference metric in this paper by applying lebesgue s measure on the symmetric difference of sets the p mean symmetric difference metric d p is established to measure the difference between fuzzy numbers the basic properties of cauchy sequences of e1 d p are discussed and we show e1 k d p is complete where e1 k a a e1anda0 k k is a closed interval a0 is the closure of support set of a further an example where the space e1 d p is not complete is given

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

a parabolic inverse problem with an unknown boundary condition abstract in this paper we consider a parabolic inverse problem in which an unknown function is involved in the boundary condition and we attempt to recover this function by measuring the value of the temperature at a fixed point on the boundary the motivation for studying this problem arises from some physical models such as a heat conduction system where the heat exchange between the system and its surrounding is unknown we apply the singularity estimates for the fundamental solution of a parabolic equation along with the generalized bellman gronwall inequality to obtain the continuous dependence of the solution upon the known data uniqueness of the solution is established as a direct corollary

an interpretation of fuzzy measures and the choquet integral as an integral with respect to a fuzzy measure abstract in this paper the non additivity of sugeno s fuzzy measures is interpreted in terms of addition and the rationality of the choquet integral is discussed it is pointed out that a fuzzy measure on a set x expresses the interaction between the subsets of x and can be represented by an additive measure it is shown through concrete examples that the choquet integral is reasonable as an integral with respect to a fuzzy measure it is also found that the choquet integral is closely related with the representation of a fuzzy measure

representations of the fuzzy integral abstract several representation formulas of the fuzzy integral have been found both for general integrand 2 3 and for integrand having suitable continuity properties 2 in this paper some representations of the fuzzy integral are considered the case of a topological structure added is treated furthermore an expression of the fuzzy integral of a fuzzy variable in terms of a decreasing rearrangement of f is given

fuzzy measures and convergence abstract several theorems have been proved e g by ralescu ralescu and adams puri and ralescu and klement in order to unify the approach to uncertainty of both statistical and fuzzy origin the present paper is motivated by the same instances and deals with some extensions of the measure theoretical bases of fuzzy measures and convergence properties e g a b levi like theorem