ship recognition via its radiated sound the fractal based approaches due to the complexity of its radiated sound ship recognition is difficult fractal approaches are proposed in this study including fractal brownian motion based analysis fractal dimension analysis and wavelet analysis to augment existing feature extraction methods that are based on spectrum analysis experimental results show that fractal approaches are effective when used to augment two traditional features line and average spectra fractal approaches led to better classification results this implies that fractal approaches can capture some information not detected by traditional approaches alone

canonical fuzzy numbers of dimension two abstract recently several authors have dealt with interactive fuzzy numbers this paper proposes a new approach to interactions between fuzzy numbers by using canonical fuzzy numbers of dimension two

fuzzy n cell numbers and the differential of fuzzy n cell number value mappings in this paper we give the definition of a special kind of n dimension fuzzy numbers fuzzy n cell numbers discuss their operations and representation theorems define a complete metric on the fuzzy n cell number space and prove that the metric is equivalent to the supremum metric derived by the hausdorff metric between the level sets of the n dimension fuzzy numbers and obtain an embedding theorem of the fuzzy n cell number space isometrically embeds it into a concrete banach space we also consider the differential of the fuzzy mappings from an interval into the fuzzy n cell number space by using the embedding theorem

representation of uncertain multichannel digital signal spaces and study of pattern recognition based on metrics and difference values on fuzzy n cell number spaces in this paper we discuss the problem of characterization for uncertain multichannel digital signal spaces propose using fuzzy n cell number space to represent uncertain n channel digital signal space and put forward a method of constructing such fuzzy n cell numbers we introduce two new metrics and concepts of certain types of difference values on fuzzy n cell number space and study their properties further based on the metrics or difference values appropriately defined we put forward an algorithmic version of pattern recognition in an imprecise or uncertain environment and we also give practical examples to show the application and rationality of the proposed techniques

correlation dimension of electroglottographic data from healthy and pathologic subjects this paper considers the effects of nonstationarity noise and finite data sets on the estimation of the correlation dimension of time series data characterizing the vibratory behavior of the vocal folds the electroglottographic signal of sustained a phonations from 10 healthy subjects and 20 subjects with vocal fold pathologies were used to reconstruct the state space in successively higher embeddings using the method of lags the dimension values were calculated from the scaling region the level area of the slope plots which did not increase for higher embeddings reasonably defined scaling regions were found in all of the data from the healthy subjects and from five of the pathologic subjects with values saturating between the first and second embeddings the egg data from those five pathologic subjects were nearly periodic from the remaining 15 subjects the scaling regions were highly constricted with nonconstant slopes so that dimension values could not be confidently estimated the results suggest that the correlation dimension is a highly subjective measure which is not usefully applied to abnormal egg data it is recommended that if used correlation dimension statistics need to be presented cautiously and graphical presentation of the data should be included

linear programming with fuzzy variables in practice there are many problems in which all decision parameters are fuzzy numbers and such problems are usually solved by either possibilistic programming or multiobjective programming methods unfortunately all these methods have shortcomings in this note using the concept of comparison of fuzzy numbers we introduce a very effective method for solving these problems then we propose a new method for solving linear programming problems with fuzzy variables

embedding problem of fuzzy number space part ii abstract using a concrete structure into which we embed the fuzzy number space e1 several necessary and sufficient conditions of fuzzy set valued functions are given by means of abstract function theory

generalized differentiability for n dimensional fuzzy number valued functions and fuzzy optimization in this paper we present a characteristic theorem for the generalized difference concept of n dimensional fuzzy numbers by means of support functions the concepts of differentiability for n dimensional fuzzy number valued functions are presented and discussed using the new generalized difference the relationships of g differentiability s differentiability and l differentiability are characterized furthermore optimization problems with s convex and s differentiable fuzzy number valued functions are described

testing the assumptions of linear prediction analysis in normal vowels in this paper we develop an improved surrogate data test to show experimental evidence for all the simple vowels of u s english for both male and female speakers that gaussian linear prediction analysis a ubiquitous technique in current speech technologies cannot be used to extract all the dynamical structure of real speech time series the test provides robust evidence undermining the validity of these linear techniques supporting the assumptions of either dynamical nonlinearity and or non gaussianity common to more recent complex efforts at dynamical modeling speech time series however an additional finding is that the classical assumptions cannot be ruled out entirely and plausible evidence is given to explain the success of the linear gaussian theory as a weak approximation to the true nonlinear non gaussian dynamics this supports the use of appropriate hybrid linear nonlinear non gaussian modeling with a calibrated calculation of statistic and particular choice of experimental protocol some of the known systematic problems of the method of surrogate data testing are circumvented to obtain results to support the conclusions to a high level of significance

interactive fuzzy programming for multi level linear programming problems with fuzzy parameters this paper presents interactive fuzzy programming for multi level linear programming problems with fuzzy parameters in fuzzy programming for multi level linear programming problems recently developed by lai et al since the fuzzy goals are determined for both an objective function and decision variables at the upper level undesirable solutions are produced when these fuzzy goals are inconsistent in order to overcome such problems after eliminating the fuzzy goals for decision variables interactive fuzzy programming for multi level linear programming problems with fuzzy parameters is presented in our interactive method after determining the fuzzy goals of the decision makers at all levels a satisfactory solution is derived efficiently by updating the satisfactory degrees of decision makers with considerations of overall satisfactory balance among all levels illustrative numerical examples for two level and three level linear programming problems are provided to demonstrate the feasibility of the proposed method

fractal dimensions of speech sounds computation and application to automatic speech recognition the dynamics of airflow during speech production may often result in some small or large degree of turbulence in this paper the geometry of speech turbulence as reflected in the fragmentation of the time signal is quantified by using fractal models an efficient algorithm for estimating the short time fractal dimension of speech signals based on multiscale morphological filtering is described and its potential for speech segmentation and phonetic classification discussed also reported are experimental results on using the short time fractal dimension of speech signals at multiple scales as additional features in an automatic speech recognition system using hidden markov models which provide a modest improvement in speech recognition performance

dimension estimation of discrete time fractional brownian motion with applications to image texture classification fractional brownian motion fbm is a suitable description model for a large number of natural shapes and phenomena in applications it is imperative to estimate the fractal dimension from sampled data namely discrete time fbm dfbm to this aim the increment of dfbm referred to as discrete time fractional gaussian noise dfgn is invoked as an auxiliary tool the regular part of dfgn is first filtered out via levinson s algorithm the power spectral density of the regular process is found to satisfy a power law that its exponent can be well fitted by a quadratic function of fractal dimension a new method is then proposed to estimate the fractal dimension of dfbm from the given data set the computational complexity and statistical properties are investigated moreover the proposed algorithm is robust with respect to amplitude scaling and shifting as well as time shifting on the data finally the effectiveness of this estimator is demonstrated via a classification problem of natural texture images

estimation of 1 f noise several models have emerged for describing 1 f sup spl gamma noise processes based on these various techniques for estimating the properties of such processes have been developed this paper provides theoretical analysis of a new wavelet based approach which has the advantages of having low computational complexity and being able to handle the case where the 1 f sup spl gamma noise might be embedded in a further white noise process however the analysis conducted here shows that these advantages are balanced by the fact that the wavelet based scheme is only consistent for spectral exponents spl gamma in the range spl gamma spl isin 0 1 this is in contradiction to the results suggested in previous empirical studies when spl gamma spl isin 0 1 this paper also establishes that wavelet based maximum likelihood methods are asymptotically gaussian and efficient finally the asymptotic rate of mean square convergence of the parameter estimates is established and is shown to slow as spl gamma approaches one combined with a survey of non wavelet based methods these new results give a perspective on the various tradeoffs to be considered when modeling and estimating 1 f sup spl gamma noise processes

a shortest path problem on a network with fuzzy arc lengths abstract we concentrate on a shortest path problem on a network in which a fuzzy number instead of a real number is assigned to each arc length introducing an order relation between fuzzy numbers based on fuzzy min a nondominated path or pareto optimal path from the specified node to every other node is defined an algorithm for solving the problem is developed on the basis of the multiple labeling method for a multicriteria shortest path as a result a number of nondominated paths can be obtained and is offered to a decision maker however a number of nondominated paths derived from large scale network may be too numerous for him to choose a preferable path due to this situation we propose a method to reduce the number of paths according to a possibility level the proposed algorithm is numerically evaluated on large scale random networks

evolution equations for continuous scale morphological filtering multiscale signal analysis has emerged as a useful framework for many computer vision and signal processing tasks morphological filters can be used to develop nonlinear multiscale operations that have certain advantages over linear multiscale approaches in that they preserve important signal features such as edges the authors discuss several nonlinear partial differential equations that model the scale evolution associated with continuous space multiscale morphological erosions dilations openings and closings these equations relate the rate of change of the multiscale signal ensemble as scale increases to a nonlinear operator acting on the space of signals the nonlinear operator is characterized by the shape and dimensionality of the structuring element used by the morphological operators generally taking the form of a nonlinear function of certain partial differential operators

joint canonical fuzzy numbers abstract starting from ramik and nakamura s report 1991 we introduce and fully characterize the joint canonical fuzzy numbers of arbitrary dimension the crucial part is to find the least value of the maximum of absolute values of several linear combinations surprisingly there is a formula for it based upon determinants formed by the coefficients of the linear combinations finally we give a full description of joint canonical fuzzy numbers of dimension 2 provided by 5 infinite families

am fm energy detection and separation in noise using multiband energy operators this paper develops a multiband or wavelet approach for capturing the am fm components of modulated signals immersed in noise the technique utilizes the recently popularized nonlinear energy operator psi s s sup 2 ss to isolate the am fm energy and an energy separation algorithm esa to extract the instantaneous amplitudes and frequencies it is demonstrated that the performance of the energy operator esa approach is vastly improved if the signal is first filtered through a bank of bandpass filters and at each instant analyzed via psi and the esa using the dominant local channel response moreover it is found that uniform worst case performance across the frequency spectrum is attained by using a constant q or multiscale wavelet like filter bank the elementary stochastic properties of psi and of the esa are developed first the performance of psi and the esa when applied to bandpass filtered versions of an am fm signal plus noise combination is then analyzed the predicted performance is greatly improved by filtering if the local signal frequencies occur in band these observations motivate the multiband energy operator and esa approach ensuring the in band analysis of local am pm energy in particular the multi bands must have the constant q or wavelet scaling property to ensure uniform performance across bands the theoretical predictions and the simulation results indicate that improved practical strategies are feasible for tracking and identifying am fm components in signals possessing pattern coherencies manifested as local concentrations of frequencies

morphological filters part i their set theoretic analysis and relations to linear shift invariant filters this paper examines the set theoretic interpretation of morphological filters in the framework of mathematical morphology and introduces the representation of classical linear filters in terms of morphological correlations which involve supremum infimum operations and additions binary signals are classified as sets and multilevel signals as functions two set theoretic representations of signals are reviewed filters are classified as set processing sp or function processing fp conditions are provided for certain fp filters that pass binary signals to commute with signal thresholding because then they can be analyzed and implemented as sp filters the basic morphological operations of set erosion dilation opening and closing are related to minkowski set operations and are used to construct fp morphological filters emphasis is then given to analytically and geometrically quantifying the similarities and differences between morphological filtering of signals by sets and functions the latter case allows the definition of morphological convolutions and correlations toward this goal various properties of fp morphological filters are also examined linear shift invariant filters due to their translation invariance are uniquely characterized by their kernel which is a special collection of input signals increasing linear filters are represented as the supremum of erosions by their kernel functions if the filters are also discrete and have a finite extent impulse response they can be represented as the supremum of erosions only by their minimal with respect to a signal ordering kernel functions stable linear filters can be represented as the sum of at most two weighted suprema of erosions these results demonstrate the power of mathematical morphology as a unifying approach to both linear and nonlinear signal shaping strategies

random modulation a review a unified treatment of various aspects of random modulation is presented with emphasis on the spectral properties of fm signals the study includes reexamination of rice s representation woodward s theorem fsk and processes with normal markov and cyclostationary frequencies

on the restudy of fuzzy complex analysis part 1 the sequence and series of fuzzy complex numbers and their convergences this paper studies the convergence of the sequence and series of fuzzy complex numbers we define the metric convergence and levelwise convergence of sequences on the metric space of fuzzy complex numbers and discuss the relationship between two convergences all this may be a foundation for researching fuzzy complex analysis

fuzzy complex analysis ii integration abstract this paper continues the author s research in fuzzy complex analysis where we now define and study the basic properties of a fuzzy contour integral for fuzzy mappings which map a rectifiable curve in the complex plane into fuzzy complex numbers

towards fuzzy differential calculus part 1 integration of fuzzy mappings abstract this paper deals with fuzzy set valued mappings of the real line and more particularly focuses on mappings from the real line to the set of convex normal fuzzy sets of the real line these mappings can also be viewed as fuzzy relations using zadeh s extension principle the integral of such fuzzy mappings over a crisp interval is defined provided a special analytical representation of the fuzzy mapping the practical computation of such an integral is shown to be easy practically speaking it yields the fuzzy surface of a fuzzily bounded area

a nonlinear dynamical systems analysis of fricative consonants acoustic waveforms of the strident fricatives s z sh and yog spoken by two native american english speakers are analyzed using modern chaotic analysis techniques fricative data are extracted from both intervocalic and sustained utterances for comparison acoustic waveforms of the vowels a i and u are also analyzed for 44 of the unvoiced fricative tokens in vcv contexts and 59 of the sustained voiced fricatives indications of low dimensional dynamics could be found with the given limitations of stationarity the low dimensional chaotic behavior is exhibited by a correlation dimension d2 ranging between 3 and 7 2 and by positive maximum lyapunov exponents les for the remaining fricatives results suggest that the dimensional complexity therein is greater than the maximum d2 value that could be reliably estimated from the available data about 7 8 for the intervocalic cases and 9 for the sustained cases intervocalic voiced fricatives are excluded from the analysis due to stat

approximate reasoning with time abstract the need to make time dependent assumptions is frequently encountered in many systems especially in dynamical systems this paper presents a theoretical study of the representation and manipulation of some vague concepts in the temporally changing world our approach to the modeling is based on zadeh s theory of possibility we introduce a concept of similarity index in reasoning with time we present two different types of widely used models one rule based and another resolution based for reasoning with time we consider simply yet concrete examples to illustrate the usefulness of the proposed models

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

on polygonal fuzzy sets and numbers in this paper we propose a new mathematical formalization of the concept of polygonal fuzzy numbers and an extension of this notion to fuzzy sets on r n we study the mathematical structure of these families of fuzzy sets and show that each family is a complete and separable metric space when endowed with the generalized hausdorff metric moreover we show that for n 1 the families of polygonal fuzzy numbers are isomorphic to some convex and closed convex cone of a finite dimensional space we obtain generalizations and extensions of some previous results on polygonal fuzzy numbers and simplified proofs of some well known results about approximation of fuzzy n dimensional quantities finally some developments about the approximation of families of fuzzy sets are introduced

the dimension of chaotic attractors dimension is perhaps the most basic property of an attractor in this paper we discuss a variety of different definitions of dimension compute their values for a typical example and review previous work on the dimension of chaotic attractors the relevant definitions of dimension are of two general types those that depend only on metric properties and those that depend on the frequency with which a typical trajectory visits different regions of the attractor both our example and the previous work that we review support the conclusion that all of the frequency dependent dimensions take on the same value which we call the dimension of the natural measure and all of the metric dimensions take on a common value which we call the fractal dimension furthermore the dimension of the natural measure is typically equal to the lyapunov dimension which is defined in terms of lyapunov numbers and thus is usually far easier to calculate than any other definition because it is computable and more physically relevant we feel that the dimension of the natural measure is more important than the fractal dimension

on fuzzy n cell numbers and n dimension fuzzy vectors fuzzy n cell numbers are a kind of special n dimension fuzzy numbers whose sets of cuts are all hyperrectangles n dimension fuzzy vectors are the cartesian products of n one dimension fuzzy numbers in this paper we show that the fuzzy n cell number space and the n dimension fuzzy vector space are identical and obtain the relations of the joint membership function and the edge membership functions of a fuzzy n cell number i e a n dimension fuzzy vector using fuzzy vector form representations of fuzzy n cell numbers we study the metric of two fuzzy n cell numbers the supremum of a set of fuzzy n cell numbers and operational rules of addition scalar multiplication and multiplication of fuzzy n cell numbers and get the fuzzy vector form characterizations of the differentiability measurability and integrability of fuzzy n cell number valued fuzzy mappings

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

phase modulated resonances modeled as self similar processes with application to turbulent sounds in this paper we propose a nonlinear stochastic model for time varying resonances where the instantaneous phase and frequency of a sinusoidal oscillation is allowed to vary proportionally to an spl alpha stable self similar stochastic processes the main motivation of our work stems from previous experimental and theoretical evidence that speech resonances in fricative sounds can be modeled phenomenologically as am fm signals with randomly varying instantaneous frequencies and that several signal classes related to turbulent phenomena are self similar 1 f processes our general approach is to model the instantaneous phase of an am fm resonance as a self similar spl alpha stable process as a special case this random phase model includes the class of random fractal signals known as fractional brownian motion we theoretically explore this random modulation model and analytically derive its autocorrelation and power spectrum we also propose an algorithm to fit this model to arbitrary resonances with random phase modulation further we apply the above ideas to real speech data and demonstrate that this model is suitable for resonances of fricative sounds

some remarks for fuzzy complex analysis abstract this paper gives some results for fuzzy complex sets generalize and improve the corresponding work of fuzzy complex numbers in 1 we also introduce the derivative and integral of functions mapping complex numbers into the set of generalized fuzzy complex numbers and it is different to the definitions in 2 4 all this may be a foundation for researching fuzzy complex analysis

possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem in this paper we review some fuzzy linear programming methods and techniques from a practical point of view in the rst part the general history and the approach of fuzzy mathematical programming are introduced using a numerical example some models of fuzzy linear programming are described in the second part of the paper fuzzy mathematical programming approaches are compared to stochastic programming ones the advantages and disadvantages of fuzzy mathematical programming approaches are exemplied in the setting of an optimal portfolio selection problem finally some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed c 2000 elsevier science b v all rights reserved

numerical solutions of fuzzy differential equations abstract numerical algorithms for solving fuzzy ordinary differential equations fode are considered a scheme based on the classical euler method is discussed in detail and this is followed by a complete error analysis the algorithm is illustrated by solving several linear and nonlinear fuzzy cauchy problems

estimation of fractal dimension of images using a fixed mass approach a method from the field of chaotic dynamics is applied for the estimation of fractal dimension of images the method is compared with other well known algorithms on a set of computer generated images of known fractal dimension the results confirm the superiority of the method in terms of accuracy dynamic range and computational time 1999 published by elsevier science b v all rights reserved

fractal dimension of color fractal images fractal dimension is a very useful metric for the analysis of the images with self similar content such as textures for its computation there exist several approaches the probabilistic algorithm being accepted as the most elegant approach however all the existing methods are defined for 1 d signals or binary images with extension to grayscale images our purpose is to propose a color version of the probabilistic algorithm for the computation of the fractal dimension to validate this new approach we also propose an extension of the existing algorithm for the generation of probabilistic fractals in order to obtain color fractal images then we show the results of our experiments and conclude this paper

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

fuzzy complex numbers abstract this paper first defines fuzzy complex numbers and shows closure under the basic arithmetic operations it is shown that arithmetic of fuzzy complex numbers may be performed in terms of cuts next two special types of fuzzy complex numbers based on the forms z x iy and z re i for regular complex numbers are investigated introducing a metric on the space of fuzzy complex numbers then allows us to discuss continuity and differentiability of fuzzy complex functions

signal processing with fractals a wavelet based approach wavelet transmission statistically self similar signals detection and estimation with 1 processes deterministically self similar signals fractal modulation linear self similar signals

the capacity for a class of fractal functions we present a formula for the capacity of the graphs of certain fractal functions we show that this formula can also be obtained using the lyapunov exponents of an associated dynamical system

fractional brownian motion a maximum likelihood estimator and its application to image texture fractals have been shown to be useful in characterizing texture in a variety of contexts use of this methodology normally involves measurement of a parameter h which is directly related to fractal dimension in this work the basic theory of fractional brownian motion is extended to the discrete case it is shown that the power spectral density of such a discrete process is only approximately proportional to f a instead of in direct proportion as in the continuous case an asymptotic cramer rao bound is derived for the variance of an estimate of h subsequently a maximum likelihood estimator mle is developed to estimate h it is shown that the variance of this estimator nearly achieves the minimum bound a generation algorithm for discrete fractional motion is presented and used to demonstrate the capabilities of the mle when the discrete fractional brownian process is contaminated with additive gaussian noise the results show that even at signal to noise ratios of 30 db significant errors in estimation of h can result when noise is present the mle is then applied to x ray images of the human calcaneus to demonstrate how the line to line formulation can be applied to the two dimensional case these results indicate that it has strong potential for quantifying texture

multiple resolution texture analysis and classification textures are classified based on the change in their properties with changing resolution the area of the gray level surface is measured at serveral resolutions this area decreases at coarser resolutions since fine details that contribute to the area disappear fractal properties of the picture are computed from the rate of this decrease in area and are used for texture comparison and classification the relation of a texture picture to its negative and directional properties are also discussed

canonical fuzzy numbers of dimension two and fuzzy utility difference for understanding preferential judgments abstract a notion of canonical fuzzy numbers of dimension two is introduced to represent flexible joint distributions of two fuzzy numbers whose membership functions are of a common functional type the relationships between fuzzy numbers are given by normalized scalar called relational factors in the joint distributions then the canonical fuzzy numbers are adopted to operate fuzzy utility differences and their aggregations for understanding human uncertain preferential judgments among multiattribute alternatives

on the spectrum of fractional brownian motions fractional brownian motions fbms provide useful models for a number of physical phenomena whose empirical spectra obey power laws of fractional order however due to the nonstationary nature of these processes the precise meaning of such spectra remains generally unclear two complementary approaches are proposed which are intended to clarify this point the first one based on a time frequency analysis takes into account the nonstationary nature of fbm and puts emphasis on time averaged measurements the second one based on a time scale analysis is matched to self similarity properties of fbm and reveals an underlying stationary structure relative to each time scaling

measuring the fractal dimension of signals morphological covers and iterative optimization fractals can model many classes of time series data the fractal dimension is an important characteristic of fractals that contains information about their geometrical structure at multiple scales the covering methods are a class of efficient approaches to measure the fractal dimension of an arbitrary fractal signal by creating multiscale covers around the signal s graph in this paper we develop a general method that uses multiscale morphological operations with varying structuring elements to unify and extend the theory and digital implementations of covering methods it is theoretically estab lished that for the fractal dimension computation covering one dimensional signals with planar sets is equivalent to mor phologically transforming the signal by one dimensional func tions which reduces the computational complexity from quad ratic in the signal s length to linear then a morphological covering algorithm is developed and applied to discrete time signals synthesized from weierstrass functions fractal inter polation functions and fractional brownian motion further for deterministic parametric fractals depending on a single pa rameter related to their dimension we develop an optimization method that starts from an initial estimate and iteratively con verges to the true fractal dimension by searching in the param eter space and minimizing a distance between the original sig nal and all such signals from the same class experimental results are also provided to demonstrate the good performance of the developed methods

probabilistic pseudo morphology for grayscale and color images mathematical morphology offers popular image processing tools successfully used for binary and grayscale images recently its extension to color images has become of interest and several approaches were proposed due to various issues arising from the vectorial nature of the data none of them imposed as a generally valid solution we propose a probabilistic pseudo morphological approach by estimating two pseudo extrema based on chebyshev inequality the framework embeds a parameter which allows controlling the linear versus non linear behavior of the probabilistic pseudo morphological operators we compare our approach for grayscale images with the classical morphology and we emphasize the impact of this parameter on the results then we extend the approach to color images using principal component analysis as validation criteria we use the estimation of the color fractal dimension color textured image segmentation and color texture classification furthermore we compare our proposed method against two widely used approaches one morphological and one pseudo morphological we propose a pseudo morphology based on probabilistic tools we use chebyshev inequality and pca for estimating pseudo extrema of a set our operators are linear or non linear depending on the choice of a parameter we extend the approach to multivariate images particularly for the color domain validation is performed through texture feature extraction

matrix perturbation analysis for weakly coupled oscillators the central pattern generator for controlling animal locomotion is generally not a single oscillator but a group of interconnected oscillators although the whole group can be analyzed as a bulky single oscillator it is difficult with such an approach to reveal the essential mechanism of phase coordination among oscillators in this paper a new approach based on the multivariable harmonic balance is used to analyze a group of identical oscillators that are weakly coupled to each other specifically a lower dimensional matrix representing the coupling structure is abstracted from the overall neuronal connectivity matrix of large dimension so that the coupling matrix captures the essential mechanism for phase coordination of the oscillators moreover this framework provides an effective way to design the neuronal interconnections to achieve prescribed coordination among the oscillators

power law shot noise and its relationship to long memory spl alpha stable processes we consider the shot noise process whose associated impulse response is a decaying power law kernel of the form t sup spl beta 2 1 we show that this power law poisson model gives rise to a process that at each time instant is an spl alpha stable random variable if spl beta 1 the power law poisson process has a power law spectrum we show that although in the case spl beta 1 the power spectrum does not exist the process still exhibits long memory in a generalized sense the power law shot noise process appears in many applications in engineering and physics the proposed results can be used to study such processes as well as to synthesize a random process with long range dependence

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

weighted pseudometric approximation of 2 dimensional fuzzy numbers by fuzzy 2 cell prismoid numbers preserving the centroid abstract up to now there have been many research results about approximations of fuzzy numbers by specific fuzzy numbers under preservation of some operators however there are few investigations about approximations of n dimensional fuzzy numbers the main reason is that the structure of n dimensional fuzzy numbers are more complex this paper devotes to seek an approximation operator that produces a special kind of 2 dimensional fuzzy number which is the nearest one to the given 2 dimensional fuzzy number along the direction k the concept of four edges approximation for 2 dimensional fuzzy numbers is defined which is a special kind of 2 dimensional fuzzy numbers at the same time the concept of fuzzy 2 cell prismoid numbers is introduced and the nearest fuzzy 2 cell prismoid numbers of 2 dimensional fuzzy numbers which preserve the centroid of the core for the 2 dimensional fuzzy numbers with respect to the weighted pseudometric are discussed finally with respect to the criteria scale invariance identity criterion and nearness criterion some properties of the approximation operator are presented

fuzziness and branch and bound procedures applications to separation sequencing abstract the aim of the paper is to identify optimal and near optimal distillation sequences according to a particular objective function definition the potential solutions are valuated from the point of view of practical considerations rather than purely costing methods four rules of thumb addressing column sequencing expressed in vague and imprecise terms are implemented and quantified by the fuzzy set theory the integer programming problem is solved by a branch and bound procedure where the bounding and branching schemes are carried out from the four heuristic rules with fuzzy quantification furthermore the fuzzy set theory is also implemented for modelling data uncertainties particularly the partial molar flow rates from the results obtained with the fuzzy branch and bound procedure involving fuzzy data we conclude that fuzzy set theory can be considered as a promising tool for modelling uncertainty and vagueness and may have many other applications in process systems engineering

stable fuzzy logic design of point to point control for mechanical systems an approach for the development of fuzzy point to point control laws for second order mechanical systems is presented asymptotic stability of the resulting closed loop system is proved using lyapunov stability theory closed loop performance and robustness are quantified in terms of the parameters of membership functions as opposed to most existing fuzzy control laws the closed loop stability of the proposed controller does not depend on the knowledge of the entire dynamics moreover the approach does not require the plant to be open loop stable the proposed approach is demonstrated on design and simulation study of a fuzzy controller for a two link robotic arm

towards fuzzy differential calculus part 2 integration on fuzzy intervals abstract the problem of integrating mappings over fuzzy domains has already received some attention in the literature however there is not a unique approach but several definitions have been proposed each carrying its own meaning this paper tries to emphasize the relationships and the differences between the various points of view

fractal dimension of color fractal images with correlated color components we mathematically prove that color fractal images with two and three correlated color components generated with the midpoint displacement approach obey the property of self similarity thus enabling the estimation of their color fractal dimension we generate various sets of color fractal images with two and three correlated color components controlled both by the hurst parameter and the variance covariance matrix with and without a global normalization and use them for the calibration of the embraced color fractal dimension estimator we improve the existing fractal dimension estimator based on probabilistic box counting by reducing the variance of the regression line estimators through the iterative elimination of most error ed measurement points we independently estimate the variance covariance matrix and hurst parameter for the sets of generated color fractal images with correlated color components we show the experimental results and discuss both the improvements and the limitations of the proposed approach

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

fuzzy complex analysis i differentiation abstract we consider functions mapping real numbers into the set of generalized complex fuzzy numbers c we define two derivatives of such functions which are generalizations of the derivative of real fuzzy mappings presented by dubois and prade 4 5 sufficient conditions on the function are given so that derivative will be a function mapping real numbers into c if the functional value is always a rectangular complex fuzzy number made up to lr real fuzzy numbers then we show that the derivative is easily computed from the derivatives of the lr fuzzy numbers other properties of the derivatives are presented

a fuzzy relational identification algorithm and its application to predict the behaviour of a motor drive system fuzzy relational identification builds a relational model describing a system s behaviour by a nonlinear mapping between its variables in this paper we propose a new fuzzy relational algorithm based on the simplified max min relational equation the algorithm presents an adaptation method applied to the gravity centre of each fuzzy set based on the error integral value between the measured and predicted system s output and uses the concept of time variant universe of discourse the identification algorithm also includes a method to attenuate the noise influence in the extracted system s relational model using a fuzzy filtering mechanism the algorithm is applied to a one step forward prediction of a simulated and experimental motor drive system the identified model has its input output variables stator reference current and motor speed signal treated as fuzzy sets whereas the relations existing between them are described by means of a matrix r defining the relational model extracted by the algorithm the results show the good potentialities of the algorithm in predicting the behaviour of the system and in attenuating through the fuzzy filtering method possible noise distortions in the relational model

learning continuous trajectories in recurrent neural networks with time dependent weights the paper is concerned with a general learning with arbitrary criterion and state dependent constraints of continuous trajectories by means of recurrent neural networks with time varying weights the learning process is transformed into an optimal control framework where the weights to be found are treated as controls a learning algorithm based on a variational formulation of pontryagin s maximum principle is proposed this algorithm is shown to converge under reasonable conditions to an optimal solution the neural networks with time dependent weights make it possible to efficiently find an admissible solution i e initial weights satisfying state constraints which then serves as an initial guess to carry out a proper minimization of a given criterion the proposed methodology may be directly applicable to both classification of temporal sequences and to optimal tracking of nonlinear dynamic systems numerical examples are also given which demonstrate the efficiency of the approach presented

fuzzy approximation relations on fuzzy n cell number space and their applications in classification in this paper the problems of fuzzy binary relations on fuzzy n cell number space and their applications are investigated firstly we have defined some fuzzy approximation relations on fuzzy n cell number space and studied their properties secondly as application we have developed an algorithmic version of classification in an imprecise or uncertain environment by using the fuzzy approximation relations practical examples are provided to show the application and rationality of the proposed techniques

signal modeling with self similar spl alpha stable processes the fractional levy stable motion model the purpose of the correspondence is the introduction of fractional levy stable motion flsm as a model for signals with long memory and high variability commonly encountered in natural processes we present a concise description of this model from a signal processing viewpoint and its successful application to real world infrared signals for the purpose of resolution enhancement via stochastic interpolation

a gauss newton method for the synthesis of periodic outputs with central pattern generators it is assumed that a central pattern generator possesses an exponentially stable limit cycle which originates a periodic output signal we propose a method based on a gauss newton iteration to determine the values of the neural coupling parameters that allows to approximate a given reference output signal we present two applications the first is a ring network of morris lecar neurons where the output of the system is the sum of the membrane potential of all neurons the second is a network of six neural cells for the generation of the leg movements of a hexapod

ranking of multidimensional uncertain information based on metrics on the fuzzy ellipsoid number space on the usual high dimensional fuzzy number space the usual supremum metric d derived by the hausdorff metric between the level sets of usual n dimension fuzzy numbers and the p metric rho p are the most common metrics however due to the complexity of the level sets of usual n dimensional fuzzy numbers the two kinds of metrics not only have a tendency to be rougher but also are difficult to give concrete expression formulas this affects their theory and application research in this paper some new metrics on fuzzy ellipsoid number space are introduced which not only can better reveal the difference between two different fuzzy ellipsoid numbers but also have concrete expression formulas expressed with the level set functions of fuzzy ellipsoid numbers and the properties of the new introduced metrics and the relationships between the new metrics and the usual metrics d and rho p are studied and some results are obtained then we give the concept of supremum infimum of bounded subsets of fuzzy ellipsoid number space and obtain its concrete calculation formula and then by using the obtained results we propose a method to rank multidimensional uncertain information and give a practical example to show the application and the rationality of the proposed techniques