robust spatially constrained fuzzy c means algorithm for brain mr image segmentation abstract objective accurate brain tissue segmentation from magnetic resonance mr images is an essential step in quantitative brain image analysis and hence has attracted extensive research attention however due to the existence of noise and intensity inhomogeneity in brain mr images many segmentation algorithms suffer from limited robustness to outliers over smoothness for segmentations and limited segmentation accuracy for image details to further improve the accuracy for brain mr image segmentation a robust spatially constrained fuzzy c means rscfcm algorithm is proposed in this paper method firstly a novel spatial factor is proposed to overcome the impact of noise in the images by incorporating the spatial information amongst neighborhood pixels the proposed spatial factor is constructed based on the posterior probabilities and prior probabilities and takes the spatial direction into account it plays a role as linear filters for smoothing and restoring images corrupted by noise therefore the proposed spatial factor is fast and easy to implement and can preserve more details secondly the negative log posterior is utilized as dissimilarity function by taking the prior probabilities into account which can further improve the ability to identify the class for each pixel finally to overcome the impact of intensity inhomogeneity we approximate the bias field at the pixel by pixel level by using a linear combination of orthogonal polynomials the fuzzy objective function is then integrated with the bias field estimation model to overcome the intensity inhomogeneity in the image and segment the brain mr images simultaneously results to demonstrate the performances of the proposed algorithm for the images with without skull stripping the first group of experiments is carried out in clinical 3t weighted brain mr images which contain quite serious intensity inhomogeneity and noise then we quantitatively compare our algorithm to state of the art segmentation approaches by using jaccard similarity on benchmark images obtained from ibsr and brainweb with different level of noise and intensity inhomogeneity the comparison results demonstrate that the proposed algorithm can produce higher accuracy segmentation and has stronger ability of denoising especially in the area with abundant textures and details conclusion in this paper the rscfcm algorithm is proposed by utilizing the negative log posterior as the dissimilarity function introducing a novel factor and integrating the bias field estimation model into the fuzzy objective function this algorithm successfully overcomes the drawbacks of existing fcm type clustering schemes and em type mixture models our statistical results mean and standard deviation of jaccard similarity for each tissue on both synthetic and clinical images show that the proposed algorithm can overcome the difficulties caused by noise and bias fields and is capable of improving over 5 segmentation accuracy comparing with several state of the art algorithms

exclusion and persistence in deterministic and stochastic chemostat models abstract we first introduce and analyze a variant of the deterministic single substrate chemostat model in this model microbe removal and growth rates depend on biomass concentration with removal terms increasing faster than growth terms using a comparison principle we show that persistence of all species is possible in this scenario then we turn to modelling the influence of random fluctuations by setting up and analyzing a stochastic differential equation in particular we show that random effects may lead to extinction in scenarios where the deterministic model predicts persistence on the other hand we also establish some stochastic persistence results

graph grammars with neighbourhood controlled embedding abstract a central feature that distinguishes graph grammars we consider grammars generating sets of node labelled undirected graphs only from string grammars is that in the former one has to provide a mechanism by which a daughter graph the right hand side of a production can be embedded in the rest of the mother graph while in the latter this embedding is provided automatically by the structure that all strings possess left to right orientation in this paper we consider a possible classification of embedding mechanisms for node rewriting graph grammars this classification originates from the basic ideas of 9 on the one hand it allows one to fit a number of existing notions of a graph grammar into a common framework and on the other hand it points out new natural possibilities for defining the embedding mechanism in a graph grammar the relationship between the graph language generating power of graph grammars using various embedding mechanisms is established

a stochastic model for internal hiv dynamics in this paper we analyse a stochastic model representing hiv internal virus dynamics the stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling we show that the model established in this paper possesses non negative solutions as this is essential in any population dynamics model we also carry out analysis on the asymptotic behaviour of the model we approximate one of the variables by a mean reverting process and find out the mean and variance of this process numerical simulations conclude the paper

development of fuzzy and control charts using α cuts statistical process control spc is an approach that uses statistical techniques to monitor the process shewhart introduced the control charts that are one of the most important techniques of quality control to detect if assignable causes exist the widely used control charts are and these are called traditional variable control charts in the traditional variable control charts center line upper control limit and lower control limit are represented by numeric values a process is either in control or out of control depending on numeric observation values for many problems control limits could not be so precise uncertainty comes from the measurement system including operators and gauges and environmental conditions in this context fuzzy set theory is a useful tool to handle this uncertainty numeric control limits can be transformed to fuzzy control limits by using membership functions if a sample mean is too close to the control limits and the used measurement system is not so sensitive the decision may be faulty fuzzy control limits provide a more accurate and flexible evaluation this study constructs the fuzzy and control charts with a cuts an application is presented for fuzzy control charts by using fuzzy and control charts the flexibility of traditional control limits is increased

on the structure of rough prime primary ideals and rough fuzzy prime primary ideals in commutative rings this paper is a continuation of ideas presented by davvaz roughness in rings inform sci 164 2004 147 163 roughness based on fuzzy ideals inform sci 176 2006 2417 2437 we introduce the notions of rough prime primary ideals and rough fuzzy prime primary ideals in a ring and give some properties of such ideals also we discuss the relations between the upper and lower rough prime primary ideals and the upper and lower approximations of their homomorphism images

persistence and extinction for a class of stochastic sis epidemic models with nonlinear incidence rate abstract in this paper a class of stochastic sis epidemic models with nonlinear incidence rate is investigated it is shown that the extinction and persistence of the disease in probability are determined by a threshold value r 0 that is if r 0 1 and an additional condition holds then disease dies out and if r 0 1 then disease is weak permanent with probability one to obtain the permanence in the mean of the disease a new quantity r 0 is introduced and it is proved that if r 0 1 the disease is permanent in the mean with probability one furthermore the numerical simulations are presented to illustrate some open problems given in remarks 1 3 and 5 of this paper

a measure theoretic axiomatization of fuzzy sets abstract using measurement theory this paper examines three empirical structures that underlie the representation of fuzzy sets the fuzzy membership structure the fuzzy component structure and the fuzzy system structure these qualitative structures justify the use of the standard min max system to represent fuzzy sets the results of this study facilitate the development of a sound measurement theoretic axiomatization of fuzzy systems

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

a review and comparison of six reasoning methods abstract five fuzzy reasoning methods are reviewed and their performance is compared with respect to a fuzzy control system model developed by an objective method based on three sets of real life data it is found from the investigation that the reasoning precision the calculation time and the number of possible input states to which a given reasoning method responds differ according to each reasoning method generally the point valued reasoning methods which are based on the assumption that connectives are crisp give better precision and shorter calculation time when the connectives are assumed to be linguistic reasoning with interval valued fuzzy sets are more appropriate to represent linguistic uncertainty for this reason type ii fuzziness generated with interval valued fuzzy sets are better handled with interval valued reasoning methods

a fuzzy minimax clustering model and its applications fuzzy clustering is an effective clustering approach which associates a data point with multiple clusters standard fuzzy clustering models like fuzzy c means are based on minimizing the total cluster variation which is defined as the sum of the distances between the data points and their corresponding cluster centers weighted by the membership degrees in this paper we propose a fuzzy minimax clustering model by minimizing the maximum value of the set of weighted cluster variations in such a way that they satisfy a prior distribution we derive a necessary condition for the extremum point of the fuzzy minimax clustering model and then design an iterative algorithm for solving the extremum point several numerical examples on comparing fuzzy c means and fuzzy minimax clustering models are given which demonstrate that the prior distribution improves the quality of the clustering results significantly

a stochastic model of aids and condom use in this paper we introduce stochasticity into a model of aids and condom use via the technique of parameter perturbation which is standard in stochastic population modelling we show that the model established in this paper possesses non negative solutions as desired in any population dynamics we also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system

fuzzy p measure on the real line abstract the fuzzy measurable space on the real line say is defined by means of fuzzy relation less or equal 5 the main properties of are given these results are used for investigation of fuzzy p measure on the principal emphasis is laid on the connections between a fuzzy p measure and its cumulative distribution function a theorem extending a fuzzy p measure to is shown

a model for the measurement of membership and the consequences of its empirical implementation representation and uniqueness theorems are presented for the fundamental measurement of the membership of a fuzzy set when the domain of discourse is order dense the conclusion that membership is on an interval scale is justified by the inapplicability of extensive measurement to fuzziness and the lack of a natural origin for membership some descriptive statistics are also presented from an empirical study currently in progress to construct membership functions they suggest that subjects differ in their perception of fuzziness and that the models in the literature for certain linguistic operators such as not very and antonym are not sufficiently general to account for the range of individual perceptions of vague attributes a more general mathematical model is proposed the question of the meaningfulness of statements about membership functions is also discussed in the light of the assertion that membership can be fundamentally measured at best on an interval scale some of the difficulties which arise in fuzzy set theory due to this property are illustrated and a solution is suggested involving the use of a function which is derived from membership but is on an absolute scale

asymptotic properties of an hiv aids model with a time delay a mathematical model for hiv aids with explicit incubation period is presented as a system of discrete time delay differential equations and its important mathematical features are analysed the disease free and endemic equilibria are found and their local stability investigated we use the lyapunov functional approach to show the global stability of the endemic equilibrium qualitative analysis of the model including positivity and boundedness of solutions and persistence are also presented the hiv aids model is numerically analysed to asses the effects of incubation period on the dynamics of hiv aids and the demographic impact of the epidemic using the demographic and epidemiological parameters for zimbabwe

fuzzy sets and decision analysis abstract this survey points out recent advances in multiple attribute decision making methods dealing with fuzzy or ill defined information fuzzy maut as well as fuzzy outranking methods are reviewed aggregation procedures choice problems and treatment of interactive attributes are covered trends in research and open problems are indicated

interval type 2 credibilistic clustering for pattern recognition this paper presents a new approach to interval type 2 fuzzy clustering in order to consider compactness within the clusters and separation of them simultaneously the objective function of this paper is designed such that it generates both degrees of membership and non membership of each data in each cluster and integrates them using credibility concept also a new approach to separation of clusters is proposed and utilized in designing the objective function in this approach the borders of clusters and therefore their compactness contribute in attaining their separation so the separation of clusters is not assessed only by the distance of their centers the credibility degrees are transformed to interval type 2 form to handle different sources of uncertainty finally a new validity index to characterize the number of clusters based on proposed approach to separation of clusters and choquet integrals are proposed the advantages of paper contributions are illustrated using several examples a new objective function based fuzzy clustering is introduced using credibility concept a new approach to separation of clusters is presented a new validity index is designed by proposed approach to separation and choquet integral the obtained results show that proposed model can handle different types of clusters

stationary distribution and extinction of a stochastic seir epidemic model with standard incidence abstract in this paper we consider a stochastic seir epidemic model with standard incidence by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the existence of ergodic stationary distribution to the model our result does not depend on the positive endemic equilibrium e of the deterministic system which improves the previous result to a greater extent moreover we also establish sufficient conditions for extinction of the disease

interval type 2 relative entropy fuzzy c means clustering fuzzy set theory especially type 2 fuzzy set theory provides an efficient tool for handling uncertainties and vagueness in real world observations among various clustering techniques type 2 fuzzy clustering methods are the most effective methods in the case of having no prior knowledge about observations while uncertainties in type 2 fuzzy clustering parameters are investigated by researchers uncertainties associated with membership degrees are not very well discussed in the literature in this paper investigating the latter uncertainties is our concern and interval type 2 relative entropy fuzzy c means it2 refcm clustering method is proposed the computational complexity of the proposed method is discussed and its performance is examined using several experiments the obtained results show that the proposed method has a very good ability in detecting noises and assignment of suitable membership degrees to observations

the asymptotic behaviours of an epidemic model with two correlated stochastic perturbations abstract this paper mainly discussed the asymptotic dynamics of stochastic si epidemic model and its improved model taking two stochastic disturbances into account in the deterministic model in the form of gaussian white noises we obtained its invariant probability distribution by applying fokker planck equation we mainly focuses on the influence of the size of the correlation coefficient of two stochastic perturbations on stochastic epidemic model under two stochastic disturbance the correlative of two stochastic disturbances can affect the dynamics of the epidemic model and the effects are different if we introduce the stochastic disturbance in different ways

the reproductive number for an hiv model with differential infectivity and staged progression we formulate an hiv epidemic model with differential infectivity and staged disease progression to account for variations in viral loads and in the rate of disease progression in infected individuals the stability of the infection free equilibrium determines the threshold conditions under which the modeled disease either dies out or persists in the population this stability expressed in terms of the epidemic reproductive number can be determined by the spectral radius of the next generation operator or from the eigenvalues of the jacobian matrix for the model system linearized about the infection free equilibrium we derive an explicit formula for the reproductive number employing both of these techniques by investigating the spectral radius of the next generation operator and by directly applying m matrix theory with recursive forward and backward inductions to characterize the eigenvalues of the jacobian matrix in terms of the reproductive number

a mathematical approach to hiv infection dynamics in order to obtain a comprehensive form of mathematical models describing nonlinear phenomena such as hiv infection process and aids disease progression it is efficient to introduce a general class of time dependent evolution equations in such a way that the associated nonlinear operator is decomposed into the sum of a differential operator and a perturbation which is nonlinear in general and also satisfies no global continuity condition an attempt is then made to combine the implicit approach usually adapted for convective diffusion operators and explicit approach more suited to treat continuous type operators representing various physiological interactions resulting in a semi implicit product formula decomposing the operators in this way and considering their individual properties it is seen that approximation solvability of the original model is verified under suitable conditions once appropriate terms are formulated to describe treatment by antiretroviral therapy the time dependence of the reaction terms appears and such product formula is useful for generating approximate numerical solutions to the governing equations with this knowledge a continuous model for hiv disease progression is formulated and physiological interpretations are provided the abstract theory is then applied to show existence of unique solutions to the continuous model describing the behavior of the hiv virus in the human body and its reaction to treatment by antiretroviral therapy the product formula suggests appropriate discrete models describing the dynamics of host pathogen interactions with hiv1 and is applied to perform numerical simulations based on the model of the hiv infection process and disease progression finally the results of our numerical simulations are visualized and it is observed that our results agree with medical and physiological aspects

a stochastic sis epidemic model incorporating media coverage in a two patch setting in this paper we investigate the stochastic disease dynamics of an sis epidemic model on two patches incorporating media coverage we give the global existence and positivity of the solutions and the sufficient conditions for almost surely exponentially stability of the disease free equilibrium which means that the disease will be stochastic extinction furthermore we perform some numerical simulations to validate the analytical finding

solution of multivariable fuzzy equations abstract a method for the solution of multivariable fuzzy equations and inequalities is proposed the proposed method is an extension of sanchez technique for a single fuzzy equation a numerical example is given

threshold behavior in a stochastic siqr epidemic model with standard incidence and regime switching abstract this paper is concerned with the dynamical behavior of a stochastic siqr epidemic model with standard incidence which is disturbed by both white and telegraph noises firstly we obtain sufficient conditions for persistence in the mean of the disease then we establish sufficient conditions for extinction of the disease in addition in the case of persistence we get sufficient conditions for the existence of positive recurrence of the solutions by constructing a suitable stochastic lyapunov function with regime switching meanwhile the threshold between persistence in the mean and extinction of the stochastic system is also obtained finally some numerical simulations are introduced to demonstrate the analytical results

a new credibilistic clustering algorithm abstract this paper focuses on credibilistic clustering approach a data clustering method partitions unlabeled data sets into clusters and labels them for various goals such as computer vision and pattern recognition there are different models for objective function based fuzzy clustering such as fuzzy c means fcm possibilistic c mean pcm and their combinations credibilistic clustering is a new approach in this field in this paper a new credibilistic clustering model is introduced in which credibility measure is applied instead of possibility measure in possibilistic clustering also in objective function the separation of clusters is considered in addition to the compactness within clusters the steps of clustering are designed based on this approach finally the main issues about model are discussed and the results of computational experiments are presented to show the efficiency of the proposed model

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

type 2 fuzzy neural networks with fuzzy clustering and differential evolution optimization in many real world problems involving pattern recognition system identification and modeling control decision making and forecasting of time series available data are quite often of uncertain nature an interesting alternative is to employ type 2 fuzzy sets which augment fuzzy models with expressive power to develop models which efficiently capture the factor of uncertainty the three dimensional membership functions of type 2 fuzzy sets offer additional degrees of freedom that make it possible to directly and more effectively account for model s uncertainties type 2 fuzzy logic systems developed with the aid of evolutionary optimization forms a useful modeling tool subsequently resulting in a collection of efficient if then rules the type 2 fuzzy neural networks take advantage of capabilities of fuzzy clustering by generating type 2 fuzzy rule base resulting in a small number of rules and then optimizing membership functions of type 2 fuzzy sets present in the antecedent and consequent parts of the rules the clustering itself is realized with the aid of differential evolution several examples including a benchmark problem of identification of nonlinear system are considered the reported comparative analysis of experimental results is used to quantify the performance of the developed networks

a convex semi nonnegative matrix factorisation approach to fuzzy c means clustering we propose an alternative approach to fuzzy c means clustering which eliminates the weighting exponent parameter of conventional algorithms it is based on a particular convex factorisation of data matrix the proposed method is invariant under certain linear transformations of the data including principal component analysis we tested its accuracy using both synthetic data and real datasets and compared it to that provided by the usual fuzzy c means algorithm we were able to ascertain that our proposal can be a credible yet easier alternative to this approach to fuzzy clustering moreover it showed no noticeable sensitivity to the initial guess of the partition matrix

minimax e stable cluster validity index for type 2 fuzziness in this paper we concentrate on the usage of uncertainty associated with the level of fuzziness in determination of the number of clusters in fcm for any data set we propose a minimax e stable cluster validity index based on the uncertainty associated with the level of fuzziness within the framework of interval valued type 2 fuzziness if the data have a clustered structure the optimum number of clusters may be assumed to have minimum uncertainty under upper and lower levels of fuzziness upper and lower values of the level of fuzziness for fuzzy c mean fcm clustering methodology have been found as m 2 6 and 1 4 respectively in our previous studies our investigation shows that the stability of cluster centers with respect to the level of fuzziness is sufficient for the determination of the number of clusters

stability of an seir epidemic model with independent stochastic perturbations abstract for an epidemic model of the type mentioned we prove a theorem on almost sure exponential stability of the disease free equilibrium for small values of the diffusion parameter we describe the stability of the disease free equilibrium point in terms of an appropriate analogue r of the basic reproduction number r 0 of the deterministic special case whenever 0 then r r 0 for small values of the stability theorem guarantees almost sure exponential stability whenever r 1 we also discuss the effect of increasing

the threshold of a stochastic sis epidemic model with vaccination this paper is concerned with the long time behavior of a stochastic sis epidemic model with vaccination sufficient conditions for extinction and persistence in mean are obtained we find a threshold of the stochastic model which determines the outcome of the disease in case the white noises are small at last some numerical simulations are carried out to support our results

results on nlc grammars with one letter terminal alphabets abstract node label controlled graph grammars nlc grammars are a mechanism to generate sets of graphs called graph languages this paper examines the generating power of nlc grammars with a restricted connection relation and some closure properties of the class of nlc languages also a modified language generating mechanism for nlc grammars is introduced and the resulting class of graph languages is compared to the class of nlc languages all results are based on grammars with one letter terminal alphabets

the long time behavior of di sir epidemic model with stochastic perturbation in this paper we present a di sir epidemic model with two categories stochastic perturbations the long time behavior of the two stochastic systems is studied mainly we show how the solution goes around the infection free equilibrium and the endemic equilibrium of deterministic system under different conditions

interval valued possibilistic fuzzy c means clustering algorithm type 2 fuzzy sets have drawn increasing research attentions in the pattern recognition community since it is capable of modeling various uncertainties that cannot be appropriately managed by usual fuzzy sets although it has been introduced to data clustering most widely used clustering approaches based on type 2 fuzzy sets still suffer from inherent drawbacks such as the sensitiveness to outliers and initializations in this paper we incorporate the interval valued fuzzy sets into the hybrid fuzzy clustering scheme and thus propose the interval valued possibilistic fuzzy c means ipfcm clustering algorithm we use both fuzzy memberships and possibilistic typicalities to model the uncertainty implied in the data sets and develop solutions to overcome the difficulties caused by type 2 fuzzy sets such as the construction of footprint of uncertainty type reduction and defuzzification we compare the proposed algorithm with five fuzzy clustering approaches including the fcm pcm pfcm ifcm and ipcm on two dimensional gaussian data sets and four multi dimensional benchmark data sets we also apply these clustering techniques to segment the brain magnetic resonance images and natural images our results show that the proposed ipfcm algorithm is more robust to outliers and initializations and can produce more accurate clustering results

enhanced fuzzy system models with improved fuzzy clustering algorithm although traditional fuzzy models have proven to have high capacity of approximating the real world systems they have some challenges such as computational complexity optimization problems subjectivity etc in order to solve some of these problems this paper proposes a new fuzzy system modeling approach based on improved fuzzy functions to model systems with continuous output variable the new modeling approach introduces three features i an improved fuzzy clustering ifc algorithm ii a new structure identification algorithm and iii a nonparametric inference engine the ifc algorithm yields simultaneous estimates of parameters of c regression models together with fuzzy c partitioning of the data to calculate improved membership values with a new membership function the structure identification of the new approach utilizes ifc instead of standard fuzzy c means clustering algorithm to fuzzy partition the data and it uses improved membership values as additional input variables along with the original scalar input variables for two different choices of regression methods least squares estimation or support vector regression to determine ldquofuzzy functionsrdquo for each cluster with novel ifc one could learn the system behavior more accurately compared to other fsm models the nonparametric inference engine is a new approach which uses the alike nearest neighbor method for reasoning empirical comparisons indicate that the proposed approach yields comparable or better accuracy than fuzzy or neuro fuzzy models based on fuzzy rules bases as well as other soft computing methods

stochastic permanence of an siqs epidemic model with saturated incidence and independent random perturbations abstract this article discusses a stochastic siqs epidemic model with saturated incidence we assume that random perturbations always fluctuate at the endemic equilibrium the existence of a global positive solution is obtained by constructing a suitable lyapunov function under some suitable conditions we derive the stochastic boundedness and stochastic permanence of the solutions of a stochastic siqs model some numerical simulations are carried out to check our results

analysis of a stochastic hiv 1 infection model with degenerate diffusion abstract this paper studies a stochastic hiv 1 infection model with degenerate diffusion the asymptotic dynamics of the stochastic model are shown to be governed by a threshold parameter when the parameter is negative the infection is predicted to go extinct exponentially while the level of healthy cells converges weakly to a unique invariant measure when the threshold parameter is positive the solution of the stochastic model converges polynomially to a unique invariant probability measure indicating that the system admits a unique ergodic stationary distribution numerical simulations are conducted to show the analytical results these results highlight the role of environmental noise in the spread of hiv 1 the method can also be applied to the non degenerate systems

upper and lower values for the level of fuzziness in fcm the level of fuzziness is a parameter in fuzzy system modeling which is a source of uncertainty in order to explore the effect of this uncertainty one needs to investigate and identify effective upper and lower boundaries of the level of fuzziness for this purpose fuzzy c means fcm clustering methodology is investigated to determine the effective upper and lower boundaries of the level of fuzziness in order to capture the uncertainty generated by this parameter in this regard we propose to expand the membership function around important information points of fcm these important information points are cluster centers and the mass center at these points it is known that the level of fuzziness has no effect on the membership values in this way we identify the counter intuitive behavior of membership function near these particular information points it will be shown that the upper and lower values of the level of fuzziness can be identified hence the uncertainty generated by this parameter can be encapsulated

fuzzy clustering of time series in the frequency domain traditional and fuzzy cluster analyses are applicable to variables whose values are uncorrelated hence in order to cluster time series data which are usually serially correlated one needs to extract features from the time series the values of which are uncorrelated the periodogram which is an estimator of the spectral density function of a time series is a feature that can be used in the cluster analysis of time series because its ordinates are uncorrelated additionally the normalized periodogram and the logarithm of the normalized periodogram are also features that can be used in this paper we consider a fuzzy clustering approach for time series based on the estimated cepstrum the cepstrum is the spectrum of the logarithm of the spectral density function we show in our simulation studies for the typical generating processes that have been considered fuzzy clustering based on the cepstral coefficients performs very well compared to when it is based on other features

global stability of two group sir model with random perturbation abstract in this paper we discuss the two group sir model introduced by guo li and shuai h b guo m y li z shuai global stability of the endemic equilibrium of multigroup sir epidemic models can appl math q 14 2006 259 284 allowing random fluctuation around the endemic equilibrium we prove the endemic equilibrium of the model with random perturbation is stochastic asymptotically stable in the large in addition the stability condition is obtained by the construction of lyapunov function finally numerical simulations are presented to illustrate our mathematical findings

dynamical behavior of a stochastic sei epidemic model with saturation incidence and logistic growth abstract in this paper we investigate the dynamical behavior of a stochastic sei epidemic model with saturation incidence and logistic growth firstly by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the solutions to the model then we obtain sufficient conditions for extinction of the disease in two cases that is the first case is that the susceptible population survival and infected and exposed populations extinction the second case is that all the populations extinction

the ergodicity and extinction of stochastically perturbed sir and seir epidemic models with saturated incidence abstract in this paper we include stochastic perturbations into sir and seir epidemic models with saturated incidence and investigate their dynamics according to the basic reproduction number r 0 the long time behavior of the two stochastic systems is studied mainly we utilize stochastic lyapunov functions to show under some conditions the solution has the ergodic property as r 0 1 while exponential stability as r 0 1 at last we make simulations to conform our analytical results

restrictions on nlc graph grammars several models of graph grammars have been studied with the objective of generating graphs from graphs using a finite set of derivation rules in this way possibly infinite sets of graphs called graph languages can be finitely defined one aspect that must be addressed in any such model is the embedding problem that is when a production is applied how does the new subgraph get reconnected to the original graph node label controlled nlc grammars solve this problem in an elegant way that depends only on the labels of nodes in the new and original graphs this paper examines certain restrictions on nlc grammars similar to the chomsky or greibach normal forms for context free string grammars for example one restriction we consider requires each production to produce a terminal labeled node similar to greibach normal form we also consider restrictions on the form which the embedding mechanism can take our result is that each of the restrictions we examine causes a reduction in generating power for the grammars finally we discuss some directions for future research on nlc grammars

stationary distribution and extinction of a stochastic sirs epidemic model with standard incidence abstract in this paper we consider a stochastic sirs epidemic model with standard incidence by constructing suitable stochastic lyapunov function we establish sufficient conditions for the existence of ergodic stationary distribution of the model moreover we also establish sufficient conditions for extinction of the disease

type i and type ii fuzzy system modeling abstract two system modeling approaches are proposed with a unification of fuzzy methodologies type i and type ii knowledge representation are reviewed together with their proposed approximate reasoning schemes type i representation and inference are based on boolean normal forms type i models are myopic because in these models either the disjunctive or the conjunctive boolean normal forms are selected rather arbitrarily for knowledge representation and inference and then they are fuzzified whereas in type ii models representation and inference are based on fuzzy disjunctive and conjunctive normal forms which are derived from the fuzzy truth tables