fuzzy least squares linear regression analysis using shape preserving operations abstract in this paper we introduce a new class of fuzzy linear regression model with fuzzy input fuzzy output data using shape preserving arithmetic operations on l r fuzzy numbers for least squares fitting a mixed nonlinear programming approach is used to derive the satisfying solution this answers one of diamond s questions inform sci 46 1988 141

convergence of numerical solution to stochastic delay differential equation with poisson jump and markovian switching the main purpose of this paper is to study the convergence of numerical solutions to a class of stochastic delay differential equations with poisson jump and markovian switching a numerical approximation scheme is proposed to approximate the solution to stochastic delay differential equations with poisson jump and markovian switching it is proved that the euler approximation solution converge to the analytic solution in probability under weaker conditions some known results are generalized and improved an example is provided to illustrate our theory

convergence and stability of numerical solutions to sddes with markovian switching a class of linear stochastic delay differential equations with markovian switching is considered the main aim of this paper is to investigate the convergence and stability of the euler method of the equations it is proved that the euler method is convergent with strong order p 1 2 the ms stable properties of the euler scheme are also studied

convex solutions of polynomial like iterative equations in this paper convex solutions and concave solutions of polynomial like iterative equations are investigated a result for non monotonic solutions is given first and applied then to prove the existence of convex continuous solutions and concave ones furthermore another condition for convex solutions which is weaker in some aspects is also given the uniqueness and stability of those solutions are also discussed

convergence of numerical solutions to stochastic age dependent population equations with markovian switching in this paper a class of stochastic age dependent population equations with markovian switching is considered the main aim of this paper is to investigate the convergence of the numerical approximation of stochastic age dependent population equations with markovian switching it is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions an example is given for illustration

min and max operators for gradual intervals this paper presents a new and a more general formulation of the min and max operations for gradual intervals initially proposed for the special case of triangular fuzzy intervals gradual intervals generalize the conventional interval representation by increasing its specificity thereby making it possible to represent the imprecision and the uncertainty via the notion of gradualness in this context a new interpretation of fuzzy intervals through the notion of gradual intervals is developed the originality of the proposed methodology lies in the extension of inter interval relations to the gradual case according to midpoint radius representation

a possibilistic regression based on gradual interval b splines application for hyperspectral imaging lake sediments abstract according to an epistemic view of intervals this paper proposes a possibilistic regression based on gradual interval b splines to represent the input output data mapping in this context an improvement of the parametric fuzzy regression through the notion of gradual interval b splines is proposed the proposed gradual regression based on b splines can be regarded as an extension of the nonparametric interval based regression where an uncertain dimension is integrated the proposed method is validated through illustrative and comparative examples moreover it is applied for modeling the input output behavior between reflectance and wavelengths in an application for hyperspectral imaging for lake sediments

convergence of numerical solutions to neutral stochastic delay differential equations with markovian switching recently numerical solutions of stochastic differential equations have received a great deal of attention it is surprising that there are not any numerical methods established for neutral stochastic delay differential equations yet in the paper the euler maruyama method for neutral stochastic delay differential equations is developed the key aim is to show that the numerical solutions will converge to the true solutions under the local lipschitz condition

convergence of numerical solutions to stochastic differential equations with markovian switching abstract the paper develops strong approximation schemes for solutions of stochastic differential equations with markovian switching sdewmss the convergent orders of existing strong numerical schemes all are 0 5 this paper provides a convergence theorem for the construction of strong approximations of any given order of convergence for sdewmss and then constructs the order 1 scheme the order 1 5 scheme the paper also develops a new way to simulate the markov chain and hence the order 1 scheme finally a numerical example is provided to illustrate the theoretical results

fuzzy least squares algorithms for interactive fuzzy linear regression models fuzzy regression analysis can be thought of as a fuzzy variation of classical regression analysis it has been widely studied and applied in diverse areas in general the analysis of fuzzy regression models can be roughly divided into two categories the first is based on tanaka s linear programming approach the second category is based on the fuzzy least squares approach in this paper new types of fuzzy least squares algorithms with a noise cluster for interactive fuzzy linear regression models are proposed these algorithms are robust for the estimation of fuzzy linear regression models especially when outliers are present numerical examples are given to detail the effectiveness of this approach

iterative equations in banach spaces abstract let x be a banach space let k x f x x lipschitz f id sup and let p k x k x f k x by applying the banach contraction principle we prove that if p is sufficiently close in a certain sense to the identity then the equation p f f has a unique solution f as a corollary we obtain results on iterative equations of the types i a i f i x f x or i a i f i x f x with operator coefficients in banach spaces

strong predictor corrector euler maruyama methods for stochastic differential equations with markovian switching in this paper numerical methods for solving stochastic differential equations with markovian switching sdewmss are developed by pathwise approximation the proposed family of strong predictor corrector euler maruyama methods is designed to overcome the propagation of errors during the simulation of an approximate path this paper not only shows the strong convergence of the numerical solution to the exact solution but also reveals the order of the error under some conditions on the coefficient functions a natural analogue of the p stability criterion is studied numerical examples are given to illustrate the computational efficiency of the new predictor corrector euler maruyama approximation

transversal homoclinic points of a class of conservative diffeomorphisms abstract we develop a global graph transformation to obtain estimates for certain invariant manifolds of a class of area preserving diffeomorphisms with symmetries the existence of homoclinic or heteroclinic points and the analyticity of the angle between the invariant manifolds at them is proved for the henon and the standard maps a lower bound of this angle is given for a large set of values of the parameters

convergence and stability of the semi implicit euler method for a linear stochastic differential delay equation the paper deals with convergence and stability of the semi implicit euler method for a linear stochastic differential delay equation it is proved that the semi implicit euler method is convergent with strong order p the conditions under which the method is ms stable and gms stable are determined and the numerical experiments are given

from fuzzy regression to gradual regression interval based analysis and extensions abstract this paper proposes an analysis of parametric interval based regression methodologies according to ontic and epistemic visions of intervals when assuming an epistemic point of view a new interpretation of fuzzy regression through the notion of gradual intervals is developed which leads to gradual regression gradual regression is viewed as an extension of the imprecise interval based regression which is obtained by integrating an uncertain dimension gradual intervals can yield improved specificity compared to conventional intervals and jointly consider the concepts of imprecision and uncertainty through a single and coherent formalism the formulation of the gradual regression problem its resolution and the propagation of the information through the obtained regressive models are carried out via gradual interval arithmetic the proposed method allows not only the extension of the interval vision to the gradual case but also interesting interpretations according to non additive confidence measure theories possibility and belief functions

solutions of equivariance for a polynomial like iterative equation using fixed point theorems we discuss continuous solutions of equivariance for a polynomial like iterative equation on the real line where is a closed subgroup of the general linear group gl r our main results guarantee the existence of solutions with certain kinds of symmetry we show that under restrictive hypotheses similar results can be proved in a higher dimensional case where the symmetry group is a topologically finitely generated subgroup of the group generated by rotations and dilations in n dimensional euclidean space

ms stability of the euler maruyama method for stochastic differential delay equations the aim of this paper is to investigate the stability of the euler maruyama method for the stochastic differential equations with time delay the definition of ms stability of numerical methods is established the condition of the mean square stability of analytical solution is obtained for a linear scalar system with multiplicative noise and the ms stability of the numerical scheme is proved

decreasing solutions and convex solutions of the polynomial like iterative equation abstract in this paper we prove the existence and uniqueness of decreasing solutions for the polynomial like iterative equation so as to answer problem 2 in j zhang l yang w zhang some advances on functional equations adv math china 24 1995 385 405 or problem 3 in w zhang j a baker continuous solutions of a polynomial like iterative equation with variable coefficients ann polon math 73 2000 29 36 furthermore we completely investigate increasing convex or concave solutions and decreasing convex or concave solutions of this equation so that the results obtained in w zhang k nikodem b xu convex solutions of polynomial like iterative equations j math anal appl 315 2006 29 40 are improved

interval regression by tolerance analysis approach in interval linear regression analysis we are given crisp or interval data and we are to determine appropriate interval regression parameters there are various methods for interval regression many of them possess the property that while some of the resulting interval regression parameters are very wide the other parameters are crisp this drawback is the main limiting factor for such methods and much effort has been devoted to overcoming it we propose a method motivated by tolerance analysis in linear systems our method yields intervals for regression parameters the widths of which are proportional to an in advance given vector of parameters moreover the method is computationally very cheap and provides a natural measure of quality of a model first we formulate the method for the basic model of crisp input crisp output data and then extend it to crisp input interval output and interval input interval output models for the interval valued cases we study several formulations of the solution concept possibility strong possibility weak possibility necessity here strong possibility is a new concept proposed as a natural counterpart to the remaining ones we prove that the method provides optimal interval parameters meeting centrality and proportionality requirements we also show that the method provides interval regression parameters satisfying various versions of tanaka lee s inclusion property we also derive a form of a complementarity theorem for the weak possibility and necessity solution concepts since practical problems may be affected by outlying observations we show that our approach is easily adapted to deal with them we illustrate the theory by examples

possibilistic linear regression analysis for fuzzy data abstract fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined recently it has become important to deal with fuzzy data in connection with expert knowledge three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data since our formulations can be reduced to linear programming problems the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters this approach can be regarded as a fuzzy interval analysis in a fuzzy environment

the general exact bijective continuous solution of feigenbaum s functional equation solutionsf of feigenbaum s functional equationf f x 1 f x where 0 is a fixed real number account for many of the fascinating properties of the behaviour of successive iterates of one parameter families of nonlinear maps in connection with the phenomenon of intermittency interesting families of exact solutions have recently been found for 0 these solutions can all be derived from continuous bijective solutions which are topologically equivalent to translations in this paper thegeneral exact continuous bijective solution is found for any 0 positive or negative in particular it is shown that forany 0 there are solutions which areinequivalent to translations and it is shown that bijective solutions equivalent to translations exist only when 0 1 these results considerably enlarge the stock of available exact solutions of feigenbaum s equation

introduction to the numerical analysis of stochastic delay differential equations abstract we consider the problem of the numerical solution of stochastic delay differential equations of ito form d x t f x t x t d t g x t x t d w t t 0 t and x t t for t 0 with given f g wiener noise w and given 0 with a prescribed initial function we indicate the nature of the equations of interest and give a convergence proof for explicit single step methods some illustrative numerical examples using a strong euler maruyama scheme 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

a revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals conventional fuzzy regression using possibilistic concepts allows the identification of models from uncertain data sets however some limitations still exist this paper deals with a revisited approach for possibilistic fuzzy regression methods indeed a new modified fuzzy linear model form is introduced where the identified model output can envelop all the observed data and ensure a total inclusion property moreover this model output can have any kind of spread tendency in this framework the identification problem is reformulated according to a new criterion that assesses the model fuzziness independently from the collected data distribution the potential of the proposed method with regard to the conventional approach is illustrated by simulation examples

hyersulam stability of the iterative equation with a general boundary restriction hyersulam stability has played an important role not only in the theory of functional equations but also in a variety of branches of mathematics such as differential equations integral equations and linear operators in the present paper we will discuss the hyersulam stability of the iterative equation with a general boundary restriction by the construction of a uniformly convergent sequence of functions we prove that for every approximate solution of such an equation there exists an exact solution near it

numerical methods for nonlinear stochastic differential equations with jumps we present and analyse two implicit methods for ito stochastic differential equations sdes with poisson driven jumps the first method ssbe is a split step extension of the backward euler method the second method cssbe arises from the introduction of a compensated martingale form of the poisson process we show that both methods are amenable to rigorous analysis when a one sided lipschitz condition rather than a more restrictive global lipschitz condition holds for the drift our analysis covers strong convergence and nonlinear stability we prove that both methods give strong convergence when the drift coefficient is one sided lipschitz and the diffusion and jump coefficients are globally lipschitz on the way to proving these results we show that a compensated form of the euler maruyama method converges strongly when the sde coefficients satisfy a local lipschitz condition and the pth moment of the exact and numerical solution are bounded for some p 2 under our assumptions both ssbe and cssbe give well defined unique solutions for sufficiently small stepsizes and ssbe has the advantage that the restriction is independent of the jump intensity we also study the ability of the methods to reproduce exponential mean square stability in the case where the drift has a negative one sided lipschitz constant this work extends the deterministic nonlinear stability theory in numerical analysis we find that ssbe preserves stability under a stepsize constraint that is independent of the initial data cssbe satisfies an even stronger condition and gives a generalization of b stability finally we specialize to a linear test problem and show that cssbe has a natural extension of deterministic a stability the difference in stability properties of the ssbe and cssbe methods emphasizes that the addition of a jump term has a significant effect that cannot be deduced directly from the non jump literature

robust stability and controllability of stochastic differential delay equations with markovian switching in this paper we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with markovian switching some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with markovian switching

extended support vector interval regression networks for interval input output data in many applications it is natural to use interval data because of uncertainty existence in the measurements variability in defining terms such as the temperature during a given day description for extremely behavior such as the maximum wind speed in a given area etc in order to handle such interval data a novel approach called the interval support vector interval regression networks isvirns is proposed the isvirns is extended from our previous work the support vector interval regression networks svirns it is easy to find that svirns can handle interval output data but for input data they must be crisp in this study the hausdorff distance is employed as the distance measure of interval data and is incorporated into the kernel functions of svirns to determine the initial structure of isvirns because the proposed approach can provide a better initial structure for isvirns it can have a faster convergent speed the experimental results with real data sets show the validity of the proposed isvirns

interval regression analysis using support vector networks support vector machines svms have been very successful in pattern classification and function estimation problems for crisp data in this paper the v support vector interval regression network v svirn is proposed to evaluate interval linear and nonlinear regression models for crisp input and output data as it is difficult to select an appropriate value of the insensitive tube width in e support vector regression network the proposed v svirn alleviates this problem by utilizing a new parametric insensitive loss function the proposed v svirn automatically adjusts a flexible parametric insensitive zone of arbitrary shape and minimal size to include the given data besides the proposed method can achieve automatic accuracy control in the interval regression analysis task for a priori chosen v at most a fraction v of the data points lie outside the interval model constructed by the proposed v svirn to be more precise v is an upper bound on the fraction of training errors and a lower bound on the fraction of support vectors hence the selection of v is more intuitive moreover the proposed algorithm here is a model free method in the sense that we do not have to assume the underlying model function experimental results are then presented which show the proposed v svirn is useful in practice especially when the noise is heteroscedastic that is the noise strongly depends on the input value x

fuzzy c ordered medoids clustering for interval valued data fuzzy clustering for interval valued data helps us to find natural vague boundaries in such data the fuzzy c medoids clustering fcmdc method is one of the most popular clustering methods based on a partitioning around medoids approach however one of the greatest disadvantages of this method is its sensitivity to the presence of outliers in data this paper introduces a new robust fuzzy clustering method named fuzzy c ordered medoids clustering for interval valued data fcomdc id the huber s m estimators and the yager s ordered weighted averaging owa operators are used in the method proposed to make it robust to outliers the described algorithm is compared with the fuzzy c medoids method in the experiments performed on synthetic data with different types of outliers a real application of the fcomdc id is also provided highlightsfuzzy clustering for interval valued data helps us to find natural vague boundaries in such data a new robust fuzzy clustering method named fuzzy c ordered medoids clustering for interval valued data fcomdc id is proposedthe method uses both the huber s m estimators and the yager s owa operators to obtain its robustness experiments performed on synthetic data with different types of outliers and a real application are provided

mean square stability of semi implicit euler method for linear stochastic differential equations with multiple delays and markovian switching in this paper we study the mean square ms stability and general mean square gms stability of semi implicit euler method for linear stochastic differential equations with multiple delays and markovian switching it is proved that semi implicit euler method is ms stable and gms stable under suitable conditions a numerical example is provided to illustrate the theoretical results

support vector interval regression machine for crisp input and output data support vector regression svr has been very successful in function estimation problems for crisp data in this paper we propose a robust method to evaluate interval regression models for crisp input and output data combining the possibility estimation formulation integrating the property of central tendency with the principle of standard svr the proposed method is robust in the sense that outliers do not affect the resulting interval regression furthermore the proposed method is model free method since we do not have to assume the underlying model function for interval nonlinear regression model with crisp input and output in particular this method performs better and is conceptually simpler than support vector interval regression networks svirns which utilize two radial basis function networks to identify the upper and lower sides of data interval five examples are provided to show the validity and applicability of the proposed method

comparison principle and stability of ito stochastic differential delay equations with poisson jump and markovian switching abstract in this paper the comparison principle for the nonlinear ito stochastic differential delay equations with poisson jump and markovian switching is established later using this comparison principle we obtain some stability criteria including stability in probability asymptotic stability in probability stability in the p th mean asymptotic stability in the p th mean and the p th moment exponential stability of such equations some known results are generalized and improved

convergence of numerical solutions to stochastic differential delay equations with poisson jump and markovian switching in general stochastic delay different equations with poisson jump and markovian switching do not have explicit solutions appropriate numerical approximations such as the euler scheme are therefore a vital tool in exploring their properties unfortunately the numerical methods for stochastic delay differential equations with poisson jump and markovian switching sddewpjmss have never been studied in this paper we proved that the euler approximate solutions will converge to the exact solutions for sddewpjmss under local lipschitz condition this result is more general than what they deal with the markovian switching term or the jump term

numerical solutions of stochastic differential delay equations under local lipschitz condition in this paper a variant of the euler maruyama method is used to define the numerical solutions for stochastic differential delay equations sddes with variable delay the key aim is to show that the numerical solutions will converge to the true solutions of the sddes under the local lipschitz condition

identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters abstract we have already discussed several models of the possibilities linear regression analysis under the assumption that probabilitioes parameters in the models are non interactive i e the possibilistic distribution of parameters is defined by minimum operators in this paper quadratic membership functions as defined by a celmi s are considered to propose an identification method of interactive fuzzy parameters in possibilistic linear systems our method can be reduced to linear programming so that it is very easy to obtain the posssibilistic distribution of parameters

convergence of numerical solutions to stochastic age structured population equations with diffusions and markovian switching in this paper it is considered for a class of stochastic age structured population equations with diffusions and markovian switching most kind of equations are nonlinear and cannot be solved explicitly so the construction of efficient computational methods is of great importance the main aim of this paper is to develop a numerical scheme and investigate the convergence of numerical approximation an example is given for illustration

an orderwise polynomial regression procedure for fuzzy data a procedure for polynomial fit with fuzzy data is presented as in real case studies there is often dependence between modes and spreads we propose a regression polynomial model capable to take into account possible interactions between the estimated spreads and modes this method finds applications in several fields such as reliability quality control psychometrics marketing image processing etc an application to a software reliability problem is also presented

convergence of numerical solutions to stochastic delay differential equations with jumps this paper studies a class of stochastic delay differential equations with jumps sddejs explicit solutions can hardly be obtained for the sddejs appropriate numerical approximation schemes such as the euler scheme are needed to apply sddejs in practice or to study their properties in this paper it is proved that the euler approximation solutions converge to the analytic solution for sddejs under weaker conditions than the linear growth condition and global lipschitz condition an example is given for illustration

interval linear systems as a necessary step in fuzzy linear systems this article clarifies what it means to solve a system of fuzzy linear equations relying on the fact that they are a direct extension of interval linear systems of equations already studied in a specific interval mathematics literature we highlight four distinct definitions of a systems of linear equations where coefficients are replaced by intervals each of which based on a generalization of scalar equality to intervals each of the four extensions of interval linear systems has a corresponding solution set whose calculation can be carried out by a general unified method based on a relatively new concept of constraint intervals we also consider the smallest multidimensional intervals containing the solution sets we propose several extensions of the interval setting to systems of linear equations where coefficients are fuzzy intervals this unified setting clarifies many of the anomalous or inconsistent published results in various fuzzy interval linear systems studies

on the possibilistic approach to linear regression models involving uncertain indeterminate or interval data abstract we consider linear regression models where both input data the observations of independent variables and output data the observations of the dependent variable are affected by loss of information caused by uncertainty indeterminacy rounding or censoring instead of real valued crisp data only intervals are available we study a possibilistic generalization of the least squares estimator so called ols set for the interval model investigation of the ols set allows us to quantify whether the replacement of real valued crisp data by interval values can have a significant impact on our knowledge of the value of the ols estimator we show that in the general case very elementary questions about properties of the ols set are computationally intractable assuming p np we also focus on restricted versions of the general interval linear regression model to the crisp input case taking the advantage of the fact that in the crisp input interval output model the ols set is a zonotope we design both exact and approximate methods for its description we also discuss special cases of the regression model e g a model with repeated observations

generic gâteaux differentiability of convex functions on small sets the theory of generic differentiability of convex functions on banach spaces is by now a well explored part of infinite dimensional geometry all the attempts to solve this kind of problem have in common as a working hypothesis one special feature of the finite dimensional case namely convex functions are always considered to be defined on convex sets with nonempty interior but typically a convex set in a banach space does not have interior points even when it is not contained in a closed hyperplane so this raises the problem of expounding a theory of differentiability of convex functions defined on small sets i e sets without interior points in our paper n2 we have made an attempt to solve this problem discussing questions of generic frechet differentiability of convex functions on small sets in the present paper we deal with problems of generic gateauxdifferentiability in this context

least squares fitting of compact set valued data in contexts where set valued data occur in a natural manner it is reasonable to ask whether such data can be directly processed for example to develop numerical techniques for constructing multifunction models which are a best fit to a body of set valued observations this note proposes methods of least squares fitting of such data for the case where each datum is a nonempty compact interval of the real line two models will be considered a interval valued output observed from interval valued input and b interval valued output resulting from exact real input

a set arithmetic based linear regression model for modelling interval valued responses through real valued variables a new linear regression model for an interval valued response and a real valued explanatory variable is presented the approach is based on the interval arithmetic comparisons with previous methods are discussed the new linear model is theoretically analyzed and the regression parameters are estimated some properties of the regression estimators are investigated finally the performance of the procedure is illustrated using both a real life application and simulation studies

dependency between degree of fit and input noise in fuzzy linear regression using non symmetric fuzzy triangular coefficients fuzzy linear regression flr model can be thought of as a fuzzy variation of classical linear regression model it has been widely studied and applied in diverse fields when noise exists in data it is a very meaningful topic to reveal the dependency between the parameter h i e the threshold value used to measure degree of fit in flr model and the input noise in this paper the flr model is first extended to its regularized version i e regularized fuzzy linear regression rflr model so as to enhance its generalization capability then rflr model is explained as the corresponding equivalent maximum a posteriori map problem finally the general dependency relationship that the parameter h with noisy input should follow is derived particular attention is paid to the regression model using non symmetric fuzzy triangular coefficients it turns out that with the existence of typical gaussian noisy input the parameter h is inversely proportional to the input noise our experimental results here also confirm this theoretical claim obviously this theoretical result will be helpful to make a good choice for the parameter h and to apply flr techniques effectively in practical applications

extended fuzzy regression models using regularization method regularization approach to regression can be easily found in statistics and information science literatures the technique of regularization was introduced as a way of controlling the smoothness properties of regression function the main purpose of this paper is to extend the models of diamond inform sci 46 1988 141 to fuzzy multiple linear regression models and to extend the model f3 with numerical input of diamond inform sci 46 1988 141 to fuzzy nonlinear model here all extensions are based on regularization technique

successive approximation to solutions of stochastic differential equations with jumps in local non lipschitz conditions in this paper by using successive approximation the existence and uniqueness of initial value problem for stochastic differential equations driven by both wiener process and poisson process are studied under a local non lipschitz conditions moreover the numerical solutions are shown to converge uniformly to the analytical solutions of the stochastic differential equation with jumps

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

convergence of numerical solutions to stochastic pantograph equations with markovian switching in this paper a class of stochastic pantograph equations with markovian switching is considered the main purpose is to investigate the convergence of the euler method of the equations it is proved that the euler approximation solution converge to the analytic solution in probability under weaker conditions an example is provided to illustrate our theory

fuzzy linear least squares for the identification of possibilistic regression models abstract the stochastic approach to regression e g the least squares method is a commonly used technique in a wide range of disciplines as it offers an intuitive and well founded solution to the problem of fitting a set of parameters to existing data specifically in the case where the parameters of meta models are identified the linear least squares formulation receives wide appreciation among engineers due to its simple yet powerful formulation and solution usually this approach provides a reasonable fit depending largely on the quality of the model that is employed however it has two main drawbacks from a statistical point of view the premises justifying its use cannot always be assumed in good faith and most importantly the resulting model will almost certainly fail at correctly predicting the output without falling victim to the effect of over fitting the presented fuzzy regression algorithm originates from a set of different axioms for the solution of the linear least squares problem it is able to provide the worst case optimal parameter variation necessary to cover all of the crisp data points while encoding meaningful information in the membership function this is accomplished by means of a sensible fuzzification procedure of the crisp data points and the application of an exact inverse fuzzy arithmetic for estimating the fuzzy valued parameters of the model in question

gradual numbers and their application to fuzzy interval analysis in this paper we introduce a new way of looking at fuzzy intervals instead of considering them as fuzzy sets we see them as crisp sets of entities we call gradual real numbers they are a gradual extension of real numbers not of intervals such a concept is apparently missing in fuzzy set theory gradual numbers basically have the same algebraic properties as real numbers but they are functions a fuzzy interval is then viewed as a pair of fuzzy thresholds which are monotonic gradual real numbers this view enables interval analysis to be directly extended to fuzzy intervals without resorting to alpha cuts in agreement with zadeh s extension principle several results show that interval analysis methods can be directly adapted to fuzzy interval computation where end points of intervals are changed into left and right fuzzy bounds our approach is illustrated on two known problems computing fuzzy weighted averages and determining fuzzy floats and latest starting times in activity network scheduling

dynamics of a quadratic map in two complex variables abstract we study the map c 2 c 2 defined by w z z z w2 and the associated collection of sequences zj satisfying the recurrence zj 2 zj 1 z2j iteration of is equivalent to the study of such sequences we analyze growth rates of the sequences positive sequences periodic and asymptotically periodic sequences and establish the existence of doubly infinite homoclinic sequences non zero sequences whose limits as j are 0 we investigate some associated functional equations f x 2 f x 1 f x 2 and l l x l x x2