cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

triangular norm based addition of fuzzy intervals triangular norm based addition of fuzzy intervals on the extended real line is reduced to the addition of shapes on 0 the addition of fuzzy intervals including lr fuzzy intervals lr fuzzy numbers lt and tr fuzzy numbers based on limit t norms is recalled for continuous archimedean t norms special types of incoming summands allowing the exact output computation are introduced several examples are given

t norm based addition of fuzzy intervals abstract the aim of this paper is to provide new results regarding the effective practical computation of t norm based additions of lr fuzzy intervals

design sensitivities in problems involving material and geometric nonlinearities abstract the subject of this paper is the determination of design sensitivity coefficients dscs for linear elasticity and nonlinear both material and geometric problems in solid mechanics dscs here refer to rates of change of response variables such as displacements or stresses in a deforming solid body with respect to parameters called design variables that control the initial undeformed shape of the body in nonlinear problems these dscs are history dependent the direct differentiation approach dda of the relevant derivative boundary element method dbem formulation is employed here to obtain the dscs modelling of sharp corners on the boundary of a body is given special attention here numerical results are presented for illustrative examples the numerically obtained sensitivities even for stresses on the boundary of a body are shown in general to be very accurate typically it is difficult to obtain dscs for boundary stresses accurately by other methods yet they are very useful for optimal shape design of bodies ongoing research is currently focused on numerical calculation of dscs for large deformation problems and use of these dscs in process optimization an important future application area of this work is optimal design of manufacturing processes such as extrusion or forging

generalized differentiability of fuzzy valued functions in the present paper using novel generalizations of the hukuhara difference for fuzzy sets we introduce and study new generalized differentiability concepts for fuzzy valued functions several properties of the new concepts are investigated and they are compared to similar fuzzy differentiabilities finding connections between them characterization and relatively simple expressions are provided for the new derivatives

fuzzy differential equations with interactive derivative in this paper we introduce and study new concept of differentiability for fuzzy set valued functions this derivative considers possible local interactivity in the process studied several properties of differentiability and integrability are investigated for the new concept and they are compared to similar fuzzy differentiabilities like hukuhara differentiability and generalized hukuhara differentiability furthermore we establish theorems as the fundamental theorem of calculus ultimately we exhibit some results for fuzzy initial value problem and an application

inversion formulas for the linearized problem for an inverse boundary value problem in elastic prospection the problem of determining an unknown pair gamma lambda mu of lame parameters inside a body by its dirichlet to neumann data map lambda gamma is considered using explicit exact solutions for the case of constant gamma it is seen that the deflection h between gamma h and gamma is uniquely determined by the first order approximation of lambda gamma h at gamma

corrected score function for errors in variables models methodology and application to generalized linear models summary statistical models whose independent variables are subject to measurement errors are often referred to as errors in variables models to correct for the effects of measurement error on parameter estimation this paper considers a correction for score functions a corrected score function is one whose expectation with respect to the measurement error distribution coincides with the usual score function based on the unknown true independent variables this approach makes it possible to do inference as well as estimation of model parameters without additional assumptions the corrected score functions of some generalized linear models are obtained

solutions of higher order linear fuzzy differential equations with interactive fuzzy values abstract in this study we consider higher order linear differential equations with additional conditions initial and or boundary given by interactive fuzzy numbers the concept of interactivity arises from the notion of a joint possibility distribution j the proposed method for solving fuzzy differential equations is based on an extension of the classical solution via sup j extension which is a generalization of zadeh s extension principle we prove that under certain conditions the solution via zadeh s extension principle is equal to the convex hull of the solutions produced by the sup j extension we also show that the solutions based on the frechet derivatives of fuzzy functions coincide with the solutions obtained via the sup j extension all of the results are illustrated based on a 3rd order fuzzy boundary value problem

necessary and sufficient conditions for the equality of interactive and non interactive extensions of continuous functions abstract in this contribution we find the class of n dimensional joint possibility distributions with the property that the interactive extension principle coincides with the non interactive extension principle as long as the interactive operations are determined by continuous functions strictly increasing in each argument this result completes recent studies by the authors where the particular case of interactive additions and multiplications versus non interactive additions and multiplications were investigated in addition this time we propose results that also cover the cases when we know the fuzzy numbers only from their membership functions it means that we eliminated the limitations that appear when we cannot pass from membership function representation to parametric representation of fuzzy numbers as important new applications we mention the study on the completely correlated fuzzy numbers also of note is that we propose two simple methods to extend bidimensional joint possibility distributions to n dimensional joint possibility distributions one method is based on an inductive construction while the other one is based on a pairwise construction

a parametrized sum of fuzzy numbers with applications to fuzzy initial value problems abstract this paper presents a new parametrized family of joint possibility distributions that can be used to control the pompeiu hausdorff norm of the sum resulting from the extension principle we are able to generate sums with norms covering the entire interval ranging from the smallest possible value to the largest one finally we apply our approach to numerical methods for solving first order fuzzy initial value problems

conforming boundary elements in plane elasticity for shape design sensitivity the structural design sensitivity analysis of a two dimensional continuum using conforming continuous boundary elements is investigated implicit differentiation of the discretized boundary integral equations is performed to obtain design sensitivities in an efficient manner by avoiding the factorization of the perturbed matrices a singular formulation of the boundary element method is used implicit differentiation of the boundary integral equations produces terms that contain derivatives of the fundamental solutions employed in the analysis the behaviour of the singularity of these derivatives of the boundary element kernel functions with respect to the design variables is investigated a rigid body motion technique is presented to obtain the singular terms in the resulting sensitivity matrices thus avoiding the problems associated with their numerical integration a formulation for obtaining the design sensitivities of the continua under body forces of the gravitational and centrifugal types is also presented the design sensitivity results are seen to be of the same order of accuracy as the boundary element analysis results numerical data comparing the performance of conforming and non conforming formulations in the calculation of design sensitivities are also presented the accuracy of the present results is demonstrated through comparisons with existing analytical results

generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations the usual concept of differentiability of fuzzy number valued functions has the following shortcoming if c is a fuzzy number and g a b r is an usual real valued function differentiable on x 0 a b with g x 0 0 then f x c g x is not differentiable on x 0 in this paper we introduce and study generalized concepts of differentiability of any order n n which solves this shortcoming newton leibnitz type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied also some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c g x are given

on interactive fuzzy boundary value problems abstract in this paper we use the concept of interactivity between fuzzy numbers for the solution to a linear fuzzy boundary value problem fbvp we show that a solution of a fbvp with non interactive fuzzy numbers as boundary values can be obtained by the zadeh s extension principle in addition we show it is possible to obtain a fuzzy solution by means of the extension principle based on joint possibility distributions for the case where the boundary values are given by interactive fuzzy numbers examples of fbvps with both cases interactive and non interactive are presented also from arithmetic operations for linearly correlated fuzzy numbers we compare our solutions to the one proposed by gasilov et al we conclude that the fuzzy solution in the interactive case when the boundary values are linearly correlated fuzzy numbers is contained in the fuzzy solution for the non interactive case finally we present the fuzzy solution for a nonlinear fbvp with gaussian fuzzy numbers as boundary values

on generalization on nguyen s theorem abstract the goal of this paper is to generalize certain results of nguyen 1 concerning the cuts of two place functions defined by the zadeh s extension principle to the case of extended two place functions defined via a sup t norm convolution

a boundary element formulation for the inverse elastostatics problem iesp of flaw detection a boundary integral formulation is presented for the detection of flaws in planar structural members from the displacement measurements given at some boundary locations and the applied loading such inverse problems usually start with an initial guess for the flaw location and size and proceed towards the final configuration in a sequence of iterative steps a finite element formulation will require a remeshing of the object corresponding to the revised flaw configuration in each iteration making the procedure computationally expensive and cumbersome no such remeshing is required for the boundary element approach the inverse problem is written as an optimization problem with the objective function being the sum of the squares of the differences between the measured displacements and the computed displacements for the assumed flaw configuration the geometric condition that the flaw lies within the domain of the object is imposed using the internal penalty function approach in which the objective function is augmented by the constraint using a penalty parameter a first order regularization procedure is also implemented to modify the objective function in order to minimize the numerical fluctuations that may be caused in the numerical procedure due to errors in the experimental measurements for displacements the flaw configuration is defined in terms of geometric parameters and the sensitivities with respect to these parameters are obtained in the boundary element framework using the implicit differentiation approach a series of numerical examples involving the detection of circular and elliptical flaws of various sizes and orientations are solved using the present approach good predictions of the flaw shape and location are obtained

analytical expressions for the addition of fuzzy intervals abstract the addition of fuzzy quantities is undeniably the most important operation in fuzzy arithmetic in this paper we consider the general case of the addition of fuzzy intervals based on a continuous triangular norm we start our discussion with an extensive literature review in which we recall explicit formulae for the addition based on the strongest and the weakest triangular norm for the addition based on the algebraic product and several recent results for the addition based on a continuous archimedean triangular norm including specific theorems for strict and nilpotent triangular norms subsequently the addition based on an ordinal sum is studied and it is shown how this addition can be transformed into a series of additions based on the summands of this ordinal sum this important observation implies that the addition based on an arbitrary continuous triangular norm can be practically performed provided the summands of the corresponding ordinal sum representation and the fuzzy intervals involved fulfil the appropriate conditions mentioned in the overview this is illustrated by means of several examples

semiparametric inference in the proportional odds regression model abstract for fitting the proportional odds regression model with right censored survival times we introduce some weighted empirical odds functions these functions are solutions of some self consistency equations and have a nice martingale representation from these functions several classes of new regression estimators such as the pseudo maximum likelihood estimator martingale residual based estimators and minimum distance estimators are derived these estimators have desirable properties such as easy computation asymptotic normality via a martingale analysis and reliable asymptotic covariance estimation in closed form extensive numerical studies show that the minimum l 2 distance estimators have very good finite sample behaviors compared to existing methods results of some simulation studies and applications to a real dataset are given the weighted odds function based approach also provides inference on the baseline odds function and some measures for lack of fit analysis

covariate measurement errors and parameter estimation in a failure time regression model summary estimation in cox s failure time regression model is considered when the regression vector is subject to measurement error a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters this partial likelihood function may involve the baseline hazard function as well as the regression parameter but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates approaches to regression estimation using the overall likelihood function and a marginal likelihood function based on failure time ranks are also indicated illustration of the possible effect of covariate errors on relative risk estimation is provided

a bem based pattern search solution for a class of inverse elastostatic problems a boundary element based solution employing the hooke jeeves pattern search method is developed to determine internal cavity geometries in the inverse elastostatics problem in contrast to existing methods which employ gradient based solutions the developed method does not require gradient information and consequently results in a simpler solution procedure a boundary difference function bdf that provides a guide for the initial guess is introduced the unknown cavity geometry is first assumed to be circular and the algorithm is run until the general location of the cavity is determined subsequent refinement of the detected cavity geometry is affected using a periodic cubic spline discretization numerical results are presented to illustrate the effectiveness of the boundary difference function and to demonstrate the successful detection of the cavity the effects of simulated experimental inputs with prescribed error are also presented

bem first order regularisation method in linear elasticity for boundary identification in this paper we study the identification of an unknown portion of the boundary of a two dimensional domain occupied by an isotropic linear elastic material from additional cauchy data on the remaining known portion of the boundary this inverse problem is approached using the boundary element method bem in conjunction with the tikhonov first order regularisation procedure the choice of the regularisation parameter is based on the l curve criterion the numerical results obtained show that the proposed method produces a convergent and stable solution

on interactive fuzzy numbers in this paper we will introduce a measure of interactivity between marginal distributions of a joint possibility distribution c as the expected value of the interactivity relation between the level sets of its marginal distributions

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

regression calibration in failure time regression in this paper we study a regression calibration method for failure time regression analysis when data on some covariates are missing or mismeasured the method estimates the missing data based on the data structure estimated from a validation data set a random subsample of the study cohort in which covariates are always observed ordinary cox 1972 journal of the royal statistical society series b 34 187 220 regression is then applied to estimate the regression coefficients using the observed covariates in the validation data set and the estimated covariates in the nonvalidation data set the method can be easily implemented we present the asymptotic theory of the proposed estimator finite sample performance is examined and compared with an estimated partial likelihood estimator and other related methods via simulation studies where the proposed method performs well even though it is technically inconsistent finally we illustrate the method with a mouse leukemia data set

necessary and sufficient conditions for the equality of the interactive and non interactive sums of two fuzzy numbers this study aims to answer the open question proposed by carlsson et al 2004 4 which asks whether it is possible to find the properties needed by a joint possibility distribution function such that the interactive sum with respect to this function and the standard sum of two fuzzy numbers will coincide we provide the necessary and sufficient conditions such that this equality would hold in addition we find the necessary and sufficient conditions such that the interactive and standard sums will coincide at some point in the domain in order to obtain an interactive addition that does not coincide with the standard addition we show that we need to search for a joint possibility distribution that coincides as little as possible with the independent joint possibility distribution throughout the so called diagonal of the two fuzzy numbers as simple consequences we deduce similar results for triangular norm based additions of fuzzy numbers

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

a pseudo partial likelihood method for semiparametric survival regression with covariate errors this article presents an estimator for the regression coefficient vector in the cox proportional hazards model with covariate error the estimator is obtained by maximizing a likelihood type function similar to the cox partial likelihood the likelihood function involves the cumulative baseline hazard function for which a simple estimator is substituted the method is capable of handling general covariate error structures it is not restricted to the independent additive error model it can be applied to studies with either an external or internal validation sample and also to studies with replicate measurements of the surrogate covariate the estimator is shown to be consistent and asymptotically normal and an estimate of the asymptotic covariance matrix is derived some extensions to general transformation survival models are indicated simulation studies are presented for a setup with a single error prone binary covariate and a setup with a single error prone normally distributed covariate these si

an inverse method for determining elastic material properties and a material interface the problem consists of determining the location and size of a circular inclusion in a finite matrix and the elastic material properties of the inclusion and the matrix

analysis of transformation models with censored data summary in this paper we consider a class of semi parametric transformation models under which an unknown transformation of the survival time is linearly related to the covariates with various completely specified error distributions this class of regression models includes the proportional hazards and proportional odds models inference procedures derived from a class of generalised estimating equations are proposed to examine the covariate effects with censored observations numerical studies are conducted to investigate the properties of our proposals for practical sample sizes these transformation models coupled with the new simple inference procedures provide many useful alternatives to the cox regression model in survival analysis

calculus for linearly correlated fuzzy function using frechet derivative and riemann integral abstract in this manuscript we study integration and derivative theories for interactive fuzzy processes these theories are based on the frechet derivative and the riemann integral in addition we present a connection between these two theories i e some problems may be formulated in both ways we establish the fundamental theorem of calculus theorem of existence and the local uniqueness of the solution of fuzzy differential equations and some techniques to solve fuzzy initial value problems to illustrate the usefulness of the developed theory we investigate the radioactive decay model

the generalized fuzzy derivative is interactive abstract in this article we prove that the generalized difference between a b r f c i e fuzzy numbers with continuous endpoints is given by an interactive difference to be more precise we construct a certain joint possibility distribution i such that the generalized difference coincides with the sup i extension of the subtraction as an immediate consequence we have that every notion of difference between a b r f c that has so far appeared in the literature can be derived from a sup j extension for some particular choice of j moreover we show that both the generalized and the generalized hukuhara derivative of a function f r r f c at x r can be expressed as the limit for h 0 of a difference quotient where the difference is an interactive difference for each h for short we say that the generalized as well as the generalized hukuhara difference is interactive