optimal multinational capital budgeting under uncertainty this paper discusses the multinational capital budgeting problem when there are some candidate foreign projects which project s should the investor choose in the paper special cash flows and value sources of foreign projects are introduced regarding project parameters such as construction costs annual net operating cash flows terminal values of the projects as well as the foreign exchange rates as uncertain variables the paper proposes one new uncertain zero one integer model for optimal multinational project selection to solve the problem a hybrid intelligent algorithm integrating the 99 methods and genetic algorithm is provided as an illustration an application example is also presented

formulation of elastostatic hybrid trefftz stress elements abstract the hybrid trefftz stress hts element is derived from the fundamental conditions of linear elastostatics the stress and boundary displacement fields are directly approximated consistent finite element variables are so defined as to obtain boundary integral expressions for the finite element equilibrium and compatibility conditions encoded by dual transformations independent of the constitutive relations reciprocity is preserved in the finite element elasticity relations which are also found to be described by boundary integral arrays when the trefftz constraint is enforced consequent upon duality and reciprocity the resulting boundary integral solving system is symmetric and sparse the energy statements associated with the hybrid trefftz stress element are established and the conditions for the existence uniqueness multiplicity and static and kinematic admissibility of the finite element solutions are presented the hts clement is compared with the displacement frame based hybrid trefftz ht d element of jirousek it is shown that the ht d element is in fact an hybrid stress element the numerical tests performed to assess the relative performances of the hts and ht d elements show that better accuracy levels are obtained using discontinuous boundary approximation bases

sample size calculations in the presence of competing risks recently with the growth of statistical developments for competing risks analysis some methods have been proposed to compute sample size in this context these methods differ from a modelling approach one is based on the cox regression model for the cause specific hazard while another relies on the fine and gray regression model for the subdistribution hazard of a competing risk in this work we compare these approaches derive a new sample size for comparing cumulative incidence functions when the hazards are not proportional either cause specific or subdistribution and give practical advices to choose the approach best suited for the study question

redundancy optimization problems with uncertainty of combining randomness and fuzziness by using random fuzzy lifetimes as basic parameters three types of system performance expected system lifetime system lifetime and system reliability are presented some random fuzzy simulations are employed to estimate the system performance furthermore a spectrum of random fuzzy models are constructed for redundancy optimization problems in order to solve these models a hybrid intelligent algorithm is used finally some numerical examples are provided for the sake of illustration

an integrated decision support approach for project investors in risky and uncertain environments in project investment decisions it is often assumed that estimated values of project parameters are certain and they would not deviate by the time however project parameters normally change during a life cycle of the project therefore an existence of a deviation or gap between forecasted values and actual values is inevitable because of the uncertainty of the future forecasting the true and exact values of project parameters is almost impossible in this study an integrated decision support approach based on simulation and fuzzy set theory is proposed for project investors in risky and uncertain environments this approach determines the risk levels of the projects and helps investors to make investment decisions in the scope of the study a flowchart is presented to guide to decision maker in different situations of information uncertainty that belongs to project parameter values via this flowchart the values of project parameters can be chosen depending on how they are determined deterministic stochastic or fuzzy by project analyst besides calculating and analyzing the project risk in all possible situations would be easier illustrative examples are given to demonstrate the application of this approach

expected value of fuzzy variable and fuzzy expected value models this paper will present a novel concept of expected values of fuzzy variables which is essentially a type of choquet integral and coincides with that of random variables in order to calculate the expected value of general fuzzy variable a fuzzy simulation technique is also designed finally we construct a spectrum of fuzzy expected value models and integrate fuzzy simulation neural network and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models

some inequalities of random fuzzy variableswith application to moment convergence random fuzzy variables are functions from possibility spaces to the set of random variables in this paper in order further to discuss the mathematical properties of random fuzzy variables some inequalities for random fuzzy variables are first proved based on the concepts of chance measures and expected value operators finally as applications of inequalities obtained moment convergence theorems are proved

a simple approach to power and sample size calculations in logistic regression and cox regression models for a given regression problem it is possible to identify a suitably defined equivalent two sample problem such that the power or sample size obtained for the two sample problem also applies to the regression problem for a standard linear regression model the equivalent two sample problem is easily identified but for generalized linear models and for cox regression models the situation is more complicated an approximately equivalent two sample problem may however also be identified here in particular we show that for logistic regression and cox regression models the equivalent two sample problem is obtained by selecting two equally sized samples for which the parameters differ by a value equal to the slope times twice the standard deviation of the independent variable and further requiring that the overall expected number of events is unchanged in a simulation study we examine the validity of this approach to power calculations in logistic regression and cox regression models several different covariate distributions are considered for selected values of the overall response probability and a range of alternatives for the cox regression model we consider both constant and non constant hazard rates the results show that in general the approach is remarkably accurate even in relatively small samples some discrepancies are however found in small samples with few events and a highly skewed covariate distribution comparison with results based on alternative methods for logistic regression models with a single continuous covariate indicates that the proposed method is at least as good as its competitors the method is easy to implement and therefore provides a simple way to extend the range of problems that can be covered by the usual formulas for power and sample size determination

chance constrained programming models for capital budgeting with npv as fuzzy parameters in an uncertain economic environment experts knowledge about outlays and cash inflows of available projects consists of much vagueness instead of randomness investment outlays and annual net cash flows of a project are usually predicted by using experts knowledge fuzzy variables can overcome the difficulties in predicting these parameters in this paper capital budgeting problem with fuzzy investment outlays and fuzzy annual net cash flows is studied based on credibility measure net present value npv method is employed and two fuzzy chance constrained programming models for capital budgeting problem are provided a fuzzy simulation based genetic algorithm is provided for solving the proposed model problems two numerical examples are also presented to illustrate the modelling idea and the effectiveness of the proposed algorithm

transportation projects selection process using fuzzy sets theory government transportation agencies are faced with the problem of efficiently selecting a subset of transportation projects for implementation this selection process is based on multiple objectives which are often measured in incommensurable units usually the problem is treated by neglecting or biasing the qualitative characteristics of the various projects moreover the usual selection methods cannot deal effectively with the decision makers preferences or vagueness fuzzy sets theory is able to cope with inexact information and therefore is believed to be an appropriate tool for use in the projects selection process this work presents an efficient technique for the selection of transportation projects using fuzzy sets theory the selection procedure is a multiple objectives process and projects are rated both on a quantitative and qualitative basis using linguistic variables in order to describe appropriately a given transportation policy both fuzzy weighted average and noncompensatory fuzzy decision rules are used in the proposed approach in addition this work contains a case study of a selection process of interurban road projects in israel the results of the proposed method obtained by a fuzzy expert system are compared with the results obtained by an ordinary crisp process

bias and sensitivity analysis when estimating treatment effects from the cox model with omitted covariates summary omission of relevant covariates can lead to bias when estimating treatment or exposure effects from survival data in both randomized controlled trials and observational studies this paper presents a general approach to assessing bias when covariates are omitted from the cox model the proposed method is applicable to both randomized and non randomized studies we distinguish between the effects of three possible sources of bias omission of a balanced covariate data censoring and unmeasured confounding asymptotic formulae for determining the bias are derived from the large sample properties of the maximum likelihood estimator a simulation study is used to demonstrate the validity of the bias formulae and to characterize the influence of the different sources of bias it is shown that the bias converges to fixed limits as the effect of the omitted covariate increases irrespective of the degree of confounding the bias formulae are used as the basis for developing a new method of sensitivity analysis to assess the impact of omitted covariates on estimates of treatment or exposure effects in simulation studies the proposed method gave unbiased treatment estimates and confidence intervals with good coverage when the true sensitivity parameters were known we describe application of the method to a randomized controlled trial and a non randomized study

the fuzzy quadratic assignment problem with penalty new models and genetic algorithm the assignment problem is to find the total costs optimal jobs assignment schedule where n jobs are allocated to n workers and each worker receives exactly just one job such that the total cost is optimal the quadratic assignment problem with penalty takes three types of costs into consideration direct cost interactive cost an penalty in this paper the fuzzy quadratic assignment problem with penalty is formulated as expected value model chance constrained programming and dependent chance programming according to various decision criteria and the crisp equivalents are given furthermore hybrid genetic algorithm is designed for solving the proposed fuzzy programming models

a robust approach to the decision rules of npv and irr for simple projects we propose a robust approach to the decision rules of net present value npv and internal rate of return irr by building an analogy between robust optimization approach proposed in the literature and decision rules of npv and irr by considering uncertainty in cash flows as proposed in the literature we assume that the parameters cash inflows and cash outflows in our case belong to a symmetric and bounded interval set and define a series of decision rules of npv and irr by considering robustness

sample size considerations for the evaluation of prognostic factors in survival analysis when the role of a new prognostic factor is investigated careful planning of an appropriate study is required this includes an assessment of the power of the study in terms of sample sizes an adequate analysis of the independent prognostic effect of a new factor has to be adjusted for the existing standard factors with survival time as endpoint this will usually be done with the cox proportional hazards model sample size and power formulae in survival analysis have been developed by schoenfeld for randomized treatment comparisons in the analysis of prognostic factors the covariates included are expected to be correlated with the factor of primary interest in this situation the existing sample size and power formulae are not valid and may not be applied in this paper schoenfeld s formula is first extended to the situation where a correlated factor is included in the analysis the validity of the resulting approximate asymptotic formula is investigated for its asymptotic behaviour by numerical integration and for its finite behaviour by simulation second an approximate formula for sample size and power is provided to detect an interaction between the interesting and a second correlated factor this extends the formula for independent effects finally the approach is illustrated by an example on the prognostic impact of dna ploidy and other factors in advanced ovarian cancer

minimax chance constrained programming models for fuzzy decision systems abstract the existing chance constrained programming for fuzzy decision systems is essentially a kind of maximax models optimistic models which maximize the maximum possible return this paper presents a spectrum of minimax models as opposed to maximax models based on chance constrained programming as well as chance constrained multi objective programming and chance constrained goal programming in which the minimax models will select the alternative that provides the best of the worst possible return finally a fuzzy simulation based genetic algorithm will be designed for solving minimax models and illustrated by some numerical examples

postbuckling analysis of thin plates by a hybrid trefftz finite element method abstract a hybrid trefftz finite element ht fe model for postbuckling analysis of thin plates is presented based on a modified variational principle with the aid of incremental form of equilibrium equations all non linear terms may be viewed as pseudo loads and then the in plane and out of plane equations can be uncoupled as a consequence the solution procedure for the postbuckling plate becomes very simple two numerical examples are considered to illustrate the correctness and accuracy of the proposed formulation

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

hybrid finite element formulations for elastodynamic analysis in the frequency domain abstract three alternative sets of hybrid formulations to solve linear elastodynamic problems by the finite element method are presented they are termed hybrid mixed hybrid and hybrid trefftz and differ essentially on the field conditions that the approximation functions are constrained to satisfy locally two models namely the displacement and the stress models are obtained for each formulation depending on whether the tractions or the boundary displacements are the field chosen to implement interelement continuity a fourier time discretization is used to uncouple the solving system in the frequency domain the basic space discretization criterion is implemented directly on the fundamental relations of elastodynamics and used to derive the stress and displacement models of the hybrid mixed formulation the hybrid and hybrid trefftz formulations are presented in sequence as the variants of the hybrid mixed formulation obtained by progressively increasing the constraints on the approximation bases numerical implementation aspects are briefly discussed and the performance of the finite element models is illustrated with numerical applications

the fast solution of poisson s and the biharmonic equations on irregular regions we present fast methods for solving laplace s and the biharmonic equations on irregular regions with smooth boundaries the methods used for solving both equations make use of fast poisson solvers on a rectangular region in which the irregular region is embedded they also both use an integral equation formulation of the problem where the integral equations are fredholm integral equations of the second kind the main idea is to use the integral equation formulation to define a discontinuous extension of the solution to the rest of the rectangular region fast solvers are then used to compute the extended solution aside from solving the equations we have also been able to compute derivatives of the solutions with little loss of accuracy when the data was sufficiently smooth

sample size formula for the proportional hazards regression model a formula is derived for determining the number of observations necessary to test the equality of two survival distributions when concomitant information is incorporated this formula should be useful in designing clinical trials with a heterogeneous patient population schoenfeld 1981 biometrika 68 316 319 derived the asymptotic power of a class of statistics used to test the equality of two survival distributions that result is extended to the case where concomitant information is available for each individual and where the proportional hazards model holds the loss of efficiency caused by ignoring concomitant variables is also computed

a new approach to fuzzy programming abstract a fuzzy program is defined in the usual way as a sequence of statements instruction which are considered as functions possibly fuzzy functions and fuzzy predicates defined on the given input domain the essential difference in the approach presented in this paper is the new interpretation of the execution of fuzzy programs and a new method of evaluating fuzzy predicates the result of the fuzzy program execution is an appropriate fuzzy subset in the output domain

power analysis for multivariable cox regression models in power analysis for multivariable cox regression models variance of the estimated log hazard ratio for the treatment effect is usually approximated by inverting the expected null information matrix because in many typical power analysis settings assumed true values of the hazard ratios are not necessarily close to unity the accuracy of this approximation is not theoretically guaranteed to address this problem the null variance expression in power calculations can be replaced with one of the alternative expressions derived under the assumed true value of the hazard ratio for the treatment effect this approach is explored analytically and by simulations in the present paper we consider several alternative variance expressions and compare their performance to that of the traditional null variance expression theoretical analysis and simulations demonstrate that whereas the null variance expression performs well in many nonnull settings it can also be very inaccurate substantially underestimating or overestimating the true variance in a wide range of realistic scenarios particularly those where the numbers of treated and control subjects are very different and the true hazard ratio is not close to one the alternative variance expressions have much better theoretical properties confirmed in simulations the most accurate of these expressions has a relatively simple form it is the sum of inverse expected event counts under treatment and under control scaled up by a variance inflation factor

generalized finite element analysis with t complete boundary solution functions the use of a complete and nonsingular set of trefftz functions in the solution of quasi harmonic equations is demonstrated and shown to be often superior to the more conventional singularity distribution in boundary type approximation procedures for coupling separate domains of such solution and indeed of deriving equivalent finite elements are demonstrated

applications of fuzzy set theory to mathematical programming mathematical programming is one of the areas to which fuzzy set theory has been applied extensively primarily based on bellman and zadeh s model of decision in fuzzy environments models have been suggested which allow flexibility in constraints and fuzziness in the objective function in traditional linear and nonlinear programming in integer and fractional programming and in dynamic programming these models in turn have been used to offer computationally efficient approaches for solving vector maximum problems this paper surveys major models and theories in this area and offers some indication on future developments which can be expected

fuzzy quadratic minimum spanning tree problem in this paper a fuzzy quadratic minimum spanning tree problem is formulated as expected value model chance constrained programming and dependent chance programming according to different decision criteria then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers furthermore a simulation based genetic algorithm using prufer number representation is designed for solving the proposed fuzzy programming models as well as their crisp equivalents finally a numerical example is provided for illustrating the effectiveness of the genetic algorithm

fuzzy capital budgeting fuzzy equivalents of all the classical capital budgeting investment choice methods are generalised or proposed these equivalents can be used to evaluate and compare projects in which the cash ows duration time and required rate of return cost of capital are given imprecisely in the form of a fuzzy number c 2000 elsevier science b v all rights reserved

chance constrained programming with fuzzy parameters this paper extends chance constrained programming from stochastic to fuzzy environments analogous to stochastic programming some crisp equivalents of chance constraints in fuzzy environments are presented we also propose a technique of fuzzy simulation for the chance constraints which are usually hard to be converted to their crisp equivalents finally a fuzzy simulation based genetic algorithm is designed for solving this kind of problems and some numerical examples are discussed

fuzzy capital rationing model in this paper we study the fuzzification of weingartner s pure capital rationing model and its analysis we develop a primal dual pair based on t norm t conorm relation for the constraints and objective function for a fully fuzzified pure capital rationing problem except project selection variables we define the a interval under which the weak duality is proved we perform sensitivity analysis for a change in a budget level or in a cash flow level of a non basic as well as a basic variable we analyze the problem based on duality and complementary slackness results we illustrate the proposed model by computational analysis and interpret the results

a new particular solution strategy for hyperbolic boundary value problems using hybrid trefftz displacement elements summary a new indirect approach to the problem of approximating the particular solution of non homogeneous hyperbolic boundary value problems is presented unlike the dual reciprocity method which constructs approximate particular solutions using radial basis functions polynomials or trigonometric functions the method reported here uses the homogeneous solutions of the problem obtained by discarding all time derivative terms from the governing equation nevertheless what typifies the present approach from a conceptual standpoint is the option of not using these trial functions exclusively for the approximation of the particular solution but to fully integrate them with the trefftz compliant homogeneous solution basis the particular solution trial basis is capable of significantly improving the trefftz solution even when the original equation is genuinely homogeneous an advantage that is lost if the basis is used exclusively for the recovery of the source terms similarly a sufficiently refined trefftz compliant basis is able to compensate for possible weaknesses of the particular solution approximation the method is implemented using the displacement model of the hybrid trefftz finite element method the functions used in the particular solution basis reduce most terms of the matrix of coefficients to boundary integral expressions and preserve the hermitian sparse and localized structure of the solving system that typifies hybrid trefftz formulations even when domain integrals are present they are generally easy to handle because the integrand presents no singularity copyright 2015 john wiley sons ltd

dealing with competing risks testing covariates and calculating sample size it is universally agreed that kaplan meier estimates overestimate the probability of the event of interest in the presence of competing risks kalbfleisch and prentice recommend using the cumulative incidence as an estimate of the probability of an event of interest however there is no consensus on how to test the effect of a covariate in the presence of competing risks using simulations this paper illustrates that the cox proportional hazards model gives valid results when employed in testing the effect of a covariate on the hazard rate and when estimating the hazard ratio a method to calculate the sample size for testing the effect of a covariate on outcome in the presence of competing risks is also provided