on the use of concordant pairs in matched case control studies a new estimator of the common odds ratio in one to one matched case control studies is proposed the connection between this estimator and the james stein estimating procedure is highlighted through the argument of estimating functions comparisons are made between this estimator the conditional maximum likelihood estimator and the estimator ignoring the matching in terms of finite sample bias mean squared error coverage probability and length of confidence interval in many situations the new estimator is found to be more efficient than the conditional maximum likelihood estimator without being as biased as the estimator that ignores matching the extension to multiple risk factors is also outlined

fuzzy goal programming complementary slackness conditions and computational schemes abstract goal programming gp is an important category in linear programming and multiobjective versions which minimize the deviation among value of each objective function and its goal with satisfying other constraints of problem in this paper we deal with fuzzy goal programming fgp which is a generalized problem in vague nature where parameters relations and goals are given as fuzzy quantities with respect to imprecise data recently inuiguchi et al m inuiguchi j ramik t tanio m vlach satisficing solutions and duality in interval and fuzzy linear programming fuzzy sets and systems 135 2003 151 177 have proved some important dual theorems on fgp which are very close to the same crisp versions in continuation to their works based on fuzzy extensions of relations we get complementary slackness conditions for fgp which have an essential role in many optimization techniques moreover we obtain the most optimistic and pessimistic satisficing solutions employing these conditions and present a convex combination of them which covers the satisficing solutions for a fixed level of certainty our practical schemes implement an efficient interior point algorithm as sub procedure so they are polynomial time algorithms

confidence interval construction for proportion difference in small sample paired studies paired dichotomous data may arise in clinical trials such as pre post test comparison studies and equivalence trials reporting parameter estimates e g odds ratio rate difference and rate ratio along with their associated confidence interval estimates becomes a necessity in many medical journals various asymptotic confidence interval estimators have long been developed for differences in correlated binary proportions nevertheless the performance of these asymptotic methods may have poor coverage properties in small samples in this article we investigate several alternative confidence interval estimators for the difference between binomial proportions based on small sample paired data specifically we consider exact and approximate unconditional confidence intervals for rate difference via inverting a score test the exact unconditional confidence interval guarantees the coverage probability and it is recommended if strict control of coverage probability is required however the exact method tends to be overly conservative and computationally demanding our empirical results show that the approximate unconditional score confidence interval estimators based on inverting the score test demonstrate reasonably good coverage properties even in small sample designs and yet they are relatively easy to implement computationally we illustrate the methods using real examples from a pain management study and a cancer study

satisficing solutions and duality in interval and fuzzy linear programming in this paper we introduce a class of fuzzy linear programming problems and define the concepts of feasible and satisficing solutions the necessary tools for dealing with such problems in this way we show that the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems we define the concept of duality and prove the weak and strong duality theorems further we define a class of interval linear programming problems as a special subclass of flp problems and apply the previous results to this special case

equivalence test and confidence interval for the difference in proportions for the paired sample design summary this paper considers a model for the di erence of two proportions in a paired or matched design of clinical trials case control studies and also sensitivity comparison studies of two laboratory tests this model includes a parameter indicating both interpatient variability of response probabilities and their correlation under the proposed model we derive a one sided test for equivalence based upon the e cient score equivalence is defined here as not more than 100 per cent inferior mcnemar s test for significance is shown to be a special case of the proposed test further a score based confidence interval for the di erence of two proportions is derived one of the features of these methods is applicability to the 2 2 table with o diagonal zero cells all the mcnemar type tests and confidence intervals published so far cannot apply to such data a monte carlo simulation study shows that the proposed test has empirical significance levels closer to the nominal a level than the other tests recently proposed and further that the proposed confidence interval has better empirical coverage probability than those of the four published methods 1998 john wiley sons ltd

regularized gap functions and error bounds for generalized mixed weak vector quasivariational inequality problems in fuzzy environments abstract in this paper we establish gap functions for a new class of generalized mixed weak vector quasivariational inequality problems in fuzzy environments in short mqvipf these functions are constructed through terms of regularized gap functions using the method of nonlinear scalarization functions moreover error bounds are provided for mqvipf via regularized gap functions under suitable assumptions the main results obtained in this paper improve and extend some corresponding known results some examples are given to illustrate our results

solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach abstract the solid transportation problem stp arises when bounds are given on three item properties the fuzzy solid transportation problem fstp appears when the nature of the data problem is fuzzy this paper deals with the fstp in the case in which the fuzziness affects the constraint set and a fuzzy solution to the problem is required moreover an arbitrary linear or nonlinear objective function is considered in order to find a fuzzy solution to the problem a parametric approach is used to obtain an auxiliary parametric solid transportation problem pstp associated to the original problem as there are no well known solution methods proposed in literature to solve effectively the pstp in this paper an evolutionary algorithm ea based solution method is proposed to solve it which can finally be applied to find a good fuzzy solution to the fstp comparisons with another conventional method are presented and the results show the ea based approach to be better as a whole

an algorithm for generalized fuzzy binary linear programming problems abstract fuzzy binary linear programming fblp problems are very essential in many fields such as assignment and assembly line balancing problems in operational research multiple projects locations and candidates selection cases in management science as well as representing and reasoning with prepositional knowledge in artificial intelligence although fblp problems play a significant role in human decision environment not very much research has focused on fblp problems this work first proposes a simple means of expressing a triangular fuzzy number as a linear function with an absolute term a method of linearizing absolute terms is also presented the developed goal programming gp model weighted by decision makers dms preference aims to optimize the expected objective function and minimize the sum of possible membership functions deviations after presented a novel way of linearizing product terms the solution algorithm is proposed to generate a crisp trade off promising solution that is also an optimal solution in a certain sense three examples equipment purchasing choice investment project selection and assigning clients to project leaders illustrate that the proposed algorithm can effectively solve generalized fblp problems

a more powerful exact test of noninferiority from binary matched pairs data assessing the therapeutic noninferiority of one medical treatment compared with another is often based on the difference in response rates from a matched binary pairs design this paper develops a new exact unconditional test for noninferiority that is more powerful than available alternatives there are two new elements presented in this paper first we introduce the likelihood ratio statistic as an alternative to the previously proposed score statistic of nam biometrics 1997 53 1422 1430 second we eliminate the nuisance parameter by estimation followed by maximization as an alternative to the partial maximization of berger and boos am stat assoc 1994 89 1012 1016 or traditional full maximization based on an extensive numerical study we recommend tests based on the score statistic the nuisance parameter being controlled by estimation followed by maximization

an interactive possibilistic programming approach for multiple objective supply chain master planning providing an efficient production plan that integrates the procurement and distribution plans into a unified framework is critical to achieving competitive advantage in this paper we consider a supply chain master planning model consisting of multiple suppliers one manufacturer and multiple distribution centers we first propose a new multi objective possibilistic mixed integer linear programming model mopmilp for integrating procurement production and distribution planning considering various conflicting objectives simultaneously as well as the imprecise nature of some critical parameters such as market demands cost time coefficients and capacity levels then after applying appropriate strategies for converting this possibilistic model into an auxiliary crisp multi objective linear model molp we propose a novel interactive fuzzy approach to solve this molp and finding a preferred compromise solution the proposed model and solution method are validated through numerical tests computational results indicate that the proposed fuzzy method outperforms other fuzzy approaches and is very promising not only for solving our problem but also for any molp model especially multi objective mixed integer models

improved confidence intervals for the difference between binomial proportions based on paired data existing methods for setting confidence intervals for the difference theta between binomial proportions based on paired data perform inadequately the asymptotic method can produce limits outside the range of validity the exact conditional method can yield an interval which is effectively only one sided both these methods also have poor coverage properties better methods are described based on the profile likelihood obtained by conditionally maximizing the proportion of discordant pairs a refinement methods 5 and 6 which aligns 1 alpha with an aggregate of tail areas produces appropriate coverage properties a computationally simpler method based on the score interval for the single proportion also performs well method 10

a fuzzy programming approach for a cell formation problem with dynamic and uncertain conditions this paper presents an integration of explicit uncertainty for a cell formation problem cfp with a dynamic condition in cellular manufacturing systems cms the dynamic condition indicates a multi period planning horizon in which product mix and demand in each period are different as a result the best cells designed for one period may not be the most efficient for subsequent periods and thus require reconfigurations moreover in real manufacturing systems some input parameters are fuzzy in nature in such cases the fluctuation in part demand and the availability of manufacturing facilities in each period can also be regarded as fuzzy in this paper a fuzzy programming based approach is developed to solve an extended mixed integer programming model of the dynamic cfp in which there are piecewise fuzzy numbers as coefficients in the objective function and the technological matrix the main purpose of this paper is to determine the optimal cell configuration in each period with the maximum degree of satisfying the fuzzy objective under the given constraints to illustrate the behavior of the proposed model and verify the performance of the developed fuzzy programming based approach we introduce a number of numerical examples to illustrate the use of the foregoing approach finally the related computational results are reported and discussed

fuzzy location problems on networks location problems concern a wide set of fields where it is usually assumed that exact data are known however in real applications the location of the facility considered can be full of linguistic vagueness that can be appropriately modelled using networks with fuzzy values thus fuzzy location problems on networks arise this paper deals with their general formulation and the description of the ways to solve them namely we show the variety of problems that can be considered in this context and for some of them we propose the most operative approaches for their solution

duality in fuzzy linear programming with possibility and necessity relations a class of fuzzy linear programming flp problems with fuzzy coefficients based on fuzzy relations is introduced the concepts of feasible and a b maximal and minimal solutions are defined the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems a new concept of duality is introduced and the weak and strong duality theorems are derived the introduced concepts and results are illustrated and discussed on a simple numerical example

binomial confidence intervals abstract for x with binomial n p distribution section 1 gives a one page table of 95 and 99 confidence intervals for p for n 1 2 30 this interval is equivariant under x n x and p 1 p has approximately equal probability tails is approximately unbiased has crow s property of minimizing the sum of the n 1 possible lengths and each of its ends is increasing in x and decreasing in n with about as regular steps as possible sections 2 and 3 consider the usual approximate confidence intervals calculations and asymptotic results show the need for the continuity correction in these even when n is large because of the nonuniformity of the binomial normal convergence as p 0 these intervals fail to have their stated asymptotic confidence coefficients simple corrections are given for this in the approximate interval x n c n x n 1 x n 1 2n it is shown that the factor c n should be replaced by c n c 2 2c n 1 n

confidence intervals for a ratio of binomial proportions based on paired data four interval estimation methods for the ratio of marginal binomial proportions are compared in terms of expected interval width and exact coverage probability two new methods are proposed that are based on combining two wilson score intervals the new methods are easy to compute and perform as well or better than the method recently proposed by nam and blackwelder two sample size formulas are proposed to approximate the sample size required to achieve an interval estimate with desired confidence level and width

an extension to possibilistic linear programming abstract this paper proposes an extension to the solution of possibilistic linear programming problems with fuzzy number parameters introduced by buckley fuzzy sets and systems31 1989 329 341 the method relies on cuts of the fuzzy number parameters to generate a succession of pairs of classical linear programs the solutions of these linear programs produce a convex possibility distribution of the optimal objective values with the corresponding levels of the decision variables the approach is illustrated with an imprecise water quality management problem

buehler confidence bounds for a reliability maintainability measure this article presents an upper confidence bound for a measure of reliability maintainability of a series system in which component repair is assumed to restore the system to its original status under exponentiality of component repair time and survival time distributions the measure m is the ratio of expected system repair time to expected system survival time moreover under this exponentiality assumption the bound is uniformly minimum among all bounds of specified level that are nondecreasing functions of the maximum likelihood estimator of m as a matter of practical interest the measure m has been incorporated into military standard mil std 470b and is an official statistic of the air force reliability maintainability information system

modulation equation and spdes on unbounded domains we consider the approximation via modulation equations for nonlinear spdes on unbounded domains with additive space time white noise close to a bifurcation an infinite band of eigenvalues changes stability and we study the impact of small space time white noise on the dynamics close to this bifurcation as a first example we study the stochastic swift hohenberg equation on the whole real line here due to the weak regularity of solutions the standard methods for modulation equations fail and we need to develop new tools to treat the approximation as an additional result we sketch the proof for local existence and uniqueness of solutions for the stochastic swift hohenberg and the complex ginzburg landau equations on the whole real line in weighted spaces that allow for unboundedness at infinity of solutions which is natural for translation invariant noise like space time white noise we use energy estimates to show that solutions of the ginzburg landau equation are holder continuous and have moments in those functions spaces this gives just enough regularity to proceed with the error estimates of the approximation result

test based exact confidence intervals for the difference of two binomial proportions summary confidence intervals are often provided to estimate a treatment difference when the sample size is small as is typical in early phases of clinical trials confidence intervals based on large sample approximations may not be reliable in this report we propose test based methods of constructing exact confidence intervals for the difference in two binomial proportions these exact confidence intervals are obtained from the unconditional distribution of two binomial responses and they guarantee the level of coverage we compare the performance of these confidence intervals to ones based on the observed difference alone we show that a large improvement can be achieved by using the standardized z test with a constrained maximum likelihood estimate of the variance

ranking function based solutions of fully fuzzified minimal cost flow problem the aim of minimal cost flow problem mcfp is to find the least transportation cost of a single commodity through a capacitated network this paper presents a model to deal with one particular group of such problems in which the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers for easier reference hereafter we refer to this group of problems as fully fuzzified mcfp to represent our model hukuhara s difference and approximated multiplication are used thereafter we sort fuzzy numbers by an order using a ranking function and show that it is a total order i e a reflexive anti symmetric transitive and complete binary relation utilizing the proposed ranking function we transform the fully fuzzified mcfp into three crisp problems solvable in polynomial time from this standpoint combinatorial algorithms are provided to solve the above mentioned problem and find the fuzzy optimal flow furthermore the proposed order is related to the importance weights of the center the left spread and the right spread of each fuzzy number thus this method is capable of handling the decision maker s risk taking by comparing some previous ranking function based works with our method the efficiency of the latter is revealed finally an application of our proposed method to petroleum industry is presented

using fuzzy numbers in network design optimization problems the fluctuations that have taken place in the worldwide economy over the past few years make it difficult to estimate the costs of the equipment that have to be used in order to design a telecommunications network the literature is replete with prescriptive integer programming models for various network design problems that do not take into account the problems inherent vagueness due to equipment costs this paper considers the real world wavelength division multiplexing wdm network design problem the vagueness that appears in this problem is assumed and handled by means of fuzzy set based methodologies a fuzzy integer linear programming model is then proposed to be used as an auxiliary model to solve the former problem with the purpose to obtain cost effective network designs this model is then solved using cplex which is a commercial high performance optimization engine

confidence intervals for the binomial parameter some new considerations several methods have been proposed to construct confidence intervals for the binomial parameter some recent papers introduced the mean coverage criterion to evaluate the performance of confidence intervals and suggested that exact methods because of their conservatism are less useful than asymptotic ones in these studies however exact intervals were always represented by the clopper pearson interval c p now we focus on sterne s interval which is also exact and known to be better than the c p in the two sided case introducing a computer intensive level adjustment procedure which allows constructing intervals that are exact in terms of mean coverage we demonstrate that sterne s interval performs better than the best asymptotic intervals even in the mean coverage context level adjustment improves the c p as well which with an appropriate level adjustment becomes equivalent to the mid p interval finally we show that the asymptotic behaviour of the mid p method is far poorer than is generally expected

approximation and attractivity properties of the degenerated ginzburg landau equation abstract we are interested in spatially extended pattern forming systems close to the threshold of the first instability in case when the so called degenerated ginzburg landau equation takes the role of the classical ginzburg landau equation as the amplitude equation of the system this is the case when the relevant nonlinear terms vanish at the bifurcation point here we prove that in this situation every small solution of the pattern forming system develops in such a way that after a certain time it can be approximated by the solutions of the degenerated ginzburg landau equation in this paper we restrict ourselves to a swift hohenberg kuramoto shivashinsky equation as a model for such a pattern forming system

nonlinear stability of taylor vortices in infinite cylinders we consider the taylor couette problem in an infinitely extended cylindrical domain in the case when couette flow is weakly unstable and a family of spatially periodic equilibria called the taylor vortices has bifurcated from this trivial ground state we show that those taylor vortices which are not linearly unstable in the sense of eckhaus are in fact nonlinearly stable with respect to small spatially localized perturbations the main difficulty in showing this result stems from the fact that on unbounded cylindrical domains the taylor vortices are only linearly marginally stable with continuous spectrum up to the imaginary axis bloch wave representations of the solutions and renormalization theory allow us to show that the nonlinear problem behaves asymptotically like the linearized one which is under a diffusive regime

on the sample size for one sided equivalence of sensitivities based upon mcnemar s test in this paper we formalize the problem of testing the one sided equivalence in the sensitivities of two medical diagnostic tests under a matched pair study design we derive conditional and unconditional sample size formulae which are decreasing functions of the probability of being diagnosed by both tests we calculate upper boundary and midpoint sample sizes results of a monte carlo simulation study that compares the proposed sample size formulae with that of lachenbruch suggest that our midpoint conditional sample size is the best choice to obtain the desired power for the type of equivalence studies discussed in the paper

the shortest path problem on networks with fuzzy parameters shortest path problem where the costs have vague values is one of the most studied problems in fuzzy sets and systems area however due to its high computational complexity previously published algorithms present peculiarities and problems that need to be addressed e g they find costs without an existing path they determine a fuzzy solution set but do not give any guidelines to help the decision maker choose the best path they can only be applied in graphs with fuzzy non negative parameters etc in this paper one proposes an iterative algorithm that assumes a generic ranking index for comparing the fuzzy numbers involved in the problem in such a way that each time in which the decision maker wants to solve a concrete problem s he can choose or propose the ranking index that best suits that problem this algorithm that solves the above remarked drawbacks is based on the ford moore bellman algorithm for classical graphs and in concrete it can be applied in graphs with negative parameters and it can detect whether there are negative circuits for the sake of illustrating the performance of the algorithm in the paper it has been here developed using only certain order relations but it is not restricted at all to use these comparison relations exclusively the proposed algorithm is easy of understanding as the theoretical base of a decision support system oriented to solving this kind of problems

possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems abstract in this paper several kinds of possibility distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems interval and triangular possibility distributions are used to express the non interactive cases between the fuzzy decision variables and exponential possibility distributions are used to represent the interrelated cases possibilistic linear programming problems based on exponential possibility distributions become non linear optimization problems in order to solve optimization problems easily algorithms for obtaining center vectors and distribution matrices in sequence are proposed by the proposed algorithms the possibility distribution of fuzzy decision variables can be obtained

short rational generating functions for solving some families of fuzzy integer programming problems in this paper we present new complexity results for solving single and multiobjective fuzzy integer programs with soft constraints and fuzzy objective function coefficients our method is based on the use of barvinok s short rational generating functions of convenient transformations of the fuzzy problems to crisp ones this analysis allows us to provide new insights on the structure of these families of fuzzy programs

unconditional exact tests for equivalence or noninferiority for paired binary endpoints problems of establishing equivalence or noninferiority between two medical diagnostic procedures involve comparisons of the response rates between correlated proportions when the sample size is small the asymptotic tests may not be reliable this article proposes an unconditional exact test procedure to assess equivalence or noninferiority two statistics a sample based test statistic and a restricted maximum likelihood estimation rmle based test statistic to define the rejection region of the exact test are considered we show the p value of the proposed unconditional exact tests can be attained at the boundary point of the null hypothesis assessment of equivalence is often based on a comparison of the confidence limits with the equivalence limits we also derive the unconditional exact confidence intervals on the difference of the two proportion means for the two test statistics a typical data set of comparing two diagnostic procedures is analyzed using the proposed unconditional exact and asymptotic methods the p value from the unconditional exact tests is generally larger than the p value from the asymptotic tests in other words an exact confidence interval is generally wider than the confidence interval obtained from an asymptotic test

solving a dynamic cell formation problem using metaheuristics in this paper solving a cell formation cf problem in dynamic condition is going to be discussed by using some traditional metaheuristic methods such as genetic algorithm ga simulated annealing sa and tabu search ts most of previous researches were done under the static condition due to the fact that cf is a np hard problem then solving the model using classical optimization methods needs a long computational time in this research a nonlinear integer model of cf is first given and then solved by ga sa and ts then the results are compared with the optimal solution and the efficiency of the proposed algorithms is discussed

a linear programming embedded genetic algorithm for an integrated cell formation and lot sizing considering product quality production lot sizing models are often used to decide the best lot size to minimize operation cost inventory cost and setup cost cellular manufacturing analyses mainly address how machines should be grouped and parts be produced in this paper a mathematical programming model is developed following an integrated approach for cell configuration and lot sizing in a dynamic manufacturing environment the model development also considers the impact of lot sizes on product quality solution of the mathematical model is to minimize both production and quality related costs the proposed model with nonlinear terms and integer variables cannot be solved for real size problems efficiently due to its np complexity to solve the model for practical purposes a linear programming embedded genetic algorithm was developed the algorithm searches over the integer variables and for each integer solution visited the corresponding values of the continuous variables are determined by solving a linear programming subproblem using the simplex algorithm numerical examples showed that the proposed method is efficient and effective in searching for near optimal solutions

fuzzy integer transportation problem an algorithm has been proposed which solves the transportation problem with fuzzy supply and demand values and the integrality condition imposed on the solution this algorithm is exact and computationally effective although the problem is formulated in the general way i e its fuzzy supply and demand values can differ from each other and be fuzzy numbers of any type

fuzzy mathematical programming based on some new inequality relations abstract this paper deals with inequality relations in fuzzy mathematical programming problem fmp not necessarily linear moreover fuzzy parameters may have nonlinear membership functions a new approach for comparing fuzzy sets is proposed which is more general than the well known proposals in the literature

improved confidence intervals for the difference between binomial proportions based on paired data by robert g newcombe statistics in medicine 17 2635 2650 1998

optimal solutions in optimization problem with objective function depending on fuzzy parameters in this paper we first introduce a broad class of fuzzy optimization problems with an objective function depending on fuzzy parameters fo problems and introduce the concept a maximal solutions of fo problems with respect to some fuzzy relation we derive a simple and natural sufficient condition for a feasible solution to be an a maximal solutions of fo problem later on we define possibly and necessarily a maximal solutions of fo problems and prove that any possibly or necessarily a maximal solution of fo problem is an a maximal solution with respect to the possibilistic fuzzy relation or necessity fuzzy relation respectively the introduced concepts and results are illustrated and discussed on two numerical examples

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

an approximate unconditional test of non inferiority between two proportions this paper investigates an approximate unconditional test for non inferiority between two independent binomial proportions the p value of the approximate unconditional test is evaluated using the maximum likelihood estimate of the nuisance parameter in this paper we clarify some differences in defining the rejection regions between the approximate unconditional and conventional conditional or unconditional exact test we compare the approximate unconditional test with the asymptotic test and unconditional exact test by chan statistics in medicine 17 1403 1413 1998 with respect to the type i error and power in general the type i errors and powers are in the decreasing order of the asymptotic approximate unconditional and unconditional exact tests in many cases the type i errors are above the nominal level from the asymptotic test and are below the nominal level from the unconditional exact test in summary when the non inferiority test is formulated in terms of the difference between two proportions the approximate unconditional test is the most desirable because it is easier to implement and generally more powerful than the unconditional exact test and its size rarely exceeds the nominal size however when a test between two proportions is formulated in terms of the ratio of two proportions such as a test of efficacy more caution should be made in selecting a test procedure the performance of the tests depends on the sample size and the range of plausible values of the nuisance parameter published in 2000 by john wiley sons ltd

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

unconditional efficient one sided confidence limits for the odds ratio based on conditional likelihood we compare various one sided confidence limits for the odds ratio in a 2 x 2 table the first group of limits relies on first order asymptotic approximations and includes limits based on the signed likelihood ratio score and wald statistics the second group of limits is based on the conditional tilted hypergeometric distribution with and without mid p correction all these limits have poor unconditional coverage properties and so we apply the general transformation of buehler j am statist assoc 1957 52 482 493 to obtain limits which are unconditionally exact the performance of these competing exact limits is assessed across a range of sample sizes and parameter values by looking at their mean size the results indicate that buehler limits generated from the conditional likelihood have the best performance with a slight preference for the mid p version this confidence limit has not been proposed before and is recommended for general use especially when the underlying probabilities are not extreme

on small sample confidence intervals for parameters in discrete distributions summary the traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level in constructing such intervals for parameters in discrete distributions less conservative behavior results from inverting a single two sided test than inverting two separate one sided tests of half the nominal level each we illustrate for a variety of discrete problems including interval estimation of a binomial parameter the difference and the ratio of two binomial parameters for independent samples and the odds ratio

measuring the satisfaction of constraints in fuzzy linear programming the paper proposes a new kind of method for solving fuzzy linear programming problems based on the satisfaction or fulfillment degree of the constraints using a new ranking method of fuzzy numbers the fulfillment of the constraints can be measured then the properties of the ranking index are discussed with this ranking index the decision maker can make the constraints tight or loose based on his optimistic or pessimistic attitude and get the optimal solution from the fuzzy constraint space the corresponding value of objective distribution function can be obtained a numerical example illustrates the merits of the approach

more powerful exact noninferiority and equivalence tests based on binary matched pairs assessing the therapeutic noninferiority or equivalence of one medical treatment compared to another is often based on the difference of response rates from a matched binary pairs design this paper develops new exact unconditional tests for noninferiority and equivalence that are more powerful than available alternatives there are three new elements presented in this paper first we introduce the lr statistic as an alternative to the previously proposed score statistic of nam 1997 second we eliminate the nuisance parameter by estimation followed by maximization as an alternative to the partial maximization of berger and boos 1994 or traditional full maximization third for testing equivalence it is standard to combine two one sided tests tost we point out that even if the one sided tests are exact and efficient the tost will be conservative and requires a further adjustment to remove this conservatism based on an extensive numerical study we recommend tests based on the score statistic the nuisance parameter being controlled by estimation followed by maximization

application of fuzzy minimum cost flow problems to network design under uncertainty this paper deals with fuzzy quantities and relations in multi objective minimum cost flow problem when t norms and t conorms are available the goal programming is applied to minimize the deviation among the multiple costs of fuzzy flows and the given targets when the fuzzy supplies and demands are satisfied to obtain the most optimistic and the most pessimistic satisficing solutions of this problem two polynomial time algorithms are introduced applying some network transformations to demonstrate the performance of this approach in actual substances network design under fuzziness is considered and an efficient scheme is proposed including genetic algorithm together with fuzzy minimum cost flow problem this scheme is applied on a pilot network for more description

exact one sided confidence limits for the difference between two correlated proportions we construct exact and optimal one sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well established optimality theory of buehler starting with five different approximate lower and upper limits we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use

the importance of the designated statistic on buehler upper limits on a system failure probability the upper limits introduced by buehler are constructed to be honest confidence limits that are as small as possible subject to the constraint that they are nondecreasing functions of a designated statistics this methodology has largely been developed for applications in reliability that involve finding an upper limit on the probability of failure p1 pk of a system of k components with probabilities of failure pi for mainly computational reasons it is common to choose the designated statistic s p1 pk where pi is an estimator of pi buehler on the other hand suggested the choice s pu1 puk where pui is a so called exact 1 1 k upper limit for pi in this article we draw attention to existing general theory suggesting that s should be chosen to be an approximate upper limit for the interest parameter not an estimator we also give numerical results suggesting that extreme loss in efficiency typically follows if s is chosen poorly our current recommendation is that s should be an a

process planning in a fuzzy environment abstract mixed integer optimization models for chemical process planning typically assume that model parameters can be accurately predicted as precise forecasts are difficult to obtain process planning usually involves uncertainty and ambiguity in the data this paper presents an application of fuzzy programming to process planning the forecast parameters are assumed to be fuzzy with a linear or triangular membership function the process planning problem is then formulated in terms of decision making in a fuzzy environment with fuzzy constraints and fuzzy net present value goals the model is transformed to a deterministic mixed integer linear program or mixed integer nonlinear program depending on the type of uncertainty involved in the problem for the nonlinear case a global optimization algorithm is developed for its solution this algorithm is applicable to general possibilistic programs and can be used as an alternative to the commonly used bisection method illustrative examples and computational results for a petrochemical complex with 38 processes and 24 products illustrate the applicability of the developed models and algorithms

fuzzy multi level minimum cost flow problems both multiple objectives and multiple hierarchies minimum cost flow problems with fuzzy costs and fuzzy capacities in the arcs are investigated to reduce the complexity a possibility programming is used to handle the vagueness in the parameters fuzzy approach can considerably simplify the problem and thus a fairly general multi level problem can be solved reasonably easily in spite of the fact that the multi level problem is np hard and very difficult to solve several numerical examples are considered to illustrate the approach

fuzzy goals and fuzzy alternatives in goal programming problems in this paper we generalize a standard goal programming gp problem to investigate gp problems with alternatives and goals being fuzzy sets and the satisfaction of a goal by a fuzzy goal function defined on alternatives set is also understood by a fuzzy relation we propose a unifying approach covering several approaches known from literature

solving fuzzy transportation problems based on extension principle abstract transportation models play an important role in logistics and supply chain management for reducing cost and improving service this paper develops a procedure to derive the fuzzy objective value of the fuzzy transportation problem in that the cost coefficients and the supply and demand quantities are fuzzy numbers the idea is based on the extension principle a pair of mathematical programs is formulated to calculate the lower and upper bounds of the fuzzy total transportation cost at possibility level from different values of the membership function of the objective value is constructed two different types of the fuzzy transportation problem are discussed one with inequality constraints and the other with equality constraints it is found that the membership function of the objective value of the equality problem is contained in that of the inequality problem since the objective value is expressed by a membership function rather than by a crisp value more information is provided for making decisions

fuzzy boolean programming problems with fuzzy costs a general study abstract this paper deals with boolean linear programming problems involving coefficients in the objective function as fuzzy numbers in the study of these problems different approaches can be proposed to use ranking fuzzy numbers methods and fuzzy preference relations obtaining auxiliary classical boolean programming problems and to use the representation theorem obtaining a convex set with extreme points defined by the lower or upper bound of the a level sets of the fuzzy coefficients and consequently an auxiliary interval boolean programming problem in this paper we develop and link the different approaches

amplitude equation for lattice maps a renormalization group approach we consider the development of instabilities of homogeneous stationary solutions of discrete time lattice maps under some generic hypotheses we derive an amplitude equation which is the space time continuous ginzburg landau equation using dynamical renormalization group methods we control the accuracy of this approximation in a large ball of its basin of attraction

tests for equivalence or non inferiority for paired binary data assessment of therapeutic equivalence or non inferiority between two medical diagnostic procedures often involves comparisons of the response rates between paired binary endpoints the commonly used and accepted approach to assessing equivalence is by comparing the asymptotic confidence interval on the difference of two response rates with some clinical meaningful equivalence limits this paper investigates two asymptotic test statistics a wald type sample based test statistic and a restricted maximum likelihood estimation rmle based test statistic to assess equivalence or non inferiority based on paired binary endpoints the sample size and power functions of the two tests are derived the actual type i error and power of the two tests are computed by enumerating the exact probabilities in the rejection region the results show that the rmle based test controls type i error better than the sample based test to establish an equivalence between two treatments with a symmetric equivalence limit of 0 15 a minimal sample size of 120 is needed the rmle based test without the continuity correction performs well at the boundary point 0 a numerical example illustrates the proposed procedures

the solution and duality of imprecise network problems duality properties have been investigated by many researchers in the recent literature they are introduced in this paper for a fully fuzzified version of the minimal cost flow problem which is a basic model in network flow theory this model illustrates the least cost of the shipment of a commodity through a capacitated network in terms of the imprecisely known available supplies at certain nodes which should be transmitted to fulfil uncertain demands at other nodes first we review on the most valuable results on fuzzy duality concepts to facilitate the discussion of this paper by applying hukuhara s difference approximated and exact multiplication and wu s scalar production we exhibit the flow in network models then we use combinatorial algorithms on a reduced problem which is derived from fully fuzzified mcfp to acquire fuzzy optimal flows to give duality theorems we utilize a total order on fuzzy numbers due to the level of risk and realize optimality conditions for providing some efficient combinatorial algorithms finally we compare our results with the previous worthwhile works to demonstrate the efficiency and power of our scheme and the reasonability of our solutions in actual decision making problems

a new exact and more powerful unconditional test of no treatment effect from binary matched pairs we consider the problem of testing for a difference in the probability of success from matched binary pairs starting with three standard inexact tests the nuisance parameter is first estimated and then the residual dependence is eliminated by maximization producing what i call an e m p value the e m p value based on mcnemar s statistic is shown numerically to dominate previous suggestions including partially maximized p values as described in berger and sidik 2003 statistical methods in medical research 12 91 108 the latter method however may have computational advantages for large samples

two step interactive satisfactory method for fuzzy multiple objective optimization with preemptive priorities this paper presents a two step interactive satisfactory optimization method for fuzzy multiple objective optimization with preemptive priorities in contrast to previous works this proposed approach guarantees the order of satisfactory degrees consistent with priorities the decision maker not only acquires satisfactory solution of all the objectives but also realizes the preemptive priority requirement among them the originally complex optimization problem is simplified and divided into two subproblems that are solved in sequence numerical examples and actual application show the proposed method s effectiveness flexibility and efficiency in comparison with results from the literature

exact tests of equivalence and efficacy with a non zero lower bound for comparative studies exact tests of equivalence and efficacy with a non zero lower bound based on two independent binomial proportions for comparative trials are proposed these exact tests are desirable for studies with small sample sizes they generalize classical methods to include testing of null hypotheses of prespecified differences and can be used to demonstrate a new treatment s efficacy or its equivalence to a standard treatment the proposed exact tests use unconditional distributions of the test statistics variances of test statistics are estimated via a constrained maximum likelihood method farrington and manning data from oncology and vaccine clinical trials are used to illustrate the exact tests

confidence intervals from the difference between two correlated proportions abstract when data arise as matched binary pairs it is often of interest to test whether or not the probabilities of an odd pair of each type are equal construction of a small sample confidence interval for the difference in these probabilities is more difficult and either approximate or conservative methods need be resorted to two methods are suggested in this article one a natural asymptotic method and the other a more generally applicable conservative method the coverage probability and average width are studied for small and moderate sample sizes

diffusive stability of spatial periodic solutions of the swift hohenberg equation we are interested in the nonlinear stability of the eckhaus stable equilibria of the swift hohenberg equation on the infinite line with respect to small integrable perturbations the difficulty in showing stability for these stationary solutions comes from the fact that their linearizations possess continuous spectrum up to zero the nonlinear stability problem is treated with renormalization theory which allows us to show that the nonlinear terms are irrelevant i e that the fully nonlinear problem behaves asymptotically as the linearized one which is under a diffusive regime

exact unconditional tests for testing non inferiority in matched pairs design the problem of testing non inferiority in a 2 2 matched pairs sample is considered two exact unconditional tests based on the standard and the confidence interval p values are proposed although tests of non inferiority have two nuisance parameters under the null hypothesis the exact tests are defined by reducing the dimension of nuisance parameter space from two to one using the monotonicity of the distribution the exact sizes and powers of these tests and the existing asymptotic test are considered the exact tests are found to be accurate in view of their size property in addition the exact test based on the confidence interval p value is more powerful than the other exact test it is shown that the asymptotic test is inaccurate that is its size exceeds the claimed nominal level therefore it recommends a cautious approach in use of the asymptotic test for the problem of testing non inferiority particularly when sample sizes are small or moderately large copyright 2003 john wiley sons ltd

algorithms of discrete optimization and their application to problems with fuzzy coefficients an approach to solving optimization problems with fuzzy coefficients in objective functions and constraints is described it consists in formulating and solving one and the same problem within the framework of mutually related models with constructing equivalent analogs with fuzzy coefficients in objective functions alone it enables one to maximally cut off dominated alternatives from below as well as from above since the approach is applied within the context of fuzzy discrete optimization problems several modified algorithms of discrete optimization are discussed these algorithms are associated with the method of normalized functions are based on a combination of formal and heuristic procedures and allow one to obtain quasi optimal solutions after a small number of steps thus overcoming the computational complexity posed the np completeness of discrete optimization problems the subsequent contraction of the decision uncertainty regions is associated with reduction of the problem to multiobjective decision making in a fuzzy environment with using techniques based on fuzzy preference relations the techniques are also directly applicable to situations in which the decision maker is required to choose alternatives from a set of explicitly available alternatives the results of the paper are of a universal character and can be applied to the design and control of systems and processes of different purposes as well as the enhancement of corresponding cad cam systems and intelligent decision making systems the results of the paper are already being used to solve problems of power engineering

simple improved confidence intervals for comparing matched proportions for binary matched pairs data this article discusses interval estimation of the difference of probabilities and an odds ratio for comparing success probabilities we present simple improvements of the commonly used wald confidence intervals for these parameters the improvement of the interval for the difference of probabilities is to add two observations to each sample before applying it the improvement for estimating an odds ratio transforms a confidence interval for a single proportion

boolean programming problems with fuzzy constraints abstract boolean linear programming problems for which there exist some lack of precision of vague nature in the constraints are considered an cut based approach is considered to solve them then an algorithm providing a fuzzy solution is proposed and analyzed the linking with other known solution methods is also studied

the 2 x 2 matched pairs trial exact unconditional design and analysis an exact unconditional method for the design and analysis of the 2 x 2 matched pairs trial is presented unlike the exact conditional method which is based on only the number of discordant pairs the exact unconditional method uses the total number n of sampled pairs this unconditional test based on a simple z statistic yields sample sizes that are generally smaller than those produced by the exact conditional test for the cases tabulated herein namely one sided alpha 01 025 and 05 along with 80 and 90 power moreover it is found to be uniformly more powerful than the latter for all the combinations of parameters considered in this paper namely alpha 01 025 and 05 and n 10 1 200 the method is illustrated by assessing various design options of an in vitro study of the effectiveness of antimicrobial agents some numerical examples of matching efficiency are also given

attractivity of the ginzburg landau mode distribution for a pattern forming system with marginally stable long modes abstract the mathematical theory of the description of pattern forming systems close to the first instability via the ginzburg landau equation is based on approximation and attractivity results this theory allowed to prove global existence results and upper semicontinuity of attractors for classical hydrodynamical stability problems such as the couette taylor problem recently approximation results for the ginzburg landau approximation for pattern forming systems with marginally stable long modes such as the benard marangoni system have been shown it is the purpose of this paper to prove the second fundamental property namely the attractivity of the ginzburg landau mode distribution for such systems

possible and necessary optimality tests in possibilistic linear programming problems in this paper two kinds of optimality concepts are introduced into fuzzy linear programming problems in order to discuss the rationality of an obtained solution one is possible optimality evaluating the possibility degree to which the solution is optimal the other the dual concept is necessary optimality evaluating the necessity degree to which the solution is optimal when possibility distributions are defined by closed intervals degrees of possible and necessary optimalities become binary necessary and sufficient conditions for possible and necessary optimalities are induced in this case extending the results methods of calculating the degrees of possible and necessary optimalities are proposed some numerical examples are given to demonstrate the proposed methods

necessity measure optimization in linear programming problems with fuzzy polytopes in this paper we treat fuzzy linear programming problems with uncertain parameters whose ranges are specified as fuzzy polytopes the problem is formulated as a necessity measure optimization model it is shown that the problem can be reduced to a semi infinite programming problem and solved by a combination of a bisection method and a relaxation procedure an algorithm in which the bisection method and the relaxation procedure converge simultaneously is proposed a simple numerical example is given to illustrate the solution procedure

multiple objective minimum cost flow problems a review in this paper theory and algorithms for solving the multiple objective minimum cost flow problem are reviewed for both the continuous and integer case exact and approximation algorithms are presented in addition a section on compromise solutions summarizes corresponding results the reference list consists of all papers known to the authors which deal with the multiple objective minimum cost flow problem

analyticity of ginzburg landau modes ginzburg landau formalism applies for dissipative systems defined on cylindrical domains which are close to the threshold of instability and for which the unstable fourier modes belong to non zero wave numbers in these situations the real part of the curve of critical eigenvalues as function drawn over the wave numbers k is positive of height o 2 and of width o here it is shown that the set of solutions which can be described by the ginzburg landau formalism is attractive to do this we demonstrate that in fourier space peaks appear at integer multiples of the critical wave number kc these peaks called ginzburg landau modes concentrate in time like e k mkc t for 0 t o 1 2 and m z the inverse fourier transform of such a ginzburg landau mode is an analytic function in a strip of width t this result extends a former work of w eckhaus

spl alpha cut fuzzy arithmetic simplifying rules and a fuzzy function optimization with a decision variable the problems of alpha cut fuzzy arithmetic have been shown like in interval arithmetic that distinct states of fuzzy parameters or fuzzy variable values may be chosen and produce an overestimated fuzziness meanwhile local extrema of a function may exist inside the support of fuzzy parameters and cause an underestimation of fuzziness and an illegal fuzzy number s result previous approaches to overcoming these problems have appeared in literature yet the computational burden of these approaches became even heavier thus this paper is based on the vertex method in literature and extensively proposes newly devised rules observed greatly useful for simplifying the vertex method these rules are devised through a function partitioned into subfunctions distinguishing the types of fuzzy parameter variable occurrences and types of subfunctions or functions with the various observations the improved efficiency has been found able to significantly reduce the combination vertex test of the vertex method for the fuzzy parameters alpha cut endpoints possibly to only a few fuzzy parameters endpoint combinations also as related a procedure for the fuzzy optimization of fuzzy functions with a fuzzy blurred argument a single variable is examined with the vertex method as well a proper and useful preliminary algorithm is proposed numerical examples with results are provided