imprecise weights in weber facility location problem abstract this paper presents a method for locating multiple facilities on a plane bounded by a convex polygon under the criterion minimize the sum of all the transportation cost where the cost per unit distances are known imprecisely assuming some fuzzy aspiration levels for each of the goals and basing these on a comparison of flat fuzzy numbers the original fuzzy problem is transferred into a crisp satisfactory model to determine a suitable solution we will maximize the minimum of the surpluses over the aspiration levels rectilinear distance norm has been taken as the scenario and may be considered as in an urban setting this induces the problem with a non linear objective function which is equivalent to a linear program a numerical example has been given to illustrate the solution procedure

residual maximum likelihood reml estimation of a neighbour model for field experiments a spatial analysis of field experiments is proposed which takes account of association between neighbouring plots the residual maximum likelihood reml method of patterson and thompson 1971 biometrika 58 545 554 is used to estimate parameters of a general neighbour model which can be expressed as an autoregressive moving average arma model three data sets are analysed to i highlight the need for a model selection procedure ii illustrate the differing results between incomplete block and neighbour analysis and the effect of including treated border plots in the design and iii illustrate the environmental variation within an experiment using prediction of trend

fuzzy logic based algorithms for maximum covering location problems this paper concerns a class of maximum covering location problems in networks in uncertain environments it is assumed that a relative weights of demand nodes are either deterministic or imprecise described by linguistic expressions and b potential facility site locations are limited to network nodes the concept of coverage is extended to include a degree of node coverage which means that the borders between the subset of covered demand nodes and the subset of uncovered demand nodes are inexact the acceptable service distance travelling times from a facility site to demand nodes are modelled by fuzzy sets three new algorithms for choosing the best facility locations are developed which assume that 1 demands at all nodes are equally important 2 relative weights of demand at nodes are deterministic and 3 weights of demand at nodes are imprecise and described by linguistic terms respectively the algorithms are based on searching among potential facility nodes by applying comparison operations on discrete fuzzy sets it is shown how to extend the proposed algorithms from one site to multi site covering problems illustrative examples of selecting locations for logistics centres in a distribution company are given

analysis of variety yield trials using two dimensional separable arima processes the two dimensional spatial analysis procedure based on separable arima processes proposed by cullis and gleeson 1991 biometrics 47 1449 1460 is used to analyze 35 cereal yield trials with incomplete block designs models with different large scale variation components and diverse small scale variation processes modeled as one dimensional and two dimensional separable arima processes were compared nineteen spatial models were considered and two criteria were used to assess spatial model adequacy a the average standard error of the pairwise variety differences sed and b the mean squared error of prediction mse based on a cross validation approach spatial analysis is more efficient in reducing residual variation than incomplete block analysis although there was no one model that best fit all the trials the two dimensional firstorder autoregressive model was the most efficient in terms of the sed and mse criteria in 21 and 14 trials respectively

statistical analysis of field experiments using neighbouring plots the paper describes and provides examples of four different applications of the use of neighbouring plot values in the analysis of agricultural field experiments the topics include the use of check plots to control environmental variation in large unreplicated variety trials spatial models based on first differences to accommodate fertility effects in trials that have some degree of replication adjustment for interplot competition using a simultaneous equations formulation and the analysis of trials in which plot values are affected by the particular treatments on neighbouring plots

regression models with spatially correlated errors abstract in this article we consider regression models for two dimensional spatial data when the errors follow a spatial unilateral first order autoregressive moving average arma model studied by basu and reinsel we give details on the convenient computation of the generalized least squares gls estimator of the regression parameters in the presence of spatially correlated errors and compare the gls estimator to the ordinary least squares ols estimator in some special cases we also consider the restricted maximum likelihood estimators of the spatial correlation model parameters which may be preferred over the maximum likelihood estimators for the special case of the spatial unilateral first order ar model details of the maximum likelihood as well as the restricted maximum likelihood estimation are given a numerical example is presented to illustrate the methods

interactive decision making in fuzzy linear optimization problems abstract this paper presents an interactive method for solving a multi criteria linear program where coefficients of the objective functions and or of the constraints are known exactly but imprecisely assuming fuzzy aspiration levels for each of the goals and basing on a comparison of flat fuzzy numbers the original fuzzy problem is transformed into a crisp satisfactory model to determine a suitable compromise solution we will maximize the minimum of the surpluses over the aspiration levels this induces a problem with a nonlinear objective function which is equivalent to a linear program

some aspects of experimental design and analysis when errors are correlated summary generalized least squares estimation is considered for some designs on the torus when the errors are assumed to follow a known second order stationary torus lattice process two general types of torus designs regular and treatment balanced are presented ordinary least squares is shown to be optimal for regular designs whilst certain treatment balanced designs are shown to be optimum under a wide range of optimality criteria the method of papadakis is investigated and shown to have simple solutions for these designs the relation of a theoretical form of papadakis s estimator to the generalized least squares estimator for the completely symmetric first order conditional torus lattice process is considered

a random field approach to the analysis of field plot experiments and other spatial experiments several nearest neighbor methods for the analysis of data from spatial experiments e g agricultural field experiments have recently been proposed these methods attempt to account for the effect of spatial heterogeneity on the estimation of treatment contrasts typically this is accomplished indirectly by differencing or by using residuals from neighboring plots to construct covariates we examine an alternative approach in which the spatial heterogeneity is modeled directly the model underlying our approach is similar to the model underlying a geostatistical kriging analysis and as in the latter model the observations are regarded collectively as a partial realization of a random field a randomization study of uniformity trial data suggests that the random field approach often provides more accurate estimates of treatment contrasts than nearest neighbor approaches in addition the random field approach is devoid of ambiguities as to the handling of border plots and is generally more flexible than nearest neighbor approaches

inequality relation between fuzzy numbers and its use in fuzzy optimization the inequality relation between two fuzzy numbers is investigated a certain type of such a relation motivated by practical interpretation is proposed and its correspondence with the usual lattice type relation generated by the extended maximum and minimum operators and its possible interpretation are discussed the concept of r l fuzzy number is introduced the class of all r l fuzzy numbers covering practically the whole set of normal convex fuzzy numbers comparing two r l fuzzy numbers of the same type the relation introduced in the paper may be replaced by four ordinary inequalities this fact may be taken advantage of in optimization problems with linear fuzzy constraints

necessary and sufficient conditions for oscillation of first order nonlinear neutral differential equations abstract in this paper we prove that every solution of the first order nonlinear neutral differential equation x t p x t q t j 1 m x t j j sign x t 1 0 t t 0 oscillates if and only if t 0 q s exp 1 ln p j 1 m j 1 s d s when j 1 m j 1 ln p 0 and t 0 q s d s when j 1 m j 1 ln p 0 where p 0 j 0 j 0 j 1 2 m q c t 0 0

a neighbour model for field experiments summary a neighbour type model is proposed as an alternative to that of wilkinson et al 1983 for the analysis of field variety trials the model assumes that the varieties are grouped into complete replicates and that the plots within a replicate are side by side a method for the estimation of the variance parameters is developed as an extension of the procedure commonly used in incomplete block designs the model is investigated using data from the 166 cereal variety trials studied by patterson hunter 1983 results show worthwhile gains in efficiency over conventional incomplete block analysis

the influence of design on validity and efficiency of neighbour methods summary neighbour methods have often been shown to be apparently more efficient than analysis of variance for the analysis of field experiments this means that the precision of the analysis estimated by the statistical method itself is smaller for the neighbour method than for the classical one this comparison is meaningful only if the analysis is valid in the sense that it estimates its own precision without bias although precise validity properties are known for the analysis of variance of randomized designs no analogous properties are known for neighbour analyses in this paper we investigate the validity and efficiency of some neighbour methods and their relations with the design first we give precise definitions of the desirable properties of the combination of design including randomization and method of analysis then we report on a simulation study we show that neighbour methods are often valid or conservative with higher efficiency than classical ones to better ensure these properties we advocate the use of randomized neighbour designs and corrections to degrees of freedom finally we discuss how these results can be used to assess neighbour methods for routine trials

are neighbour methods preferable to analysis of variance for completely systematic designs silly designs are silly summary it is shown that the usual analysis of a complete block design is weakly valid under a range of assumptions but that more sophisticated analyses of systematic block designs may not be consider a complete block design in which each block is a line of plots we shall call such a design silly if the treatments occur in the same order in each block in spite of fisher s 1935 27 warnings against silly designs they are still used partly for convenience in managing the experiment how should they be analysed candidate methods of analysis are i analysis of variance and ii classical neighbour methods by the former we mean the usual analysis of randomised complete blocks by the latter an analysis by restricted normal maximum likelihood and generalised least squares on the assumption that responses on plots in different blocks are uncorrelated and that patterns of covariance are the same within each block the restricted normal likelihood is symmetric about zero much of what follows applies to any such symmetric distribution fisher 1935 26 showed that analysis of variance for randomised complete block designs is strongly valid no matter how the data are correlated however if correlation between different plots is far from uniform then this combination of design and analysis may not be efficient for silly designs the lack of randomisation suggests that analysis of variance is not valid while the increased flexibility of the classical neighbour methods suggests that they should be better able to take account of proximity between plots this paper shows that under common assumptions both suggestions are false first a classical neighbour analysis of a silly design gives the same estimates of treatment effects as classical analysis of variance see proposition 2 secondly analysis of variance is valid in a weak sense if plots in different blocks are uncorrelated even if there is no randomisation see proposition 3 these results show that neighbour methods are of no interest for silly designs they give no true improvement over analysis of variance in fact they may be worse

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

role of the papadakis estimator in one and two dimensional field trials abstract field trials when observations are correlated with those in neighboring or nearby plots in one and two dimensions are analyzed using simultaneous autoregressive models the relationships between the maximum likelihood solutions and the corresponding well known papadakis estimators are clarified and it is shown that the maximum likelihood solutions are for specific types of designs easier to obtain directly then by iterating on the papadakis estimator as has been suggested a simulation study compares the different models and methods for one and two dimensions author

on the unbiasedness of the papadakis estimator and other nonlinear estimators of treatment contrasts in field plot experiments summary spatial methods for the analysis of field plot experiments are considered estimators of treatment contrasts obtained by these methods are generally complicated nonlinear functions of the observations sufficient conditions for these estimators to be unbiased under a postulated true model are obtained the analysis of data from field plot experiments or other spatial experiments generally includes the estimation of treatment contrasts a common approach to their estimation is to apply ordinary least squares to a linear model in which the expected value of each observation is taken to be the sum of an overall mean a treatment effect and various environmental effects such as block or row and column effects this approach yields estimators which are linear functions of the observations and which are unbiased if the assumed model is correct recently numerous spatial methods for the analysis of data from field plot experi ments have been proposed see for example bartlett 1978 wilkinson et al 1983 besag kempton 1986 williams 1986 and gleeson cullis 1987 these alternatives to a traditional least squares analysis attempt to neutralize the disruptive effect that the spatial heterogeneity of the experimental units can have on the estimation of treatment contrasts randomization studies of uniformity trial data conducted by besag kempton 1986 indicate that spatial methods yield estimators of treatments contrasts which in the presence of appreciable spatial heterogeneity are likely to be more efficient than traditional estimators however because the estimators produced by spatial methods are complicated nonlinear functions of the observations little else is known about their properties in what follows we give conditions under which these estimators are unbiased under a postulated true model

maximum likelihood estimation of models for residual covariance in spatial regression we describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters observations are assumed to be gaussian we give conditions which ensure consistency and asymptotic normality of the estimators our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators we also discuss an application of the spectral approximation to the likelihood for processes on a lattice

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12