asymptotics for in sample density forecasting this paper generalizes recent proposals of density forecasting models and it develops theory for this class of models in density forecasting the density of observations is estimated in regions where the density is not observed identification of the density in such regions is guaranteed by structural assumptions on the density that allows exact extrapolation in this paper the structural assumption is made that the density is a product of one dimensional functions the theory is quite general in assuming the shape of the region where the density is observed such models naturally arise when the time point of an observation can be written as the sum of two terms e g onset and incubation period of a disease the developed theory also allows for a multiplicative factor of seasonal effects seasonal effects are present in many actuarial biostatistical econometric and statistical studies smoothing estimators are proposed that are based on backfitting full asymptotic theory is derived for them a practical example from the insurance business is given producing a within year budget of reported insurance claims a small sample study supports the theoretical results

the existence and asymptotic properties of a backfitting projection algorithm under weak conditions we derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function the procedure employs a recent projection interpretation of popular kernel estimators provided by mammen marron turlach and wand 1997 and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in bickel klaassen ritov and wellner 1993 our procedure achieves the same bias and variance as the oracle estimator based on knowing the other components and in this sense improves on the method analysed in opsomer and ruppert 1997 we provide high level conditions independent of the sampling scheme we then verify that these conditions are satisfied in a regression and a time series autoregression under weak conditions

fluid dynamic description of flocking via the povzner boltzmann equation we introduce and discuss the possible dynamics of groups of indistinguishable agents which are interacting according to their relative positions with the aim of deriving hydrodynamic equations these models are developed to mimic the collective motion of groups of species such as bird flocks fish schools herds of quadrupeds or bacteria colonies our starting model for these interactions is the povzner equation 21 which describes a dilute gas in which binary collisions of elastic spheres depend on their relative positions following the cucker and smale model 9 we will consider binary interactions between agents that are dissipative collisions in which the coefficient of restitution depends on their relative distance under the assumption of weak dissipation it is shown that the povzner equation is modified through a correction in the form of a nonlinear friction type operator using this correction we formally obtain from the povzner equation in a direct way a fluid dynamic description of a system of agents with weak dissipative interactions with a coefficient of restitution that depends on their relative distance

global existence in l1 for the enskog equation and convergence of the solutions to solutions of the boltzmann equation for the enskog equation in a box an existence theorem is proved for initial data with finite mass energy and entropy then by letting the diameter of the molecules go to zero the weak convergence of solutions of the enskog equation to solutions of the boltzmann equation is proved

on strict lower and upper sections of weakly complete fuzzy pre orders based on co implication fono and gwet on strict lower and upper sections of fuzzy orderings fuzzy sets and systems 139 2003 583 599 introduced and studied strict lower section strict upper section and strict order interval of a given weakly complete fuzzy pre order r when the minimal regular fuzzy strict component of r is defined by the residual coimplicator of the lukasiewicz t conorm and they gave an example of application of fuzzy strict lower sections in economics in this paper we generalize their framework for the minimal regular fuzzy strict component of r defined by the residual complicator of a continuous t conorm we show that fuzzy strict sections and fuzzy strict order intervals defined in this general case generate fuzzy topologies

efficient estimation of the partly linear additive cox model the partly linear additive cox model is an extension of the linear cox model and allows flexible modeling of covariate effects semiparametrically we study asymptotic properties of the maximum partial likelihood estimator of this model with right censored data using polynomial splines we show that with a range of choices of the smoothing parameter the number of spline basis functions required for estimation of the nonparametric components the estimator of the finite dimensional regression parameter is root n consistent asymptotically normal and achieves the semiparametric information bound rates of convergence for the estimators of the nonparametric components are obtained they are comparable to the rates in nonparametric regression implementation of the estimation approach can be done easily and is illustrated by using a simulated example

rational choice under fuzzy preferences the orlovsky choice function abstract there have been many different suggestions in the literature as to how to generate exact choices on the basis of fuzzy preferences this paper seeks to provide axiomatic support to one of these choice functions due to orlovsky it is shown that under a transitivity restriction independent of max min transitivity this choice function implies and is implied by a set of simple conditions

fuzzy implication operators for difference operations for fuzzy sets and cardinality based measures of comparison in this paper we determine by means of fuzzy implication operators two classes of difference operations for fuzzy sets and two classes of symmetric difference operations for fuzzy sets which preserve properties of the classical difference operation for crisp sets and the classical symmetric difference operation for crisp sets respectively the obtained operations allow us to construct as in b de baets h de meyer transitivity preserving fuzzification schemes for cardinality based similarity measures european journal of operational research 160 2005 726 740 cardinality based similarity measures which are reflexive symmetric and transitive fuzzy relations and to propose two classes of distances metrics which are fuzzy versions of the well known distance of cardinality of the symmetric difference of crisp sets

acyclic fuzzy preferences and the orlovsky choice function a note abstract this note corrects and extends a recent axiomatic characterization of the orlovsky choice function for a particular class of transitive fuzzy relations the interest of characterizing choice functions for well behaved fuzzy relations is then discussed

approaches to collective decision making with fuzzy preference relations abstract recent experimental studies show that the predictive accuracy of many of the solution concepts derived from the collective decision making theory leaves much to be desired in a previous paper the author attempted to explain some of the inaccuracies in terms of the fuzzy indifference regions of the individuals participating in the voting game this paper gives straightforward generalizations of the solutions concepts in terms of the fuzzy social or individual preference relations it turns out that some of these new solution concepts cotain their nonfuzzy counterparts as subsets others in turn are subsets of their nonfuzzy counterparts we also discuss a method of aggregating individual nonfuzzy preferences so as to get a fuzzy social preference relation and furthermore a nonfuzzy social choice set

axiomatic characterizations of threshold choice functions for comparison functions in this paper we characterize the threshold choice functions associated with comparison functions reciprocal fuzzy relations a special of which is the orlovsky choice function with threshold our family of threshold choice functions is somewhat larger than the family of choice functions which select only those alternatives that secure a certain pre specified proportion of the votes against all other alternatives our family of threshold choice functions also include ones which select only those alternatives that exceed a certain pre specified proportion of the votes against all other alternatives this is the price we pay for omitting continuity from our axiomatic characterizations

general theory of best variants choice some aspects the conventional mechanisms of making the best choice in particular optimization mechanisms make explicit or implicit use of the structural principle of pair comparability for variants and of the specific logic of the dominant rule for choice this paper argues for going beyond the framework of pairness dominance on the structures and rules of choice and for using nonconventional structures and rules this is shown to be possible if the notions of multitudinal influences of variants is formalized in determining the best choices

estimating multiplicative and additive hazard functions by kernel methods we propose new procedures for estimating the component functions in both additive and multiplicativen onparametricm arker dependenht azard models we work with a full counting process framework that allows for left truncation and right censoring and time varying covariates our procedures are based on kernel hazard estimation as developed by nielsen and linton and on the idea of marginal integration we provide a central limit theorem for the marginal integration estimator we then define estimators based on finite step backfitting in both additive and multiplicative cases and prove that these estimators are asymptotically normal and have smaller variance than the marginal integration method

on the size of chaos in the mean field dynamics we consider the error arising from the approximation of an n particle dynamics with its description in terms of a one particle kinetic equation we estimate the distance between the j marginal of the system and the factorized state obtained in a mean field limit as n our analysis relies on the evolution equation for the correlation error rather than on the usual bbgky hierarchy the rate of convergence is shown to be o j 2 n in any bounded interval of time size of chaos as expected from heuristic arguments our formalism applies to an abstract hierarchical mean field model with bounded collision operator and a large class of initial data covering a stochastic jump processes converging to the homogeneous boltzmann and the povzner equation and b quantum systems giving rise to the hartree equation

kernel estimation in a nonparametric marker dependent hazard model we introduce a new kernel hazard estimator in a nonparametric model where the stochastic hazard depends on the current value of time and on the current value of a time dependent covariate or marker we establish the pointwise and global convergence of our estimator

rational fuzzy and sequential fuzzy choice in the setting of fuzzy choice theory we explore some relationships among known and new consistency axioms as well as consequences of rationalizability then we define the notion of sequential application of fuzzy choice functions and investigate its normative implications under related concepts of rationalizability in particular the fuzzy binariness axiom is verified by sequential fuzzy choice and the fuzzy arrow axiom when the set of alternatives is finite is preserved by the newly defined sequential procedure the latter property ensures that full rationality is preserved too

factoring fuzzy transitivity transitivity of a precise weak preference relation implies that its asymmetric component strict preference and its symmetric component indifference are transitive and conversely the transitivity of strict preference and indifference implies that the underlying weak preference relation is transitive this paper examines to what extent analogous results may be obtained for the different transitivity conditions and different methods for deriving strict preference and indifference being used in the literature of choice with fuzzy preferences

exploring the nature of covariate effects in the proportional hazards model we discuss an exploratory technique for investigating the nature of covariate effects in cox s proportional hazards model this technique features an additive term sigma p1 fj chi ij in place of the usual linear term sigma p1 chi ij beta j where chi i1 chi i2 chi ip are covariate values for the ith individual the fj are unspecified smooth functions that are estimated using scatterplot smoothers these functions can be used for descriptive purposes or to suggest transformations of the covariates the estimation technique is a variation of the local scoring algorithm for generalized additive models hastie and tibshirani 1986 statistical science 1 297 318

a stochastic system of particles modelling the euler equations we consider a system of n spheres interacting through elastic collisions at a stochastic distance in the limit n for a suitable rescaling of the interaction parameters we prove that the one particle distribution function converges to a local maxwellian whose gross density velocity and temperature satisfy the euler equation

diagnostic plots to reveal functional form for covariates in multiplicative intensity models abstract we show how plots based on the residuals from a proportional hazards model may be used to reveal the correct functional form for covariates in the model a smoothed plot of the martingale residues was suggested for this purpose by therneau grambsch and fleming 1990 biometrika 77 147 160 however its consistency required that the covariates be independent they also noted that the plot could be biased for large covariate effects we introduce two refinements which overcome these difficulties the first is based on a ratio of scatter plot smooths where the numerator is the smooth of the observed count plotted against the covariate and the denominator is a smooth of the expected count this is related to the arjas goodness of fit plot 1988 journal of the american statistical association 83 204 212 the second technique smooths the martingale residuals divided by the expected count using expected count as a weight this latter approach is related to a glm partial residual plot as well as to the iterative methods of hastie and tibshirani 1990 biometrics 46 1005 1016 and gentleman and crowley 1991 biometrics 47 1283 1296 applications to survival data sets are given

fuzzy choice functions revealed preference and rationality abstract this paper investigates the conditions under which a fuzzy set valued choice function is rationalisable by a fuzzy revealed preference relation satisfying certain regularity conditions attention is confined to the case where the domain of the choice function consists of all crisp finite subsets of the universal set of alternatives two sets of weak and strong axioms of fuzzy revealed preference wafrp and safrp are stated in both cases it turns out that wafrp is not equivalent to safrp and that safrp does not characterise rationality in the special case where every set of avialable alternatives has at least one element which is unambiguously chosen wafrp is equivalent to safrp but safrp still does not characterise rationality a fuzzy congruence condition stronger than safrp is proposed and is shown to be necessary and sufficient for rationality

smooth backfitting in practice summary compared with the classical backfitting of buja hastie and tibshirani the smooth backfitting estimator sbe of mammen linton and nielsen not only provides complete asymptotic theory under weaker conditions but is also more efficient robust and easier to calculate however the original paper describing the sbe method is complex and the practical as well as the theoretical advantages of the method have still neither been recognized nor accepted by the statistical community we focus on a clear presentation of the idea the main theoretical results and practical aspects like implementation and simplification of the algorithm we introduce a feasible cross validation procedure and apply it to the problem of data driven bandwidth choice for the sbe by simulations it is shown that the sbe and our cross validation work very well indeed in particular the sbe is less affected by sparseness of data in high dimensional regression problems or strongly correlated designs the sbe has reasonable performance even in 100 dimensional additive regression problems

regression splines in the cox model with application to covariate effects in liver disease abstract the cox proportional hazards model restricts the log hazard ratio to be linear in the covariates a smooth nonlinear covariate effect may go undetected in this model but can be well approximated by a spline function a survival model based on data from a clinical trial of primary biliary cirrhosis is developed using regression splines and the resulting log hazard ratio estimates are compared with those from nonparametric methods we remove the linear restriction on the log hazard ratio by transforming a continuous covariate into a vector of fixed knot basis splines b splines b splines are known to produce better conditioned systems of equations than the truncated power basis when used as interpolants and show similar behavior when fitting proportional hazards models we describe the procedures for and the issues arising in the estimation and the testing of the b spline coefficients although inference is not well developed for some nonparametric methods that estimate covariate effects the

existence and uniqueness for nonlinear boundary value problems in kinetic theory a boundary value problem for the stationary nonlinear boltzmann equation in a slab has been examined in a weightedl space it has been proved that the problem possesses a unique solution for boundary data small enough the proof is based on the implicit function theorem it has also been shown that for the linearized problem the fredholm alternative applies

job search and employment abstract a multistage search method based on fuzzy preference is used to analyze the processes of job search an employment decision based on fuzzy preference results in an exact choice the incorporation of fuzzy interval preference into employment decision however may lead to multiple choices which provides a theoretical justification for the existence of fuzzy supply of labor thus fuzziness in addition to randomness offers an explanation to wage dispersion

smooth backfitting in generalized additive models generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non gaussian responses including binary and count data in this paper a new likelihood approach for fitting generalized additive models is proposed it aims to maximize a smoothed likelihood the additive functions are estimated by solving a system of nonlinear integral equations an iterative algorithm based on smooth backfitting is developed from the newton kantorovich theorem asymptotic properties of the estimator and convergence of the algorithm are discussed it is shown that our proposal based on local linear fit achieves the same bias and variance as the oracle estimator that uses knowledge of the other components numerical comparison with the recently proposed two stage estimator ann statist 32 2004 2412 2443 is also made

the grad limit for a system of soft spheres a model describing the dynamics of a system of soft spheres is introduced the model contains a random mechanism which mollifies the deterministic model of hard sphere molecules it allows a rigorous deduction of the corresponding boltzmann equation for a wide class of initial data and arbitrarily long times

using fuzzy binary relations for identifying noninterior decision alternatives abstract a fuzzy noninferiority relation is introduced based on this relation fuzzy relations of preference strict preference indifference and incomparability are specified and their properties are investigated a fuzzy noninferior subset is defined and its basic characteristic properties are established an algorithm is presented for identifying a fuzzy set of noninferior alternatives in decision making situations that require the selection of a certain number of noninferior alternatives for more detailed study

ranking methods for valued preference relations abstract in this paper we study a particular method that builds a partial ranking on the basis of a valued preference relation this method which is used in the mcdm method promethee i is based on leaving and entering flows we show that this method is characterized by system of three independent axioms

fuzzy arrow type results without the pareto principle based on fuzzy pre orders in this paper we introduce appropriate properties of fuzzy preferences and fuzzy aggregation rules we use them to provide fuzzy counterparts of malawski and zhou s a note on social choice theory without the pareto principle social choice and welfare 16 1994 and wilson s social choice theory without the pareto principle journal of economic theory 5 1972 478 486 impossibility results concerning the aggregation of individual preferences which do not assume the pareto principle by weakening conditions on fuzzy social preferences we obtain a possibility result

in sample forecasting with local linear survival densities in this paper in sample forecasting is defined as forecasting a structured density to sets where it is unobserved the structured density consists of one dimensional in sample components that identify the density on such sets we focus on the multiplicative density structure which has recently been seen as the underlying structure of non life insurance forecasts in non life insurance the in sample area is defined as one triangle and the forecasting area as the triangle that 20 added to the first triangle produces a square recent approaches estimate two one dimensional components by projecting an unstructured two dimensional density estimator onto the space of multiplicatively separable functions we show that time reversal reduces the problem to two one dimensional problems where the one dimensional data are left truncated and a one dimensional survival density estimator is needed this paper then uses the local linear density smoother with 25 weighted cross validated and do validated bandwidth selectors full asymptotic theory is provided with and without time reversal finite sample studies and an application to non life insurance are included

fuzzy preference structures without incomparability abstract in this paper we establish important relationships between the basic properties of the components of a fuzzy preference structure without incomparability this study is carried out for the fuzzy preference structures introduced recently by de baets van de walle and kerre a set of remarkable theorems gives detailed insight in the relationships between the sup t transitivity of the fuzzy preference and indifference relations and the sup t transitivity of the fuzzy large preference relation several paths of thought involving t norms with or without zero divisors are explored and where required illustrative counterexamples confirm the falsity of certain implications finally we introduce the t n ferrers property of a binary fuzzy relation and show that the fuzzy preference and fuzzy large preference relations share certain types of this ferrers property

multicriteria fuzzy classification procedure procftn methodology and medical application in this paper we introduce a new classification procedure for assigning objects to predefined classes named procftn this procedure is based on a fuzzy scoring function for choosing a subset of prototypes which represent the closest resemblance with an object to be assigned it then applies the majority voting rule to assign an object to a class we also present a medical application of this procedure as an aid to assist the diagnosis of central nervous system tumours the results are compared with those obtained by other classification methods reported on the same data set including decision tree production rules neural network k nearest neighbor multilayer perceptron and logistic regression our results are very encouraging and show that the multicriteria decision analysis approach can be successfully used to help medical diagnosis

individual valued preferences and their aggregation consistency analysis in a real case in this paper we have analyzed the accomplishment of several consistency conditions in a real decision case a group of students showed their intensities of preference among the alternatives by means of linguistic labels represented by real numbers the absolute and relative fulfillments of some kinds of fuzzy transitivity properties have been studied for individual and collective preferences collective preferences have been obtained by means of a wide class of neutral and stable for translations aggregation rules which transports reciprocity from individual preferences to the collective preference we notice that in the real case studied the aggregate preferences reach higher consistency properties than individual preferences

acyclic rationality indicators of fuzzy choice functions we introduce the degree of acyclicity of a fuzzy preference relation and two acyclic rationality indicators of a fuzzy choice function c these two indicators measure the degree to which the choice function c is acyclic g rational respectively acyclic m rational we study the fuzzy condorcet property of a fuzzy choice function and the corresponding indicators we express the indicator of g rationality in terms of the condorcet property and the indicator of a consistency

on choosing rationally when preferences are fuzzy abstract in real life exact choices are induced by fuzzy preferences these choices eventually satisfy certain plausible rationality properties several alternative rules for generating exact choices from fuzzy weak preference relations are introduced and the extent to which exact choice sets generated by these rules satisfy fairly weak rationality conditions is studied max min transitivity is shown to be crucial for obtaining a positive result

rationality and aggregation of preferences in an ordinally fuzzy framework abstract the paper explores the problem of aggregating ordinally fuzzy individual preferences into ordinally fuzzy social preferences using goguen s ordinal formulation of fuzziness it is shown that given certain plausible conditions the requirement that the society s preferences should satisfy any of several alternative transitivity conditions creates a dilemma either power in the society is rather unevenly distributed or the society tends to be indecisive the problem increases as weaker transitivity conditions are replaced by stronger ones

martingale based residuals for survival models summary graphical methods based on the analysis of residuals are considered for the setting of the highly used cox 1972 regression model and for the andersen gill 1982 generalization of that model we start with a class of martingale based residuals as proposed by barlow prentice 1988 these residuals and or their transforms are useful for investigating the functional form of a covariate the proportional hazards assumption the leverage of each subject upon the estimates of 13 and the lack of model fit to a given subject 1 1 model consider a set of n independent subjects such that the counting process ni ni t t o for the ith subject in the set indicates the number of observed events experienced over time t the sample paths of the ni are step functions with jumps of size 1 and with ni 0 0 we assume that the intensity function for ni t is given by yi t da t zi t yi t ep z t dao t 1 where yi t is a 0 1 process indicating whether the ith subject is a risk at time t 13 is a vector of regression coefficients zi t is a p dimensional vector of covariate processes and ao is the baseline cumulative hazard function several familar survival models fit into this framework the andersen gill 1982 generalization of the cox 1972 model arises when ao t is completely unspecified the further restriction that yi t 1 until the first event or censoring and is 0 thereafter yields the cox model the parametric form ao t t yields a poisson model or an exponential if restricted to a single event per subject and ao t tp a weibull model our attention will focus primarily on the andersen gill and cox models however the

interval valued preference structures different languages that are offered to model vague preferences are reviewed and an interval valued language is proposed to resolve a particular difficulty encountered with other languages it is shown that interval valued languages are well defined for de morgan triples constructed by continuous triangular norms conorms and a strong negation function a new transitivity condition for vague preferences is suggested and its relationships to known transitivity conditions are established a complete characterization of intervalvalued preference structures is also provided

on the approximation of fuzzy preferences by exact relations abstract the generalized hamming distance is commonly used in determining a closest crisp relation to a given fuzzy relation which in turn is crucial in studying exact choices originating from fuzzy preferences this note illustrates a difficulty attached to this practice and proposes an alternative metric which is intuitively more appropriate in the case of fuzzy preferences some implications of this new metric on finding the nearest exact relation to a fuzzy preference ordering and on the understanding of the max min transitivity property are also discussed

equations de type de boltzmann spatialement homogenes we study the construction of a nonhomogeneous n valued markov process whose laws at fixed times evolve according to a boltzmann type equation spatially homogeneous we then consider the problem of the asymptotic propagation of chaos for a system of a large number of interacting particles

on strict lower and upper sections of fuzzy orderings strict lower sections strict upper sections and open order intervals strict order intervals are classical notions associated to crisp orderings crisp total preorders in this paper we extend these notions to fuzzy orderings we determine all the fuzzy orderings they contain all the crisp orderings which make it possible to compare two fuzzy strict lower sections and two fuzzy strict upper sections we then deduce the properties equality inclusion and intersection of fuzzy strict order intervals in this way we obtain fuzzy extensions of well known properties of crisp strict sections and crisp strict order intervals and we display one example of their applications

fuzzy sets and models of decision making abstract results of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems related to the design and control of complex systems are presented much attention is given to considering the uncertainty of goals that is associated with a multicriteria character of many optimization problems the application of a multicriteria approach is needed to solve 1 1 problems in which solution consequences cannot be estimated on the basis of a single criterion that involves the necessity of analyzing a vector of criteria and 2 2 problems that may be considered on the basis of a single criterion but their unique solutions are not achieved because the uncertainty of information produces so called decision uncertainty regions and the application of additional criteria can serve as a convincing means to contract these regions according to this two classes of models x m and x r models are considered with applying the bellman zadeh approach and techniques of fuzzy preference relations to their analysis the consideration of x r models is associated with a general approach to solving a wide class of optimization problems with fuzzy coefficients this approach consists in formulating and analyzing one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective functions alone it allows one to maximally cut off dominated alternatives the subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment with its analysis applying one of two techniques based on fuzzy preference relations the results of the paper are of a universal character and are already being used to solve problems of power engineering

operational time and in sample density forecasting in this paper we consider a new structural model for in sample density forecasting in sample density forecasting is to estimate a structured density on a region where data are observed and then re use the estimated structured density on some region where data are not observed our structural assumption is that the density is a product of one dimensional functions with one function sitting on the scale of a transformed space of observations the transformation involves another unknown one dimensional function so that our model is formulated via a known smooth function of three underlying unknown one dimensional functions we present an innovative way of estimating the one dimensional functions and show that all the estimators of the three components achieve the optimal one dimensional rate of convergence we illustrate how one can use our approach by analyzing a real dataset and also verify the tractable finite sample performance of the method via a simulation study

smooth backfitting of proportional hazards with multiplicative components smooth backfitting has proven to have a number of theoretical and practical advantages in structured regression by projecting the data down onto the structured space of interest smooth backfitting

an empirical analysis of the use of the analytic hierarchy process for estimating membership values in a fuzzy set abstract the analytic hierarchy process ahp is now a popular multicriteria decision making method and has been applied in many diverse areas despite the debate on its theoretical foundations many researchers have been using the pairwise comparison matrix and the eigenvector method suggested by saaty for obtaining priority ratings of the decision alternatives in an ahp hierarchy these priority ratings have been used as estimates of fuzzy membership values of the elements called alternatives in ahp of a fuzzy set triantaphyllou and mann have argued that saaty s scale and the eigenvector method are inadequate for estimating fuzzy membership values this paper points out the limitations in the arguments of triantaphyllou and mann about the eigenvector method it primarily concentrates on two aspects the first pertains to saaty s condition on deleting or combining two alternatives which are near copies alternatives whose priority values are close to each other within a 10 range over all criteria the second aspect concerns the use of the eigenvector method for estimating the membership values of elements of a fuzzy set the use of the eigenvector method for estimating fuzzy membership values in a fuzzy set has been justified using the empirical analysis together with theoretical support it has been amply demonstrated in this paper that the problem lies in saaty s scale and not in the eigenvector method

fuzzy preference modeling and its application to multiobjective decision making this paper reflects results of research into the construction and analysis of models within the framework of a general approach to solving optimization problems with fuzzy coefficients this approach involves a modification of traditional mathematical programming methods and is associated with formulating and solving one and the same problem within the framework of mutually interrelated models the use of the approach allows one to maximally cut off dominated alternatives the subsequent contraction of the decision uncertainty region is based on reducing the problem to models of multiobjective choosing alternatives in a fuzzy environment with the use of fuzzy preference relation techniques for analyzing these models three techniques for fuzzy preference modeling are discussed in the paper the first technique is based on the construction of membership functions of subsets of nondominated alternatives with simultaneous considering of all criteria fuzzy preference relations the second technique is of a lexicographic character and consists of step by step introducing of fuzzy preference relations the third technique is based on aggregating membership functions of subsets of nondominated alternatives corresponding to each preference relation these techniques have served for developing a corresponding system for multiobjective decision making mdms c windows of the mdms are presented for input output and some intermediate procedures the results of the paper are of a universal character and are already being used to solve power engineering naval engineering and management problems

a note on congruence conditions of fuzzy choice functions in order to reflect the fuzziness existing in a choice problem banerjee introduces the concept of fuzzy choice function meanwhile banerjee proposes three congruence conditions in assessing the rationality of a fuzzy choice function in this paper we prove some dependencies among these conditions although banerjee asserts that they are independent

soft sets an ordinal formulation of vagueness with some applications to the theory of choice abstract in the theory of fuzzy sets it is usual to represent the degree of belongingness by a number lying between 0 and 1 this paper develops an alternative framework which dispenses with such cardinal numerical representations of the degree of belongingness and relies instead on an ordinal formulation the ordinal notion of a vague set is called a soft set soft sets are shown to have a tight logical relation with the concept of l sets introduced earlier by goguen the paper also discusses applications of the framework of soft sets to several problems in the theory of choice

the problem of collective identity in a fuzzy environment we define the problem of group identification in a fuzzy environment we concentrate on the case where the society is required to self determine the belongingness of each member to a specific group characterized by a single attribute in general terms this case consists of a collective identity issue that can be regarded as an aggregation problem of individual assessments within a group here we introduce the possibility that both the original assessments and the resulting output attach partial memberships to the collectivity for each potential member we propose relevant classes of rules and some are axiomatically characterized our new approach provides a way to circumvent classical impossibility results like kasher and rubinstein s

fuzzy strict preference and social choice in this paper we generalize some classical factorizations of a fuzzy relation into a symmetric component indifference and an asymmetric and regular component regular fuzzy strict preference from the above notions we establish two properties of any regular fuzzy strict preference of a max transitive fuzzy relation which are then used to obtain new fuzzy versions of gibbard s oligarchy theorem and arrow s impossibility theorem