the consistent value of fuzzy games in the framework of fuzzy games we offer an extension of the reduced game introduced by hart and mas colell which we name the self reduced game according to consistency which related to the self reduced game we provide a definition of the consistent value which is a generalization of the shapley value of fuzzy games we adopt three existing concepts from coalitional game theory and reinterpret them in the framework of fuzzy games the first one is that there exists a unique potential function and the resulting payoff vector coincides with the consistent value second based on the properties of balanced contributions and consistency we offer several axiomatizations of the consistent value finally we propose a dynamic process to illustrate that the consistent value can be reached by players who start from an arbitrary efficient payoff vector and make successive adjustments

fuzzy interval cooperative games we introduce a core like concept called f core for games in which the worth of any coalition is given by means of a fuzzy interval such a class of cooperative games was introduced by mares in 1999 different from mares approach the f core generalizes the interval core introduced by alparslan branzei and tijs in 2008 for games where the worth of any coalition is a compact interval of the real line moreover we introduce a balanced like condition and prove that this condition is necessary but not sufficient to guarantee the f core to be non empty

survival probability of a mobile particle in a fluctuating field we study the the survival probability p t upto time t of a test particle moving in a fluctuating external field the particle moves according to some prescribed deterministic or stochastic rules and survives as long as the external field that it sees at its own location does not change sign this is a natural generalization of the static persistence when the particle is at rest that has generated considerable recent interests two types of motions of the particle are considered in one case the particle adopts a strategy to live longer and in the other it just diffuses randomly three different external fields were considered i the solution of diffusion equation ii the colour profile of the q state potts model undergoing zero temperature coarsening dynamics and iii spatially uncorrelated brownian signals in most cases studied p t sim t theta m for large t the exponent theta m is calculated via numerically analytically by approximate methods and in some cases exactly it is shown in some special cases that the survival probability of the mobile particle is related to the persistence of special patterns present in the initial configuration of a phase ordering system

games with fuzzy permission structure a conjunctive approach abstract a cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate regardless of the actions that the other players take a permission structure over the set of players describes a hierarchical organization where there are players who need permission from certain other players before they are allowed to cooperate with others various assumptions can be made about how a permission structure affects the cooperation possibilities in the conjunctive approach it is assumed that each player needs permission from all his superiors this paper deals with fuzzy permission structures in the conjunctive approach in this model players could depend partially on other players that is they may have certain degree of autonomy first we define a value for games with fuzzy permission structure that only takes into account the direct relations among players and provide a characterization for this value finally we study a value for games with fuzzy permission structure which takes account of the indirect relations among players

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

random payoff two person zero sum game with joint chance constraints abstract we study a two person zero sum game where the payoff matrix entries are random and the constraints are satisfied jointly with a given probability we prove that for the general random payoff zero sum game there exists a weak duality between the two formulations i e the optimal value of the minimizing player is an upper bound of the one of the maximizing player under certain assumptions we show that there also exists a strong duality where their optimal values are equal moreover we develop two approximation methods to solve the game problem when the payoff matrix entries are independent and normally distributed finally numerical examples are given to illustrate the performances of the proposed approaches

reaction diffusion models in one dimension with disorder we study a large class of one dimensional reaction diffusion models with quenched disorder using a real space renormalization group method rsrg which yields exact results at large time particles e g of several species undergo diffusion with random local bias sinai model and may react upon meeting we obtain a detailed description of the asymptotic states i e attractive fixed points of the rsrg such as the large time decay of the density of each specie their associated universal amplitudes and the spatial distribution of particles we also derive the spectrum of nontrivial exponents which characterize the convergence towards the asymptotic states for reactions which lead to several possible asymptotic states separated by unstable fixed points we analyze the dynamical phase diagram and obtain the critical exponents characterizing the transitions we also obtain a detailed characterization of the persistence properties for single particles as well as more complex patterns we compute the decay exponents for the probability of no crossing of a given point by respectively the single particle trajectories ensuremath theta or the thermally averaged packets overline ensuremath theta the generalized persistence exponents associated to n crossings are also obtained specifying to the process a stackrel ensuremath rightarrow a ensuremath emptyset or a with probabilities r 1 ensuremath r we compute exactly the exponents ensuremath delta r and ensuremath psi r characterizing the survival up to time t of a domain without any merging or with mergings respectively and the exponents ensuremath delta a r and ensuremath psi a r characterizing the survival up to time t of a particle a without any coalescence or with coalescences respectively overline ensuremath theta ensuremath psi and ensuremath delta obey hypergeometric equations and are numerically surprisingly close to pure system exponents though associated to a completely different diffusion length the effect of additional disorder in the reaction rates as well as some open questions are also discussed

stable distributions in stochastic fragmentation we investigate a class of stochastic fragmentation processes involving stable and unstable fragments we solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small size tail furthermore the entire range of acceptable values of decay exponent consistent with length conservation can be realized we show that the stochastic fragmentation process is non self averaging as moments exhibit significant sample to sample fluctuations additionally we find that the distributions of the moments and of extremal characteristics possess an infinite set of progressively weaker singularities

myerson values for games with fuzzy communication structure in 1977 myerson considered cooperative games with communication structure a communication structure is an undirected graph describing the bilateral relationships among the players he introduced the concept of allocation rule for a game as a function obtaining an outcome for each communication structure among the players of the game the myerson value is a specific allocation rule extending the shapley value of the game more recently the authors studied games with fuzzy communication structures using fuzzy graph theoretic ideas now we propose a general framework in order to define fuzzy myerson values players in a coalition need to measure their profit using their real individual and communication capacities at every moment because these attributes are fuzzy when the game is proposed so they look for forming connected coalitions working at the same level the different ways to obtain these partitions by levels determine different myerson values for the game several interesting examples of these ways are studied in the paper following known models in games with fuzzy coalitions the proportional model and the choquet model

an augmented probit model for missing predictable covariates in quantal bioassay with small sample size summary quantal bioassay experiments relate the amount or potency of some compound for example poison antibody or drug to a binary outcome such as death or infection in animals for infectious diseases probit regression is commonly used for inference and a key measure of potency is given by the idp the amount that results in p of the animals being infected in some experiments a validation set may be used where both direct and proxy measures of the dose are available on a subset of animals with the proxy being available on all the proxy variable can be viewed as a messy reflection of the direct variable leading to an errors in variables problem we develop a model for the validation set and use a constrained seemingly unrelated regression sur model to obtain the distribution of the direct measure conditional on the proxy we use the conditional distribution to derive a pseudo likelihood based on probit regression and use the parametric bootstrap for statistical inference we re evaluate an old experiment in 21 monkeys where neutralizing antibodies nabs to hiv were measured using an old proxy assay in all monkeys and with a new direct assay in a validation set of 11 who had sufficient stored plasma using our methods we obtain an estimate of the id1 for the new assay an important target for hiv vaccine candidates in simulations we compare the pseudo likelihood estimates with regression calibration and a full joint likelihood approach

fuzzy extensions of bargaining sets and their existence in cooperative fuzzy games recently the concept of classical bargaining set given by aumann and maschler in 1964 has been extended to fuzzy bargaining set in this paper we give a modification to correct some weakness of this extension we also extend the concept of the mas colell s bargaining set the other major type of bargaining sets to its corresponding fuzzy bargaining set our main effort is to prove existence theorems for these two types of fuzzy bargaining sets we will also give necessary and sufficient conditions for these bargaining sets to coincide with the aubin core in a continuous superadditive cooperative fuzzy game which has a crisp maximal coalition of maximum excess at each payoff vector we show that both aumann maschler and mas colell fuzzy bargaining sets of a continuous convex cooperative fuzzy game coincide with its aubin core

games with fuzzy authorization structure a cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate regardless of the actions that the other players take it is often assumed that the players are free to participate in any coalition but in some situations there are dependency relationships among the players that restrict their capacity to cooperate within some coalitions those relationships must be taken into account if we want to distribute the profits fairly in this respect several models have been proposed in literature in all of them dependency relationships are considered to be complete in the sense that either a player is allowed to fully cooperate within a coalition or they cannot cooperate at all nevertheless in some situations it is possible to consider another option that a player has a degree of freedom to cooperate within a coalition a model for those situations is presented

an algorithm based on discrete response regression models suitable to correct the bias of non response in surveys with several capture tries the use of survey plans which contemplate several tries or call backs when endeavouring to capture individual data may supply unarguable information in certain sampling situations with non ignorable non response this paper presents an algorithm whose final aim is the estimation of the individual non response probabilities from a general perspective of discrete response regression models which includes the well known probit and logit models it will be assumed that the respondents supply all the variables of interest when they are captured nevertheless the call backs continue even after previous captures for a small number of tries r which has been fixed beforehand only for estimating purposes the different retries or call backs are supposed to be carried out with different capture intensities as mentioned above the response probabilities which may vary from one individual to another are sought by discrete response regression models whose parameters are estimated from conditioned likelihoods evaluated on the respondents only the algorithm quick and easy to implement may be used even when the capture indicator matrix has been partially recorded finally the practical performance of the proposed procedure is tested and evaluated from empirical simulations whose results are undoubtedly encouraging

domain number distribution in the nonequilibrium ising model we study domain distributions in the one dimensional ising model subject to zero temperature glauber and kawasaki dynamics the survival probability of a domain s t t and an unreacted domain q1 t t are characterized by two independent nontrivial exponents we develop an independent interval approximation that provides close estimates for many characteristics of the domain length and number distributions including the scaling exponents

convex fuzzy games and participation monotonic allocation schemes in this paper the cone of convex cooperative fuzzy games is studied as in the classical case of convex crisp games these games have a large core and the fuzzy shapley value is the barycenter of the core surprisingly the core and the weber set coincide as in the classical case but the coincidence of these sets for a fuzzy game does not imply automatically convexity as in the crisp case participation monotonic allocation schemes pamas are introduced and it turns out that each core element of a convex fuzzy game is pamas extendable

linear production games with fuzzy control the aim of this paper is to analyse linear production with committee control situations arising when controllers face the possibility of graduating their options in order to model these situations we consider several kinds of fuzzy controls which can be modelled as different simple fuzzy games an lp game which is an extension of lp games with committee control introduced in curiel et al on balanced games and games with committee control or spectrum 11 1989 83 88 is obtained and its core is studied

improved regression calibration the likelihood for generalized linear models with covariate measurement error cannot in general be expressed in closed form which makes maximum likelihood estimation taxing a popular alternative is regression calibration which is computationally efficient at the cost of inconsistent estimation we propose an improved regression calibration approach a general pseudo maximum likelihood estimation method based on a conveniently decomposed form of the likelihood it is both consistent and computationally efficient and produces point estimates and estimated standard errors which are practically identical to those obtained by maximum likelihood simulations suggest that improved regression calibration which is easy to implement in standard software works well in a range of situations

on concavity and supermodularity abstract concavity and supermodularity are in general independent properties a class of functionals defined on a lattice cone of a riesz space has the choquet property when it is the case that its members are concave whenever they are supermodular we show that for some important riesz spaces both the class of positively homogeneous functionals and the class of translation invariant functionals have the choquet property we extend in this way the results of choquet g choquet theory of capacities ann inst fourier grenoble 5 1953 1954 131 295 and konig h konig the sub super additivity assertion of choquet studia math 157 2003 171 197

linear fuzzy game with coalition interaction and its coincident solutions abstract in this study we consider the solution concepts for fuzzy coalition games i e cooperative games with fuzzy coalition under a certain participation level in general cooperative games with fuzzy coalition are based on the assumption that all the fuzzy coalition values for different fuzzy coalitions must be represented by the same formula which may omit the coalition interaction under different participation ratios for players considering these conditions we propose the coincident fuzziness form for games with fuzzy coalition which are represented by a mapping from the characteristic function of the crisp game to that of the fuzzy coalition game the proposed fuzzy coalition games admit the differences in coalition interactions for different fuzzy coalitions where the coalition interactions are represented by the fuzzy coalition values in different ways or formulas for a fixed fuzzy coalition the maximum fuzzy coalition game is proven to be the choquet integral form on the condition that the associate crisp game is convex in order to seek appropriate solutions for the proposed games based on a certain participation level the fuzzy shapley axioms are defined and the explicit shapley value is represented by the shapley value of the associated crisp games moreover the fuzzy core of this proposed fuzzy coalition game is the stable solution set for the given fuzzy coalition which is also denoted by the crisp cores furthermore we study the relationship between the fuzzy shapley value and the fuzzy core by adding restrictions on the fuzzy core we propose a strong fuzzy core which is a more stable solution than the fuzzy core in addition the fuzzy core is equivalent to the strong fuzzy core under some condition

a generalization of the aumann shapley value for risk capital allocation problems abstract the paper proposes a new method to allocate risk capital to divisions or lines of business within a firm existing literature advocates an allocation rule that in game theoretic terms is equivalent to using the aumann shapley value as allocation mechanism the aumann shapley value however is only well defined if a specific differentiability condition is satisfied the rule that we propose is characterized as the limit of an average of path based allocation rules with grid size converging to zero the corresponding allocation rule is equal to the aumann shapley value if it exists if the aumann shapley value does not exist the allocation rule is equal to the weighted average of the aumann shapley values of nearby capital allocation problems

likelihood analysis for probit regression with measurement errors summary likelihood analysis is proposed for a probit regression model when one of the explanatory variables is measured with error and replicate measurements of that variable are available on some of the subjects the distribution of the measurement error and of the unknown explanatory variable conditional on the known variables are both taken to be normal the maximum likelihood estimates can be computed exactly with the em algorithm likelihood ratio tests and confidence intervals can be computed with a laplace approximation

cores and weber sets for fuzzy extensions of cooperative games this paper investigates fuzzy extensions of cooperative games and the coincidence of the solutions for fuzzy and crisp games we show that an exact game has an exact fuzzy extension such that its fuzzy core coincides with the core for games with empty cores we exploit lovasz extensions to establish the coincidence of weber sets for fuzzy and crisp games

a new method for dealing with measurement error in explanatory variables of regression models we introduce a new method moment reconstruction of correcting for measurement error in covariates in regression models the central idea is similar to regression calibration in that the values of the covariates that are measured with error are replaced by adjusted values in regression calibration the adjusted value is the expectation of the true value conditional on the measured value in moment reconstruction the adjusted value is the variance preserving empirical bayes estimate of the true value conditional on the outcome variable the adjusted values thereby have the same first two moments and the same covariance with the outcome variable as the unobserved true covariate values we show that moment reconstruction is equivalent to regression calibration in the case of linear regression but leads to different results for logistic regression for case control studies with logistic regression and covariates that are normally distributed within cases and controls we show that the resulting estimates of the regression coefficients are consistent in simulations we demonstrate that for logistic regression moment reconstruction carries less bias than regression calibration and for case control studies is superior in mean square error to the standard regression calibration approach finally we give an example of the use of moment reconstruction in linear discriminant analysis and a nonstandard problem where we wish to adjust a classification tree for measurement error in the explanatory variables

a probabilistic representation of exact games on σ algebras the purpose of this paper is to establish the intrinsic relations between the cores of exact games on s algebras and the extensions of exact games to function spaces given a probability space exact functionals are defined on l as an extension of exact games to derive a probabilistic representation for exact functionals we endow them with two probabilistic conditions law invariance and the fatou property the representation theorem for exact functionals lays a probabilistic foundation for nonatomic scalar measure games based on the notion of p convexity we also investigate the equivalent conditions for the representation of anonymous convex games

a note on the core minimal conversely consistent enlargement abstract the moulin reduction is extended by reducing the number of the players to the framework of fuzzy games based on this extended moulin reduction the axiomatic result of the core in tadenuma s 25 case does not hold in the context of fuzzy games and the core also violates the converse consistency therefore we propose the minimal core which possesses the converse consistency and is also the smallest solution satisfying the core

measuring the interactions among variables of functions over the unit hypercube abstract by considering a least squares approximation of a given square integrable function f 0 1 n r by a multilinear polynomial of a specified degree we define an index which measures the overall interaction among variables of f this definition extends the concept of banzhaf interaction index introduced in cooperative game theory our approach is partly inspired from multilinear regression analysis where interactions among the independent variables are taken into consideration we show that this interaction index has appealing properties which naturally generalize several properties of the banzhaf interaction index in particular we interpret this index as an expected value of the difference quotients of f or under certain natural conditions on f as an expected value of the derivatives of f finally we discuss a few applications of the interaction index in aggregation function theory

fully parametric and semi parametric regression models for common events with covariate measurement error in main study validation study designs the derivation of the likelihood function for binary data from two types of main study validation study designs where model covariates are measured with error is elaborated rather than limiting consideration to a restricted family of models with convenient mathematical properties we suggest that empirical considerations customized to the data at hand should drive model choices the joint likelihood function for the main study in which the covariates are measured with error and the validation study in which they are not is maximized and estimation and inference proceeds using standard theory although the choice of the measurement error model is driven by empirical considerations the relatively small validation study sizes typically seen may lead to misspecification resulting in bias in estimation and inference about exposure disease relationships by using a nonparametric form for the measurement error model the resulting semi parametric methods suggested by robins rotnitzky and zhao 1994 journal of the american statistical association 89 864 866 and robins hsieh and newey 1995 journal of the royal statistical society series b 57 409 424 are free from bias due to misspecification of the measurement error model trading efficiency for robustness as usual these fully and semi parametric methods are illustrated with a detailed example from a main study validation study of the health effects of occupational exposure to chemotherapeutics among pharmacists valanis et al 1993 american journal of hospital pharmacy 50 455 462 a constant prevalence ratio model for common binary events with gamma covariate measurement error is derived and empirically verified by the available data a careful reanalysis of the data taking measurement error fully into account leads to a threefold increase in the log relative risk and no loss of statistical power the semi parametric estimates are consistent with the parametric results providing reassurance that important bias due to misspecification of the measurement error model is unlikely

concave measures and the fuzzy core of exchange economies with heterogeneous divisible commodities the main purpose of this paper is to prove the existence of the fuzzy core of an exchange economy with a heterogeneous divisible commodity in which preferences of individuals are given by nonadditive utility functions defined on a s algebra of admissible pieces of the total endowment of the commodity the problem is formulated as the partitioning of a measurable space among finitely many individuals applying the yosida hewitt decomposition theorem we also demonstrate that partitions in the fuzzy core are supportable by prices in l 1

a simulation study of measurement error correction methods in logistic regression summary measurement error models in logistic regression have received considerable theoretical interest over the past 10 15 years in this paper we present the results of a simulation study that compares four estimation methods the so called regression calibration method probit maximum likelihood as an approximation to the logistic maximum likelihood the exact maximum likelihood method based on a logistic model and the naive estimator which is the result of simply ignoring the fact that some of the explanatory variables are measured with error we have compared the behavior of these methods in a simple additive measurement error model we show that in this situation the regression calibration method is a very good alternative to more mathematically sophisticated methods

emergence of fractals in aggregation with stochastic self replication we propose and investigate a simple model which describes the kinetics of aggregation of brownian particles with stochastic self replication an exact solution and the scaling theory are presented alongside numerical simulation which fully support all theoretical findings in particular we show analytically that the particle size distribution function exhibits dynamic scaling and we verify it numerically using the idea of data collapse furthermore the conditions under which the resulting system emerges as a fractal are found the fractal dimension of the system is given and the relationship between this fractal dimension and a conserved quantity is pointed out

max consistency complement consistency and the core of fuzzy games recently hwang introduced two extensions of the max reduced game to fuzzy games by reducing the number of the players based on these reduced games he offered analogous axiomatizations of the core related to serrano and volij in the context of fuzzy games here we continue and develop hwang s work on similar topics however we turn to a different definition of the reduced game by simultaneously reducing both the number of the players and the participation levels we propose such extensions of the complement reduced game and of the max reduced game to fuzzy games and define the related properties of consistency and converse consistency based on these properties we offer several analogous characterizations of the core related to peleg serrano and volij and tadenuma respectively

domain statistics in coarsening systems we study the domain number and size distributions in the one dimensional ising and q state potts models subject to zero temperature glauber dynamics the survival probability of a domain s t t 2c and an unreacted domain q1 t t 2d are characterized by two independent nontrivial exponents for the ising case we find c50 126 and d51 27 using numerical simulations we develop an independent interval approximation that predicts the qualitative behavior of the domain distribution and provides good estimates for the exponents exact results for the domain distribution are also obtained in several solvable cases s1063 651x 97 00110 4

covariate measurement error in generalized linear models summary the em algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors by casting the true covariates as missing data the em procedure suggests an iterative scheme in which each cycle consists of an e step requiring the computation of approximate first and second conditional moments of the true covariates given the observed data followed by an m step in which regression parameters are updated by iteratively reweighted least squares based on these approximations the proposed procedure is compared numerically with the exact maximum likelihood solution obtained by using gaussian quadrature instead of the approximations in the e step of the em algorithm and with alternative estimators for simple logistic regression with measurement error the results for the proposed procedure are encouraging a procedure is proposed in this paper for estimating regression coefficients in generalized linear models when one or more of the covariates is measured with error this work is related to the paper by carroll et al 1984 in which maximum likelihood estimates are considered for the structural logistic regression model these authors provide estimates for the computationally simpler probit regression model and suggest that the structural logistic regression can be done in principle this paper follows up on that suggestion but differs in detail from similar work by armstrong 1985 other procedures with related aims have been suggested by stefanski carroll 1985 wolter fuller 1982 and prentice 1982 for a quick introduction to the proposed method it is convenient to display the naive estimator which ignores measurement error in its standard computational form if yi is an observed response variable and xi is the observed covariate then for the model which equates the canonical parameter of the distribution of yi to xtf3 the maximum likelihood estimator of f3 can be obtained by iteratively reweighted least squares the estimate of f3 after s 1 cycles is given by

cooperative fuzzy games we derive versions of known results dealing with core equilibria and shapley values of cooperative games in the case of cooperative fuzzy games i e games defined on fuzzy subsets of the set of n players a fuzzy coalition is an n vector i associating with each player i his rate of participation i 0 1 in the fuzzy coalition and the real number v is the coalition worth assumed to be positively homogeneous if also v is superadditive or equivalently concave the fuzzy game with side payments has a nonempty core associated with the coalition worth function for any ordinary game with side payments is a fuzzy extension thereof viz the fuzzy game whose coalition worth function is the least positively homogeneous superadditive function majorizing the coalition worth function of the original game the fuzzy extension always has a nonempty core moreover if the original game has a nonempty core it coincides with that of its fuzzy extension analogous results are established for games without side payments an axiomatization of values of fuzzy games with side payments is also given the results are applied to show that the set of walras equilibria coincides with the fuzzy core of an economy

an axiomatic approach of the discrete choquet integral as a tool to aggregate interacting criteria the most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean however in many problems the criteria considered interact and a substitute to the weighted arithmetic mean has to be adopted we show that under rather natural conditions the discrete choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by taking into consideration of the interaction among criteria the axiomatic that supports the choquet integral is presented and an intuitive approach is proposed as well

cores of fuzzy games and their convexity in this paper the proper core and dominance core of a fuzzy game are introduced to guarantee equality between the proper core and the dominance core some mild conditions are provided another important issue for the convexity of the dominance core is also addressed

games on fuzzy communication structures with choquet players myerson 1977 used graph theoretic ideas to analyze cooperation structures in games in his model he considered the players in a cooperative game as vertices of a graph which undirected edges defined their communication possibilities he modified the initial games taking into account the graph and he established a fair allocation rule based on applying the shapley value to the modified game now we consider a fuzzy graph to introduce leveled communications in this paper players play in a particular cooperative way they are always interested first in the biggest feasible coalition and second in the greatest level choquet players we propose a modified game for this situation and a rule of the myerson kind

stochastic aggregation scaling properties we study the scaling properties of stochastic aggregation processes in one dimension numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent non trivial exponents corresponding to the survival probability of particles and monomers the overall behaviour agrees qualitatively with the mean field theory this theory also provides a useful approximation for the decay exponents as well as the limiting mass distribution

nontransferable utility games with fuzzy coalition restrictions abstract a value for nontransferable utility ntu games with fuzzy coalition restrictions is introduced and characterized in a similar way as the shapley value for transferable utility tu games has been extended in the literature to study games with restricted cooperation we extend the shapley ntu value to deal with ntu games in situations in which there are fuzzy dependency relationships among the players

cores of cooperative games superdifferentials of functions and the minkowski difference of sets let v be a cooperative tu game and v v1 v2 be a decomposition of v as a difference of two convex games v1 and v2 then the core c v of the game v has a similar decomposition c v c v1 c v2 where denotes the minkowski difference we prove such a decomposition as a consequence of two claims the core of a game is equal to the superdifferential of its continuation known as the choquet integral and the superdifferential of a difference of two concave functions equals the minkowski difference of corresponding superdifferentials

existence of fuzzy prekernels and mas colell bargaining sets in tu games abstract in this paper we first prove the existence of fuzzy prekernels and fuzzy nucleolus in tu fuzzy games which generalize the corresponding results for classical tu games as an application we apply the existence of fuzzy prekernels to derive an existence theorem for mas colell fuzzy bargaining sets and a stronger existence theorem for mas colell bargaining sets than the one by vohra 1991 18 we also provide an axiomatization theorem for fuzzy prekernels

the general prenucleolus of n person cooperative fuzzy games abstract in this paper we define the concept of the general prenucleolus minimizing the player complaint vector in the lexicographic order over the preimputation set for the cooperative games with fuzzy coalitions for the general prenucleolus we get a sufficient condition that the complaints of all players are in equal amount under the case of linear complaint functions concluding the proposed player excess sakawa and nishizaki 1994 15 as a result we can obtain the proposed fuzzy solutions with the corresponding linear complaint functions such as the equalizer solution molina and tejada 2002 5 and shapley function etc we prove that the least square general prenucleolus minimizing the variance of the resulting player complaints is the general prenucleolus thus an optimal solution considered from two aspects of the lexicographic order and the least square criterion is obtained in addition several general prenucleoli are proposed in terms of specific situations

fuzzy harsanyi solution for a kind of fuzzy coalition games abstract the fuzzy linear game in ref 32 is a class of fuzzy cooperative games with fuzzy coalition fuzzy coalition game for short which admits the difference of interactions for different fuzzy coalitions the fuzzy shapley value for fuzzy linear game has been studied as shapley value is just one point in the harsanyi solution it is interesting to study the explicit form of harsanyi solution in the fuzzy coalition game this paper defines the fuzzy harsanyi solution which distributes the harsanyi dividends such that the dividend shares of players in each fuzzy coalition are proportional to the corresponding players participation index when the fuzzy coalition payoff is average distributed between players in the fuzzy coalition the fuzzy harsanyi solution also coincides with the fuzzy shapley value just as their relationship in a crisp cooperative game we provide two axiomatic characterizations for the fuzzy harsanyi solution one uses axioms and the other uses distribution matrices the fuzzy harsanyi solution is a unique value on the fuzzy linear game that satisfies fuzzy efficiency fuzzy null player and fuzzy additivity property meanwhile based on probability distribution fuzzy harsanyi solution is seen as an expected marginal contribution of each player in the fuzzy coalition which provides more choices for players in the fuzzy coalition

likelihood analysis for errors in variables regression with replicate measurements summary this paper advocates likelihood analysis for regression models with measurement errors in explanatory variables for data problems in which the relevant distributions can be adequately modelled although computationally difficult maximum likelihood estimates are more efficient than those based on first and second moment assumptions and likelihood ratio inferences can be substantially better than those based on asymptotic normality of estimates the em algorithm is presented as a straightforward approach for likelihood analysis of normal linear regression with normal explanatory variables and normal replicate measurements likelihood methods for regression analysis with explanatory variable measurement error have received little attention relative to methods based on first and second moment assumptions largely because of computational difficulties uncertainty about the robustness of likelihood methods and the belief that the simpler methods perform just as well in practice with improved computational tools for likelihood analysis as discussed for example by tanner 1993 it is worthwhile to reinvestigate these issues in particular the common belief that the simpler methods perform just as well as likelihood methods may be naive first the comparison is usually cast in terms of efficiency without regard to test and confidence interval validity likelihood ratio tests and confidence intervals can be substantially better than tests and confidence intervals based on estimates and standard errors of the commonly used method of moments approaches the sampling distributions of the estimators are very often skewed especially if the measurement errors are large furthermore knowledge about the relative efficiency of the moment methods comes from a small number of efficiency comparisons from simulations of isolated situations in papers promoting these simpler methods carroll rupert stefanski 1995 7 1 an important and often overlooked issue is that the moment methods may be especially inappropriate when the distribution of the true covariates is skewed pierce et al 1992 section 2 discusses computational approaches and difficulties associated with likelihood analysis in the measurement error problem generally section 3 illustrates the em algorithm dempster laird rubin 1977 for likelihood analysis of normal linear regression with a normally distributed explanatory variable measured with normally distributed error when there are replicate measurements for at least some of the cases sections 5 and 6

reaction kinetics of cluster impurities we study the density of clustered immobile reactants in the diffusion controlled single species annihilation an initial state in which these impurities occupy a subspace of codimension d leads to a substantial enhancement of their survival probability the smoluchowski rate theory suggests that the codimensionality plays a crucial role in determining the long time behavior the system undergoes a transition at d 2 for d 2 above this critical codimension d 2 the subspace decays indefinitely at the critical codimension inverse logarithmic decay occurs ni t log t a d d above the critical codimension the decay is algebraic ni t t a d d in general the exponents governing the long time behavior depend on the dimension as well as the codimension

universal distribution of masses in a one dimensional sticky gas abstract agglomeration of particles by perfectly inelastic collisions is studied in the case of a one dimensional gas particles move freely between collisions both mass and momentum are conserved at binary encounters it is shown that under a weak mean field like hypothesis admitting the existence of correlations between the velocities of colliding particles the dynamics drives the system towards a scaling regime with a universal exponential distribution of masses

solutions for fuzzy matrix games in this paper we deal with two person zero sum games with fuzzy payoffs and fuzzy goals we have presented two models for studying two person zero sum matrix games with fuzzy payoffs and fuzzy goals we assume that each player has a fuzzy goal for each of the payoffs we obtained that the fuzzy relation approach and the max min solution are equivalent

non trivial exponents in the zero temperature dynamics of the 1d ising and potts models we consider the glauber dynamics of the q state potts model in one dimension at zero temperature starting with a random initial configuration we measure the density r t of spins which have never flipped from the beginning of the simulation until time t we find that for large t the density r t has a power law decay left r t sim t theta right where the exponent theta varies with q our simulations lead to theta simeq 37 for q 2 theta simeq 53 for q 3 and theta longrightarrow 1 as q longrightarrow infty

heterogeneity in mantel haenszel type models summary the mantel haenszel problem involves inferences about a common odds ratio in a set of 2 x 2 tables although it is a fairly standard practice to test whether the odds ratios are indeed constant there is remarkably little methodology available for proceeding when there is evidence of some heterogeneity our interest is in models where the log odds ratios ok for tables k 1 2 k are thought of as a sample from a population with mean 0 and standard deviation a and inferences are desired regarding the parameters 0 a by mantel haenszel type models we mean to include the generalization involving pairs of poisson observations rather than 2 x 2 tables where the ok are logarithms of ratios of the poisson means within pairs direct computation of the likelihood function for 0 a in these settings involves numerical integration and the main point here is a simple approximation to this likelihood the approximation is based on laplace s method and is very accurate for practical applications inference regarding the parameter 0 of primary interest may be made from the profile likelihood function an alternative approach to likelihood methods based on approximations to the marginal means and variances is also considered the methods explored here can be readily generalized to settings where the parameters ok depend on covariables as well

random walkers in one dimensional random environments exact renormalization group analysis sinai s model of diffusion in one dimension with random local bias is studied by a real space renormalization group which yields exact results at long times the effects of an additional small uniform bias force are also studied we obtain analytically the scaling form of the distribution of the position x t of a particle the probability of it not returning to the origin and the distributions of first passage times in an infinite sample as well as in the presence of a boundary and in a finite but large sample we compute the distribution of the meeting time of two particles in the same environment we also obtain a detailed analytic description of the thermally averaged trajectories by computing quantities such as the joint distribution of the number of returns and of the number of jumps forward these quantities obey multifractal scaling characterized by generalized persistence exponents ensuremath theta g which we compute in the presence of a small bias the number of returns to the origin becomes finite characterized by a universal scaling function which we obtain the full statistics of the distribution of successive times of return of thermally averaged trajectories is obtained as well as detailed analytical information about correlations between directions and times of successive jumps the two time distribution of the positions of a particle x t and x t ensuremath with tg t ensuremath is also computed exactly it is found to exhibit aging with several time regimes characterized by different behaviors in the unbiased case for t ensuremath t ensuremath ensuremath sim t ensuremath ensuremath alpha with ensuremath alpha g1 it exhibits a mathrm ln t mathrm ln t ensuremath scaling with a singularity at coinciding rescaled positions x t x t ensuremath this singularity is a novel feature and corresponds to particles that remain in a renormalized valley for closer times ensuremath alpha l1 the two time diffusion front exhibits a quasiequilibrium regime with a mathrm ln t ensuremath t ensuremath mathrm ln t ensuremath behavior which we compute the crossover to a t t ensuremath aging form in the presence of a small bias is also obtained analytically rare events corresponding to intermittent splitting of the thermal packet between separated wells which dominate some averaged observables are also characterized in detail connections with the green function of a one dimensional schr odinger problem and quantum spin chains are discussed

aggregation with multiple conservation laws aggregation processes with an arbitrary number of conserved quantities are investigated on the mean field level an exact solution for the size distribution is obtained the asymptotic form of this solution exhibits nontrivial double scaling while processes with one conserved quantity are governed by a single scale processes with multiple conservation laws exhibit an additional diffusion like scale the theory is applied to ballistic aggregation with mass and momentum conserving collisions and to diffusive aggregation with multiple species

fuzzy games a characterization of the core in this paper we extend to the cooperative fuzzy games case the reduced game introduced by davis and maschler the kernel of a cooperative game naval res logist quart 12 1965 223 259 we shall introduce two types of such a reduced game to cooperative fuzzy games and define the related properties of consistency and converse consistency we further offer two axiomatizations of the core on the domain of all cooperative fuzzy games by means of consistency and its converse