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 formulation of auctions and optimal sequencing for multiple auctions abstract current research on auctions is mainly based on the game theory in the first part of this paper we propose a fuzzy set based formulation of auctions we define fuzzy sets to represent the seller and buyers valuations bid possibilities and win possibilities analyzing the properties of these fuzzy sets we study fuzzy versions of discriminating and nondiscriminating bidding strategies for each bidder in a single object auction by using bellman and zadeh s concept of confluence of fuzzy decisions instead of the game theoretic nash equilibrium the monotonically decreasing membership function replaces of the corresponding distribution density function in milgrom and weber s auction theory in the second part of the paper we develop a soft computing approach to maximize the seller s revenue in multiple object auctions through the use of object sequencing the proposed sequencing approach is based on fuzzy rule quantification numerical experience shows the potential of the proposed approach for application in practical auctions

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

max min solutions for fuzzy multiobjective matrix games abstract in this paper we consider two person zero sum games with fuzzy multiple payoff matrices we assume that each player has a fuzzy goal for each of the payoffs a degree of attainment of the fuzzy goal is defined and the max min strategy with respect to the degree of attainment of the fuzzy goal is examined if all of the membership functions both for the fuzzy payoffs and for the fuzzy goals are linear the formulated mathematical programming problem which yields the max min strategy can be reduced to the linear programming problem by making use of sakawa s method the variable transformations and the relaxation procedure

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

quantitative stability of variational systems i the epigraphical distance this paper proposes a global measure for the distance between the elements of a variational system parametrized families of optimization problems

the cg position value for games on fuzzy communication structures abstract a cooperative game for a set of agents establishes a fair allocation of the profit obtained for their cooperation the best known of these allocations is the shapley value a communication structure defines the feasible bilateral communication relationships among the agents in a cooperative situation some solutions incorporating this information have been defined from the shapley value the myerson value the position value etc later fuzzy communication structures were introduced in a fuzzy communication structure the membership of the players and the relations among them are leveled several ways of defining the myerson value for games on fuzzy communication structure were proposed one of them is the choquet by graphs cg version now we study in this work the cg position value and its calculation the cg position value is defined as a solution for games with fuzzy communication structure which considers the bilateral communications as players so the shapley value is applied for a new game the link game over the fuzzy sets of links in the fuzzy communication structure and the profit obtained for each link is allocated between both players in the link as we see in our examples and results the cg position value is more concerned with the graphical position of the players and their communications than the other cg values in this paper we also introduce a procedure to compute exactly the position value avoiding to calculate the characteristic function of the link game for all coalitions this procedure is used to determine the cg position value finally we compare the new value with other cg values in an applied example about the power of the groups in the european parliament

resinvm3d a 3d resistivity inversion package we have developed an open source 3d matlab based resistivity inversion package the forward solution to the governing partial differential equation is efficiently computed using a second order finite volume discretization coupled with a preconditioned biconjugate stabilized gradient algorithm using the analytical solution to a potential field in a homogeneous half space we evaluate the accuracy of our numerical forward solution and subsequently develop a source correction factor that reduces forward modeling errors associated with boundary effects and source electrode singularities for the inversion algorithm we have implemented an inexact gauss newton solver with the model update being calculated using a preconditioned conjugate gradient algorithm the inversion uses a combination of zero and first order tikhonov regularization two synthetic examples demonstrate the usefulness of this code the first example considers a surface resistivity survey with 3813 measurements the discretized model s

preservation of convergence of convex sets and functions in finite dimensions we study a convergence notion which has particular relevance for convex analysis and lends itself quite naturally to successive approximation schemes in a variety of areas motivated particularly by problems in optimization subject to constraints we develop technical tools necessary for systematic use of this convergence in finite dimensional settings simple conditions are established under which this convergence for sequences of sets functions and subdifferentials is preserved under various basic operations including for example those of addition and infimal convolution in the case of functions

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

optimal coalition formation and surplus distribution two sides of one coin abstract a fuzzy coalitional game represents a situation in which players can vary the intensity at which they participate in the coalitions accessible to them as opposed to the treatment as a binary choice in the non fuzzy crisp game building on the property not made use of so far in the literature of fuzzy games that a fuzzy game can be represented as a convex program this paper shows that the optimum of such a program determines the optimal coalitions as well as the optimal rewards for the players two sides of one coin furthermore this program is seen to provide a unifying framework for representing the core the least core and the fuzzy nucleolus among others next we derive conditions for uniqueness of core rewards and to deal with non uniqueness we introduce a family of parametric perturbations of the convex program that encompasses a large number of well known concepts for selection from the core including the dutta ray solution dutta and ray 1989 the equal sacrifice solution yu 1973 the equal division solution selten 1972 and the tau value tijs 1981 we also generalize the concept of the grand coalition of contracting players by allowing for multiple technologies and we specify the conditions for this allocation to be unique and egalitarian finally we show that our formulation offers a natural extension to existing models of production economies with threats and division rules for common surplus

well posedness without semicontinuity for parametric quasiequilibria and quasioptimization abstract we consider quasiequilibrium and quasioptimization problems a relaxed level closedness notion is proposed and used together with pseudocontinuity to establish sufficient conditions for parametric well posedness and well posedness without semicontinuity assumptions we prove them in general formulations though such relaxations allow us to improve some existing results even in simple cases of r 1 several new well posedness results are also obtained for topological settings we use sensitivity analysis while for problems on metric spaces we argue on diameters and kuratowski s and hausdorff s measures of noncompactness of approximate solution sets

kernel density estimation via diffusion we present a new adaptive kernel density estimator based on linear diffusion processes the proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate in addition we propose a new plug in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods we present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability

a lexicographical solution concept in an n person cooperative fuzzy game abstract in this paper a new solution concept in an n person cooperative fuzzy game with sidepayment is proposed we first define an excess with respect to a player in a fuzzy game with sidepayment usually the concept of an excess is defined for each coalition in contrast however we define an excess of a player by summing up all the excess of a coalition to which he belongs by considering a payoff vector which minimizes the excess of a player in the lexicographical order we proposed a new solution concept in a fuzzy game as well as in a nonfuzzy game then we further consider the problem to extend a nonfuzzy game into a fuzzy game such an extension can be described by the mappings from a characteristic function in a nonfuzzy game into a characteristic function in a fuzzy game an illustrative numerical example of the proposed solution concept to some extended fuzzy games is also presented

generalized levitin polyak well posedness in constrained optimization in this paper we consider levitin polyak type well posedness for a general constrained optimization problem we introduce generalized levitin polyak well posedness and strongly generalized levitin polyak well posedness necessary and sufficient conditions for these types of well posedness are given relations among these types of well posedness are investigated finally we consider convergence of a class of penalty methods and a class of augmented lagrangian methods under the assumption of strongly generalized levitin polyak well posedness

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

capital allocation a la aumann shapley for non differentiable risk measures abstract we study capital allocation rules satisfying suitable properties for convex and quasi convex risk measures by focusing in particular on a family of capital allocation rules based on the dual representation for risk measures and inspired by the aumann shapley allocation principle these rules extend some well known methods of capital allocation for coherent and convex risk measures to the case of non gateaux differentiable risk measures we also analyze the properties of the allocation principles here introduced and discuss their suitability in the quasi convex context

epigraphical and uniform convergence of convex functions we examine when a sequence of lsc convex functions on a banach space converges uniformly on bounded sets resp compact sets provided it converges attouch wets resp painlev e kuratowski we also obtain related results for pointwise convergence and uniform convergence on weakly compact sets some known results concerning the convergence of sequences of linear functionals are shown to also hold for lsc convex functions for example a sequence of lsc convex functions converges uniformly on bounded sets to a continuous affine function provided that the convergence is uniform on weakly compact sets and the space does not contain an isomorphic copy of ell 1

average monotonic cooperative fuzzy games in this paper we study average monotonic fuzzy games a subclass of monotonic cooperative fuzzy games and prove that for a continuous average monotonic cooperative fuzzy game which has a crisp maximal coalition of maximum excess at every imputation its aubin core coincides with its fuzzy bargaining set

an equivalence relation between optimization problems connected with the well posedness let x be a hausdorff topological space and 23 be a family of real valued functions defined in x which are bounded from below taking an arbitrary f 3 we want to minimize f on x i e to find x ex such that f xo inf f x x e x this problem will be referred to as the minimization problem x f varying f in b we obtain a set of minimization problems we are interested in those functions from 23 for which the corresponding minimization problem has a unique solution and moreover some continuous dependence of this solution on the data of the problem exists such problems are called well posed the precise definition is given below suppose b is endowed with a uniform metric under which it is a complete metric space two important cases are i 8 consists of lower semicontinuous functions ii 23 consists of continuous functions in this case the following question is of some interest does the set f 23 x f is well posed contain a dense and g subset of 8 and from the point of view of the baire category is considered to be a big subset of d in a different setting including both the unconstrained and constrained case the answer to this question is positive and is given in l 7 l 12 14173 a possible reservation one may have regarding such results is mentioned by beer in 11 following kenderov 10 111 he considers the next set of constrained minimization problems cp a f 0 a c x a is compact f x r f is continuous and bounded x is tech complete it is observed in l that the reason for the topological bigness of the set mf e p af is well posed could be the fact that in cp there exist different couples giving the same minimization problem indeed let a f b g e cp a b f g but the restricti0ns f 1 a and g 1 b coincide then as

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

a variational principle for problems with functional constraints in this paper we show that in several important classes of optimization problems like mathematical programming with k smooth data quadratic programming in a hilbert space convex programming in a banach space semi infinite programming and optimal control of linear systems with quadratic cost most of the problems in the baire category sense are well posed this is derived from a general variational principle for problems with functional constraints

convex optimization and the epi distance topology let 17 x denote the proper lower semicontinuous convex functions on a banach space x equipped with the completely metrizable topology t of uniform convergence of distance functions on bounded sets a function f in 17 x is called well posed provided it has a unique minimizer and each minimizing sequence converges to this minimizer we show that well posedness of f e r x is the minimal condition that guarantees strong convergence of approximate minima of t approximating functions to the minimum of f moreover we show that most functions in 17 x taw are well posed and that this fails if 17 x is topologized by the weaker topology of mosco convergence whenever x is infinite dimensional applications to metric projections are also given including a fundamental characterization of approximative compactness

fuzzy constrained lp norm inversion of direct current resistivity data abstractwe evaluate the use of a fuzzy c means clustering procedure to improve an inverted 2d resistivity model within the iterative error minimization procedure the algorithm is coded in matlab language for the lp norm inversion of 2d direct current resistivity data and is referred to as fuzzy constrained inversion fci two additional input parameters are required to be provided by the interpreter 1 the number of geologic units in the model i e the number of clusters and 2 the mean resistivity values of each geologic unit i e cluster center values of the geologic units the efficacy of our approach is evaluated by tests carried on the synthetic and field electrical resistivity tomography ert data inversion results from the fci algorithm are presented for conventional l1 and l2 norm minimization techniques fci indicates improvement over conventional inversion approaches in differentiating the geologic units if a proper number of the geologic units is provided to the algorithm inappro

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

a new shapley value for games with fuzzy coalitions abstract this paper deals with cooperative games over fuzzy coalitions in these situations there is a continuous set of fuzzy coalitions instead of a finite set of them as in the classical case the unit square in an n dimensional space there exist in the literature two different extensions of the known shapley value for crisp games to games with fuzzy coalitions the crisp shapley value and the diagonal value the first value only uses a finite information in the set of fuzzy coalitions the vertices of the square while the second one uses a neighbourhood of the diagonal of the square we propose a new extension of the shapley value improving the crisp shapley value for games with fuzzy coalitions this new version uses the faces of the square namely an infinity quantity of information we analyze several properties of the new value we endow it with an axiomatization and we study the behavior when it is applied to known fuzziness of crisp games

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

enhancing the resolving power of least squares inversion with active constraint balancing most geophysical inverse problems are solved using least squares inversion schemes with damping or smoothness constraints to improve stability and convergence rate since the lagrangian multiplier controls resolution and stability of the inverse problem we always want to use the optimum multiplier which is not easy to get and is usually obtained by experience or a time consuming optimization process we present a new regularization approach in which the lagrangian multiplier is set as a spatial variable at each parameterized block and automatically determined via the parameter resolution matrix and spread function analysis for highly resolvable parameters a small value of the lagrangian multiplier is assigned and vice versa this approach named active constraint balancing acb tries to balance the constraints of the least squares inversion according to sensitivity for a given problem so that it enhances the resolution as well as the stability of the inversion process we demonstrate the performa

3 d inversion of gravity data we present two methods for inverting surface gravity data to recover a 3 d distribution of density contrast in the first method we transform the gravity data into pseudomagnetic data via poisson s relation and carry out the inversion using a 3 d magnetic inversion algorithm in the second we invert the gravity data directly to recover a minimum structure model in both approaches the earth is modeled by using a large number of rectangular cells of constant density and the final density distribution is obtained by minimizing a model objective function subject to fitting the observed data the model objective function has the flexibility to incorporate prior information and thus the constructed model not only fits the data but also agrees with additional geophysical and geological constraints we apply a depth weighting in the objective function to counteract the natural decay of the kernels so that the inversion yields depth information applications of the algorithms to synthetic and field data produce density models representative of true structures our results have shown that the inversion of gravity data with a properly designed objective function can yield geologically meaningful information

cooperation among agents with a proximity relation abstract a cooperative game consists of a set of players and a characteristic function determining 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 the relationships of closeness among the players should modify the bargaining among them and therefore their payoffs the first models that have studied this closeness used a priori unions or undirected graphs in the a priori union model a partition of the big coalition is supposed each element of the partition represents a group of players with the same interests the groups negotiate among them to form the grand coalition and later inside each one players bargain among them now we propose to use proximity relations to represent leveled closeness of the interests among the players and extending the a priori unions model

characterization of the equilibrium strategy of the bimatrix game with fuzzy payoff in this paper we consider fuzzy bimatrix games which mean bimatrix games with fuzzy payoff matrices we define two types of concepts of equilibrium strategy and investigate their relationships moreover we prove that these nash equilibrium strategies exist in any fuzzy bimatrix games

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 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

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

quantitative stability of variational systems iii e approximate solutions we prove that thee optimal solutions of convex optimization problems are lipschitz continuous with respect to data perturbations when these are measured in terms of the epi distance a similar property is obtained for the distance between the level sets of extended real valued functions we also show that these properties imply that thee subgradient mapping is lipschitz continuous

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

levitin polyak well posedness of generalized quasivariational inequalities with functional constraints abstract in this paper we study levitin polyak type well posedness for generalized quasivariational inequality problems with explicit constraints four types of levitin polyak well posedness will be introduced various criteria and characterizations will be derived for these types of levitin polyak well posedness

a sharp partitioning inequality for non atomic probability measures based on the mass of the infimum of the measures if 1 are non atomic probability measures on the same measurable space s then there is an measurable partition ai i 1n of s so that i ai n 1 m 1 for all i 1 n where m left mathop lambda limits i 1 n mu i right is the total mass of the largest measure dominated by each of the i s moreover this bound is attained for all n 1 and all m in 0 1 this result is an analog of the bound n 1 m 1of elton et al 5 based on the mass m of the supremum of the measures each gives a quantative generalization of a well known cake cutting inequality of urbanik 10 and of dubins and spanier 2

on characterization of equilibrium strategy of two person zero sum games with fuzzy payoffs in this paper we consider fuzzy matrix games namely two person zero sum games with fuzzy payoffs based on fuzzy max order for such games we define three kinds of concepts of minimax equilibrium strategies and investigate their properties first we shall show that these equilibrium strategies are characterized as nash equilibrium strategies of a family of parametric bi matrix games with crisp payoffs second we investigate properties of values of fuzzy matrix games by means of possibility and necessity measures in addition we give a numerical example to illustrate utility of our approaches

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

partial extensions of attouch s theorem with applications to proto derivatives of subgradient mappings attouch s theorem which gives on a reflexive banach space the equivalence between the mosco epi convergence of a sequence of convex functions and the graph convergence of the associated sequence of subgradients has many important applications in convex optimization in particular generalized derivatives have been defined in terms of the epi convergence or graph convergence of certain difference quotient mappings and attouch s theorem has been used to relate these various generalized derivatives these relations can then be used to study the stability of the solution mapping associated with a parameterized family of optimization problems we prove in a hilbert space several partial extensions of attouch s theorem to functions more general than convex these functions are called primal lower nice furthermore we use our extensions to derive a relationship between the second order epi derivatives of primal lower nice functions and the proto derivative of their associated subgradient mappings

optimal partitioning inequalities for nonatomic probability measures on considere une inegalite qui affine et quantifie un theoreme de decoupe du a urbanik 1955 et dubins et spanier 1961

edgeworth equilibria fuzzy core and equilibria of a production economy without ordered preferences the coincidence under suitable conditions between the set of walrasian allocations and the set of edgeworth equilibria for an economy with ordered preferences defined in a finite dimensional commodity space is a result by debreu and scarf the aim of this paper is to extend this result to production economies without ordered preferences defined in a hausdorff linear topological space

a banzhaf value for games with fuzzy communication structure computing the power of the political groups in the european parliament abstract in 2013 jimenez losada et al introduced several extensions of the myerson value for games with fuzzy communication structure in a fuzzy communication structure the membership of the players and the relations among them are leveled now we study a banzhaf value for these situations the myerson model is followed to define the fuzzy graph banzhaf value taking as base point the choquet integral we propose an axiomatization for this value introducing leveled amalgamation of players an algorithm to calculate this value is provided and its complexity is studied finally we show an applied example computing by this fuzzy value the power of the groups in the european parliament

an examination of procedures for determining the number of clusters in a data set a monte carlo evaluation of 30 procedures for determining the number of clusters was conducted on artificial data sets which contained either 2 3 4 or 5 distinct nonoverlapping clusters to provide a variety of clustering solutions the data sets were analyzed by four hierarchical clustering methods external criterion measures indicated excellent recovery of the true cluster structure by the methods at the correct hierarchy level thus the clustering present in the data was quite strong the simulation results for the stopping rules revealed a wide range in their ability to determine the correct number of clusters in the data several procedures worked fairly well whereas others performed rather poorly thus the latter group of rules would appear to have little validity particularly for data sets containing distinct clusters applied researchers are urged to select one or more of the better criteria however users are cautioned that the performance of some of the criteria may be data dependent

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

existence of an aumann maschler fuzzy bargaining set and fuzzy kernels in tu fuzzy games abstract in this paper we first give fuzzy extensions of the well known solution concepts of kernel and prekernel for a transferable utility tu game and establish the existence of fuzzy kernels in tu fuzzy games which generalizes the corresponding result for classical tu games by davis and maschler 5 we then prove that the fuzzy kernel is a subset of the fuzzy bargaining set in a tu fuzzy game which gives the fuzzy counterpart of the corresponding fact for classical tu games by davis and maschler as a consequence we establish the existence of fuzzy aumann maschler fuzzy bargaining sets for tu fuzzy games which generalizes the well known existence theorem for bargaining sets by aumann and maschler 1 and peleg 11

optimal partitioning inequalities in classification and multi hypotheses testing optimal partitioning a dminimax risk inequalities are obtained for the classification and multi hypotheses t ting problems best possible bounds are derived for the minimax risk for location parameter families based on the tail concentrations and levy concentrations of the distributions special attention is given to continuous distributions with the maximum likelihood ratio property and to symmetric unimodal continuous distributions bounds for general including discontinuous distributions are also obtained

bounds for α optimal partitioning of a measurable space based on several efficient partitions abstract we provide a two sided inequality for the optimal partition value of a measurable space according to a finite number of nonatomic finite measures the result extends and often improves legut inequalities for optimal partitioning of a measurable space proc amer math soc 104 1988 since the bounds are obtained considering several partitions that maximize the weighted sum of the partition values with varying weights instead of a single one furthermore we show conditions that make these bounds sharper

set valued cooperative games with fuzzy payoffs the fuzzy assignment game abstract in this paper we study cooperative games with fuzzy payoffs the main advantage of the approach presented is the incorporation into the analysis of the problem of ambiguity inherent in many real world collective decision situations we propose extensions of core concepts which maintain the fuzzy nature of allocations and lead to a more satisfactory study of the problem within the fuzzy context finally we illustrate the extended core concepts and the approach to obtain the corresponding allocations through the analysis of assignment games with uncertain profits

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

representation of preference relations on σ algebras of nonatomic measure spaces convexity and continuity the purpose of this paper is to show how preference relations on s algebras can be represented by means of nonadditive set functions that satisfy appropriate requirements of convexity and continuity on s algebras to this end we introduce convex combinations of measurable sets and quasiconcave and concave functions on s algebras which conform with the standard results in convex analysis we formulate the convexity and the continuity axioms for preference relations on s algebras with a metric topology and show the existence of utility functions for convex continuous preference relations we also show that monotone continuous preference relations are representable by fuzzy measures

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

two dimensional resistivity inversion resistivity data on a profile often must be interpreted in terms of a complex two dimensional 2 d model however trial and error modeling for such a case can be very difficult and frustrating to make interpretation easier and more objective we have developed a nonlinear inversion technique that estimates the resistivities of cells in a 2 d model of predetermined geometry based on dipole dipole resistivity data our numerical solution for the forward problem is based on the transmission surface analogy the partial derivatives of apparent resistivity with respect to model resistivities are equal to a simple function of the currents excited in the transmission surface by transmitters placed at receiver and transmitter sites thus for the dipole dipole array the inversion requires only one forward problem per iteration we use the box kanemasu method to stabilize the parameter step at each iteration we have tested our inversion technique on synthetic and field data in both cases convergence is rapi

persistence and stability of solutions of hamilton jacobi equations abstract given a convergent sequence of hamiltonians h n and a convergent sequence of initial data g n for the first order evolutionary hamilton jacobi equation we look for conditions ensuring that the sequences u n and v n of lax solutions and hopf solutions respectively converge the convergences we deal with are variational convergences we take advantage of several recent results giving criteria for the continuity of usual operations

myopic economic agents this paper presents a model of myopic tastes both in the context of intertemporal decision making and choice under uncertainty infinite dimensional consumption plans arise naturally in both contexts either involving a denumerable number of periods or a countable number of states of the world the essential feature of our model is that myopic behavior is formalized by defining topologies on the space of consumption plans which discount the future or improbable events

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

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

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 equalizer and the lexicographical solutions for cooperative fuzzy games characterization and properties in this paper we analyze the lexicographical solution for fuzzy tu games we study its properties and obtain a characterization the lexicographical solution was introduced by sakawa and nishizaki fuzzy sets and systems 61 1994 265 275 as a solution for crisp tu games and then extended as a value for fuzzy tu games we approach the problem by means of the close relationship that exists between the lexicographical solution for crisp tu games and the least square nucleolus a crisp value defined by ruiz et al internat j game theory 25 1996 113 134 previously and also based on this relationship we axiomatically characterize the equalizer solution for fuzzy tu games both values the equalizer and the lexicographical solutions are based on the consideration of a measure of dissatisfaction of players rather than coalitions

the equal allocation of nonseparable costs an extension under fuzzy behavior by considering the players and the activity levels simultaneously we propose a consistent solution which is a generalization of the equal allocation of nonseparable costs eansc on fuzzy games we also adopt two pre existing concepts from traditional game theory and reinterpret them in the framework of fuzzy games first based on the consistency which related to an extended reduced game we offer two axiomatizations of the extended eansc second by applying the excess function we propose a dynamic process to illustrate that the extended eansc can be reached by players who start from an arbitrary efficient solution and make consecutive amendments

the dubins spanier optimization problem in fair division theory abstract an optimality criterion for fair division theory introduced by dubins and spanier in 1961 is recalled with the purpose of analyzing its structure in relationship with other optimal solutions pareto and equi optimal partitions a geometric dual approach is also defined with the purpose of characterizing and identifying the dubins spanier optimal solutions

the epi distance topology continuity and stability results with applications to convex optimization problems let i x denote the proper lower semicontinuous convex functions on a banach space x equipped with the completely metrizable topology of uniform convergence of distance functions on bounded sets we show subject to some standard constraint qualifications that the operations of addition and restriction are continuous these results are applied to convex well posed optimization problems as well as to convergence of approximated solutions in infinite dimensional convex programming to linear functionals exposing convex sets and to metric projections also for any given function in i x we obtain results regarding the convergence of its inf convolution with smoothing kernels

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

single point iterative weighted fuzzy c means clustering algorithm for remote sensing image segmentation in this paper a remote sensing image segmentation procedure that utilizes a single point iterative weighted fuzzy c means clustering algorithm is proposed based upon the prior information this method can solve the fuzzy c means algorithm s problem that the clustering quality is greatly affected by the data distributing and the stochastic initializing the centrals of clustering after the probability statistics of original data the weights of data attribute are designed to adjust original samples to the uniform distribution and added in the process of cyclic iteration which could be suitable for the character of fuzzy c means algorithm so as to improve the precision furthermore appropriate initial clustering centers adjacent to the actual final clustering centers can be found by the proposed single point adjustment method which could promote the convergence speed of the overall iterative process and drastically reduce the calculation time otherwise the modified algorithm is updated from multidimensional data analysis to color images clustering moreover with the comparison experiments of the uci data sets public berkeley segmentation dataset and the actual remote sensing data the real validity of proposed algorithm is proved

occam s inversion a practical algorithm for generating smooth models from electromagnetic sounding data the inversion of electromagnetic sounding data does not yield a unique solution but inevitably a single model to interpret the observations is sought we recommend that this model be as simple or smooth as possible in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models to obtain smooth models the nonlinear forward problem is linearized about a starting model in the usual way but it is then solved explicitly for the desired model rather than for a model correction by parameterizing the model in terms of its first or second derivative with depth the minimum norm solution yields the smoothest possible model rather than fitting the experimental data as well as possible which maximizes the roughness of the model the smoothest model which fits the data to within an expected tolerance is sought a practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models resulting in a stable and rapidly convergent algorithm the inversion of both magnetotelluric and schlumberger sounding field data and a joint magnetotelluric resistivity inversion demonstrate the method and show it to have practical application

2 d resistivity modeling an approach to arrays parallel to the strike direction an algorithm for two dimensional electrical resistivity modeling using the finite element method with mixed boundary conditions can calculate the electrical potential along any arbitrary direction in the particular case of the direction parallel to the strike of the structure a numerical singularity occurs we resolved it by calculating the potential near the singularity and improving the involved interpolation of the transformed potential investigating the shape of potential in the fourier transformed space we conclude that this interpolation may combine logarithmic and exponential functions

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

on statistical data analysis based on the l1 norm and related methods an introduction to statistical data analysis l 1 norm based y dodge the place of the l 1 norm in robust estimation p j huber i historical development the historical development of the l 1 and l estimation procedures r w farebrother bounded influence inference in regression a review e ronchetti ii computational algorithms and computer packages algorithms for unconstrained l 1 linear regression j e gentle s c narula v a sposito the reduced gradient algorithm m r osborne the l 1 estimate as limiting case of an l p or huber estimate h ekblom a review of computational methods for solving the nonlinear l 1 norm estimation problem r gonin a h money fitting data through homotopy methods j p schellhorn blinwdr a fortran program for robust and bounded influence regression r dutter solving bounded influence regression problems with robsys a marazzi xplore a computing environment for exploratory regression w hardle iii estimation characterization properties and selection of variables l 1 distances in statistical inference comparison of topological functional and statistical properties i vajda the role played by l 1 in data analysis b fichet l 1 embeddings of a data structure i d g le calve assessing the accuracy of the sample median estimated standard errors vs interpolated confidence intervals s j sheather the median of a finite measure on a banach space j h b kemperman variable selection in linear model based on trimmed least squares estimator j antoch numerical techniques for finding estimates which minimize the upper bound of the absolute deviation a gaivoronski asymptotic properties of restricted l 1 estimates of regression j dupacova adaptive combination of least squares and least absolute deviations estimators y dodge j jureckova iv statistical inference procedures a comparison of asymptotic testing methods for l 1 regression r koenker least absolute errors analysis of variance j w mckean r m schrader small sample properties of least absolute errors analysis of variance r m schrader j w mckean bootstrap and inference procedures for l 1 regression g stangenhaus invariant tests in bivariate models and the l 1 criterion b m brown t p hettmansperger using regression fractiles to identify outliers s portnoy various discrepancy measures in model testing two competing regression models v v fedorov v nonparametric analysis kernel estimates of the sparsity function a h welsh what does optimal bandwidth selection mean for nonparametric regression estimation j s marron density estimation from dependent sample l gyorfi vi cluster analysis clustering by means of medoids l kaufman p j rousseeuw l 1 in fuzzy clustering e trauwaert using the l 1 norm within cluster analysis h spath vii applications an application of l 1 to astronomy p j rousseeuw

linear quadratic uncertain differential game with application to resource extraction problem uncertain differential game investigates interactive decision making of players over time and the system dynamics is described by an uncertain differential equation this paper goes further to study the two player zero sum uncertain differential game in order to guarantee the saddle point nash equilibrium a max min theorem is provided furthermore when the system dynamics is described by a linear uncertain differential equation and the performance index function is quadratic the existence of saddle point nash equilibrium is obtained via the solvability of a corresponding riccati equation finally a resource extraction problem is analyzed by using the theory proposed in this paper

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