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

generalized invariant subspaces and parameter insensitive disturbance rejection problems with static output feedback in the geometric approach some generalized invariant subspaces for uncertain linear systems are investigated and then various parameter insensitive disturbance rejection problems with static output feedback are formulated and necessary and sufficient conditions for the problems to be solvable are presented further some sufficient conditions which are useful to check the solvability conditions are presented using the notions of generalized invariant subspaces

invertibility and inversion of linear periodic systems abstract in this paper the invertibility properties of periodic discrete time systems are studied necessary and sufficient conditions for the existence and a synthesis procedure for constructing left and right inverses are given

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

disturbance localization with dead beat control for linear periodic discrete time systems in this paper the classical notion of a controlled invariant subspace together with its main properties is extended to the case of linear periodic discrete time systems and used for deriving necessary and sufficient solvability conditions for the disturbance localization problem and a synthesis procedure for the solution moreover the notions of outer and inner controllable subspaces are introduced and studied for the same class of system thus allowing the derivation of necessary and sufficient solvability conditions for the disturbance localization problem with output or state dead beat control and to give synthesis procedures for the solutions

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

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

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

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

invariant subspaces for lpv systems and their applications the aim of this paper is to extend the notion of invariant subspaces known in the geometric control theory of the linear time invariant systems to the linear parameter varying lpv systems by introducing the concept of parameter varying invariant subspaces for lpv systems affine in their parameters algorithms are given to compute many parameter varying subspaces relevant in the solution of state feedback and observer design problems

robust trajectory tracking for a class of hybrid systems an internal model principle approach this paper deals with the asymptotic tracking of periodic trajectories for hybrid systems having linear dynamics in each operating mode and isolated discrete switching events switching systems parametric uncertainties are considered and the dimension of the state vector is allowed to vary among modes to deal with the hybrid nature of the system and the possible discontinuities of its solutions at switching times a properly amended tracking control problem is defined and a feedback control law based on a discontinuous version of the classical internal model principle is proposed the innovative design of the discrete time dynamics of the compensator guarantees the robust existence of a steady state response giving zero tracking error in the controlled output and local convergence to it

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

generalized invariant subspaces for infinite dimensional systems in this paper some generalized invariant subspaces for infinite dimensional systems are investigated and then some sufficient conditions for parameter insensitive disturbance rejection problems with state feedback and with measurement output feedback to be solvable are studied

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

solvability conditions for disturbance decoupling problems with static measurement feedback two well known disturbance decoupling problems are considered a checkable necessary and sufficient condition is derived under which the disturbance decoupling problem with static measurement feedback ddpkm is solvable for a class of multi input and multi output linear time invariant systems which have a left invertible transfer matrix function from the control input to the controlled output the set of all solutions that solve the ddpkm is constructed and parametrized explicitly this set is then used to solve the disturbance decoupling problem with static measurement feedback and with internal stability ddpkms

robust disturbance decoupling problem for parameter dependent families of linear systems abstract we consider the problem of disturbance decoupling by means of a single state feedback for a whole family of systems depending on a parameter p we give a geometric necessary and sufficient condition for the existence of solution to such problem under the hypothesis that the systems of the family are generically injective and the dependence on p is polynomial or respectively the set of possible values for p is finite

disturbance localization by measurement feedback for linear periodic discrete time systems abstract the recent notions of inner controllable outer controllable and outer reconstructible subspaces together with the extension of the notion of c a b pair of subspaces to the class of linear periodic discrete time systems are the main tools used in this paper in order to study the disturbance localization problem by measurement feedback for the same class of systems by means of these concepts the necessary and sufficient solvability conditions of such a problem and synthesis procedures of the solutions are found for three different cases i e with and without an additional requirement of output or state dead beat control

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

pole placement for linear discrete time systems by periodic output feedbacks abstract necessary and sufficient conditions for the existence of a solution to the pole placement problem by periodic output feedbacks for single input single output linear discrete time systems are established an algorithm for finding a sequence of output feedback gains is presented and illustrated by a simple numerical example

multivariable multirate sampled data systems state space description transfer characteristics and nyquist criterion first a discrete time state space description is derived for multivariable multirate sampled data systems then the multirate impulse modulation mim and the symmetric coordinate multirate impulse modulation smim of a transfer matrix are defined and their relation to the discrete time state space description is clarified based on the above results four stability criteria are derived the contents of the paper will be useful to extend the modern results about continuous time and single rate sampled data control systems to the multirate sampled data case especially extensions of the ina method and of the robust stability conditions will be straightforward

fault detection and isolation of linear discrete time periodic systems using the geometric approach this technical note solves the problem to detect and isolate faults in linear periodic discrete time systems a residual generator is designed through a suitable unknown input observer with the requirement that each residual should be sensitive only to one fault and simultaneously insensitive to the other faults that can affect the system and with the additional requirement of detectability that is the transition matrix of its relative error system has all eigenvalues smaller than in modulus for a given positive p 1 the solution is based on geometric tools and it makes use of the outer observable subspace notion

a necessary and sufficient condition for parameter insensitive disturbance rejection problem with state feedback in this paper a necessary and sufficient condition for a parameter insensitive disturbance rejection problem with state feedback which was pointed out as an open problem by bhattacharyya to be solvable is proved a constructive algorithm of simultaneously a b invariant subspaces for a finite number of linear systems and a relationship between simultaneously a b invariant subspaces and generalized a b invariant subspaces play an important role to prove the main result

robust stabilization of uncertain systems by periodic feedback an uncertain control system described by a family parametrized by an unknown parameter that takes values in a known constraint set is considered the robust stabilization problem is defined as finding a dynamic output controller that globally stabilizes the uncertain system that is no matter what the parameter value chosen by nature the closed loop system is globally asymptotically stable it is shown that in the class of dynamic periodic controllers the solution to this problem exists under reasonable assumptions given for a general family of abstract non linear models those assumptions in the case of a family of linear finite dimensional models are equivalent to suitable stabilizability and detectability assumptions for this case insensitivity of the design with respect to small errors in the data is proved

a geometric approach to the synthesis of failure detection filters a geometric formulation of beard s failure detection filter problem is stated using the concepts of c a invariant and unobservability subspaces the notions of output separable and mutually detectable families of subspaces introduced by beard are also clarified it is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum moreover it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions finally the complete duality between a generalization of beard s detection filter problem and the restricted control decoupling problem is illustrated

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

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

fault detection of linear discrete time periodic systems in this note an approach to the design of optimal fault detection systems for linear discrete time periodic systems is proposed which leads to an optimized compromise between robustness to unknown disturbances and sensitivity to faults the needed computation mainly consists in solving a difference periodic riccati system the proposed approach is finally illustrated by a numerical example

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

fault detection for linear periodic systems using a geometric approach using the geometric approach a solution is given to the problem of detecting faults in linear periodic discrete time systems the solution consists on developing an unknown input observer the existing conditions are provided in terms of new geometric notion of outer observable subspace that is the dual notion of inner reachable subspace making use of the new notion a residual generator is developed such that the residual is made independent of unknown input disturbance and its output free response goes asymptotically to zero

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

detection filter design for lpv systems a geometric approach this paper investigates fault detection and isolation of linear parameter varying lpv systems by using parameter varying c a invariant subspace and parameter varying unobservability subspaces the so called detection filter approach formulated as the fundamental problem of residual generation fprg for linear time invariant lti systems is extended for a class of lpv systems the question of stability is addressed in the terms of lyapunov quadratic stability by using linear matrix inequalities the results are applied to the model of a generic small commercial aircraft

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

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

an axiomatization of the non transferable utility value abstract the ntu non transferable utility value is a solution concept for multiperson cooperative games in which utility is not transferable games without side payments introduced by shapley in 1969 it generalizes his 1953 value for tu transferable utility games many economic contexts are more naturally modelled by ntu than by tu games and indeed the ntu value has been applied with some success to a variety of economic and economic political models two well known applications are nash s solutions 1950 1953 for the bargaining problem and for two person cooperative games both of which are instances of the ntu value in this paper the author offers an axiomatization of the ntu value like any axiomatization it should enable us to understand the concept better and hence to focus discussion one can now view the ntu value as defined by the axioms with the treatment in shapley 1969 serving as a formula or method of calculation thus the ntu value joins the ranks of the tu value and nash s solution to the bargaining problem each of which is defined by axioms but usually calculated by a formula a formula whose intuitive significance is not on the face of it entirely clear

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

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

trajectory tracking for a particle in elliptical billiards an infinitely rigid unitary mass particle is considered moving on a planar region delimited by a rigid elliptical barrier elliptical billiards under the action of proper control forces a class of periodic trajectories involving an infinite sequence of non smooth impacts between the mass and the barrier at fixed times is found by using an lmis based procedure the jumps in the velocities at the impact times render difficult if not impossible to obtain the classical stability and attractivity properties for the dynamic system describing the tracking error behaviour hence the tracking control problem is properly stated using notions similar to the quasi stability concept in v lakshmikantham d d bainov and p s simeonov theory of impulsive differential equations 6 world scientific 1989 a controller whose state is subject to discontinuities based on the internal model principle is shown to solve the proposed tracking problem giving rise to control forces that are piecewise continuous fun

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

generalized controlled and conditioned invariances for linear ω periodic discrete time systems abstract in this paper the three notions of generalized controlled a b invariance generalized conditioned c a invariance and generalized a b c invariance for uncertain linear periodic discrete time systems are studied and then the parameter insensitive disturbance rejection problems with static output feedback and or with state feedback are formulated and their solvability conditions are presented

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

a geometric approach to nonlinear fault detection and isolation we present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems a necessary condition for the problem to be solvable is derived in terms of an unobservability distribution which is computable by means of suitable algorithms the existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an observable quotient subsystem unaffected by all fault signals but one for this subsystem a fault detection filter is designed

a shapley function on a class of cooperative fuzzy games abstract in this paper we make a study of the shapley values for cooperative fuzzy games games with fuzzy coalitions which admit the representation of rates of players participation to each coalition a shapley function has been introduced by another author as a function which derives the shapley value from a given pair of a fuzzy game and a fuzzy coalition however the previously proposed axioms of the shapley function can be considered unnatural furthermore the explicit form of the function has been given only on an unnatural class of fuzzy games we introduce and investigate a more natural class of fuzzy games axioms of the shapley function are renewed and an explicit form of the shapley function on the natural class is given we make sure that the obtained shapley value for a fuzzy game in the natural class has several rational properties finally an illustrative example is given

linear function dead beat observers with disturbance localization for linear periodic discrete time systems abstract in this paper the classical notion of a conditioned invariant subspace is extended to the case of linear periodic discrete time systems properly characterized and suitably specialized to the notion of an outer reconstructible subspace these ideas are used in order to find necessary and sufficient conditions for the existence of a linear function dead beat observer for such systems under unknown and unmeasurable disturbances and a synthesis procedure for such an observer

the geometric approach for linear periodic discrete time systems abstract recently the disturbance localization problem and the problems of designing disturbance decoupled observers and of giving a geometric characterization of invariant zeros were solved for linear periodic discrete time systems through an extension of the geometric approach based on the notions of controlled invariant and conditionally invariant subspaces to periodic ones here the existing periodic geometric theory is supplemented with the notions of outer reachable subspace and controllability subspace and with some further results on the previously introduced notions of inner reachable controllable subspace and outer controllable subspace in addition it is shown that any such periodic geometric theory can be restated in an equivalent time invariant form which is just the same theory written for a suitable time invariant system having an extended state space

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

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

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

a lifting based approach to observer based fault detection of linear periodic systems in this note an approach based on lifting is introduced for the observer based fault detection fd of linear discrete time periodic systems the main contribution of this note is to give an analytic expression to transform the linear time invariant lti observer based residual generator designed based on the lifted lti reformulation of the periodic system into a periodic observer based residual generator to reduce detection delay the result enables a systematic transfer of the existing observer based fd methods for discrete lti systems to discrete time periodic systems

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

asymptotic tracking of periodic trajectories for a simple mechanical system subject to nonsmooth impacts an infinitely rigid mass is considered which moves on a plane under the action of proper control forces within a closed region delimited by an infinitely massive and rigid circular barrier a suitably amended tracking problem for a class of periodic trajectories involving an infinite number of nonsmooth impacts between the mass and the barrier is formally stated and solved

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 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

disturbance decoupling with quadratic stability for switched linear systems in this paper disturbance decoupling problems without stability and with quadratic stability for switched linear systems are formulated in the framework of the so called geometric approach firstly necessary and sufficient conditions for the problem without stability to be solvable are given secondly sufficient conditions for the problem with quadratic stability to be solvable are given further for switched linear systems composed of two subsystems necessary and sufficient conditions for the problem with quadratic stability to be solvable are also investigated finally an illustrative example is shown

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

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

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem

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

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature

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