solving bimatrix games with fuzzy payoffs by introducing nature as a third player the paper elaborates on the fuzzy bimatrix games the payoffs are assumed to be fuzzy intervals with bounded support as defined by dubois and prade a new equilibrium concept is defined for this game by introducing nature as a third player and using a cuts sufficient conditions for its existence and a procedure for its computation are provided

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

fast computation of the nonlocal boundary condition in finite difference parabolic equation radiowave propagation simulations finite difference parabolic equation method fd pem codes using a nonlocal boundary condition to model radiowave propagation over electrically large domains require the computation of time consuming spatial convolution integrals for the first time we propose the use of recursive convolution rc with vector fitting vf to reduce this computational burden rc is based on the ability to express functions as a sum of exponential terms this is achieved using the vf method details of the rc formulation applied in a two dimensional 2d wide angle fd pem wa fd pem are presented together with 2d simulations which demonstrate the computational speed and accuracy of the synthesized rc wa fd pem code

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

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

embedding complete holomorphic discs through discrete sets abstract let be the open unit disc in c and let b be the open unit ball in c 2 we prove that every discrete subset of b is contained in the range of a complete proper holomorphic embedding b

equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals when the game theory is applied to real world problems such as decision making in public and managerial problems on occasions it is difficult to assess payoffs exactly because of inaccuracy of information and fuzzy understanding of situations by experts in such cases games with fuzzy payoffs in which payoffs are represented as fuzzy numbers are often considered in this paper we consider equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs we introduce fuzzy goals for payoffs in order to incorporate ambiguity of a player s judgements and assume that the player tries to maximize degrees of attainment of the fuzzy goals the fuzzy goals for payoffs and the equilibrium solution with respect to the degree of attainment of the fuzzy goal are defined two basic methods one by weighting coefficients and the other by a minimum component are employed to aggregate multiple fuzzy goals when membership functions of fuzzy payoffs and fuzzy goals are all linear and the fuzzy decision in terms of the intersection is employed the necessary conditions that pairs of strategies be the equilibrium solutions is obtained when membership functions of fuzzy payoffs are quadratic functions those of fuzzy goals are linear and the fuzzy decision in terms of the convex combination is employed we also derive the necessary conditions that pairs of strategies be the equilibrium solutions

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

embedding holomorphic discs through discrete sets the most interesting case is n 2 for n 3 this was proved by a different method in 16 for f c n and in 9 for all convex domains o c c n in the case when f2 c n 3 one can in addition prescribe a discrete set c c and require that f j z j for all j 16 for n 2 the methods of 9 and 16 only give proper holomorphic immersions of the disc through a given discrete set in 12 the main problem of course is that in dimension two one cannot remove self intersections o f complex curves by small deformations we do not know whether our theorem holds for non runge pseudoconvex domains in cn our methods do not seem to extend to this case in this direction it was proved in 6 that for every finite subset z in an arbitrary connected pseudoconvex domain f2 c c n n 1 there exist proper holomorphic mappings f d d o f the disc into 12 such that z c f d it is likely that a refinement of the construction in 6 gives proper holomorphic immersions f d f2 whose image contains a given discrete subset of 12 an example

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

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

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

existence of equilibrium solution for a non cooperative game with fuzzy goals and parameters in this paper we introduce a concept of equilibrium for a non cooperative game with fuzzy goals involving fuzzy parameters this equilibrium is based on zimmermann s approach for solving linear multiobjective problems with fuzzy goals and the concept of n s equilibrium introduced by zhukovskii for a non cooperative game with payoffs involving unknown parameters in the case of complete ignorance of their behavior we also provide a theorem of existence of this equilibrium based on the fan inequality

perfectly matched layer truncation for parabolic wave equation models solutions of the parabolic wave equation are extended to complex values of the height variable the fast decay of the solutions in certain directions of the complex plane is used to improve parabolic wave equation solvers the solution is marched on a suitably chosen contour in the complex plane rather than on the real line this interpretation of berenger s perfectly matched layer allows extremely efficient truncation of the computational domain with a split step fourier algorithm the theory is developed for both the wide angle and narrow angle parabolic wave equations and numerical results are presented

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

nash equilibrium strategy for fuzzy non cooperative games in this article two person zero sum games are investigated in the fuzzy environment several models constructed by maeda in the symmetrical fuzzy environment are extended to the models in the asymmetric fuzzy environment the existence of equilibrium strategies for these extended models is proposed in the asymmetric fuzzy environment however in some cases nash equilibrium strategies may not exist therefore two special cases are presented for which nash equilibrium strategies do exist in order to investigate the existence of weak pareto nash equilibrium strategies for fuzzy matrix games we introduce the concept of crisp bi matrix games with parameters by solving the parametric bi matrix games we obtain the weak pareto nash equilibrium strategies for the fuzzy matrix games

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

perfect boundary conditions for parabolic water wave models generalized impedance boundary conditions are presented for parabolic wave models which provide either perfect diffractive boundary conditions or perfect transmitting boundary conditions the diffractive conditions permit the modelling of waves in illuminated regions without computations in the shadow regions while the transmitting conditions allow incident and scattered waves to propagate out of the model the theory is developed for the simplest parabolic model and for a class of wide angle parabolic models numerical results are presented

a fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers the aim of this paper is to develop an effective method for solving matrix games with payoffs of triangular fuzzy numbers tfns which are arbitrary in this method it always assures that players gain floor and loss ceiling have a common tfn type fuzzy value and hereby any matrix game with payoffs of tfns has a tfn type fuzzy value based on duality theorem of linear programming lp and the representation theorem for fuzzy sets the mean and the lower and upper limits of the tfn type fuzzy value are easily computed through solving the derived lp models with data taken from 1 cut set and 0 cut set of fuzzy payoffs hereby the tfn type fuzzy value of any matrix game with payoffs of tfns can be explicitly obtained moreover we can easily compute the upper and lower bounds of any alfa cut set of the tfn type fuzzy value for any matrix game with payoffs of tfns and players optimal mixed strategies through solving the derived lp models at any specified confidence level alfa the proposed method in this paper is demonstrated with a numerical example and compared with other methods to show the validity applicability and superiority

fuzzy linear programming models to solve fuzzy matrix games abstract in this paper a zero sum two person game with imprecise values in its matrix of payoffs is considered we propose a method for its solution based on the establishment of a fuzzy linear programming f l p problem for each player the method is shown as a generalization of that conventionally used in the solution of a classical game to solve such f l p problems we propose the auxiliary models resulting from the application of some of the methods for ranking fuzzy numbers hence according to the kind of ranking method that players want to use different solutions to the former game can be obtained we show that these solutions are of the same nature as the parameters defining the game and corresponding to a fuzzy predicate that can be established as the value of the game is around

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

optimal solutions for group matrix games involving interval valued fuzzy numbers abstract traditional games theory is based on the idea of having a set of deterministic payoffs to represent actions taken by homogeneous individuals interaction among players while in several real scenarios social and business conflicts are handled by groups of actors with different technical social skills this way a group game problem can be seen as to two groups of players who individually select a strategy to win so the information given by every player in their group affects the payoffs of such game sometimes deterministic payoffs are not available and even when they can be obtained from negotiation between players they are not clearly defined indeed within groups individual players could have different perceptions of the payoffs for which we propose a uncertain based matrix games model involving interval valued fuzzy payoffs

solving constrained matrix games with payoffs of triangular fuzzy numbers constrained matrix games with payoffs of triangular fuzzy numbers tfns are a type of matrix games with payoffs expressed by tfns and sets of players strategies which are constrained so far as we know no study have yet been attempted for constrained matrix games with payoffs of tfns since there is no effective way to simultaneously incorporate the payoffs fuzziness and strategies constraints into classical and or fuzzy matrix game methods the aim of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of tfns in this methodology we introduce the concepts of alpha constrained matrix games for constrained matrix games with payoffs of tfns and the values by the duality theorem of linear programming it is proven that players gain floor and loss ceiling always have a common interval type value and hereby any alpha constrained matrix game has an interval type value moreover using the representation theorem for the fuzzy set it is proven that any constrained matrix game with payoffs of tfns always has a tfn type fuzzy value the auxiliary linear programming models are derived to compute the lower and upper bounds of the interval type value and optimal strategies of players for any alpha constrained matrix game in particular the mean and the lower and upper limits of the tfn type fuzzy value of any constrained matrix game with payoffs of tfns can be directly obtained through solving the derived three linear programming models with data taken from only 1 cut and 0 cut of payoffs hereby the tfn type fuzzy value of any constrained matrix game with payoffs of tfns are easily computed the proposed method in this paper is compared with other methods and its validity and applicability are illustrated with a numerical example

multiple goal non cooperative conflicts under uncertainty a fuzzy set approach abstract this paper investigates strategy selection for a participant in a two party non cooperative conflict which involves both uncertainty and multiple goals uncertainty arises from the players not knowing the utility functions multiple objectives appear as the result of the payoff being a vector of prizes and the players attempt to attain various goals for each prize separately the main objective is to present a fuzzy set fuzzy programming solution concept to the conflict situation in doing so we compare a bayesian player to one that employs fuzzy set techniques we point out some of the advantages of the fuzzy set method the necessary computations in the fuzzy set method are explained in detail through an example

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

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

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 general model for fuzzy linear programming abstract in the current literature there are several models of fuzzy linear programming problems the aim of this paper is first to describe the more important problems in fuzzy linear programming and second to give a general model of fuzzy linear programming problems involving all of the above ones finally a resolution method for that general model is proposed

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

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

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

on the use of the ranking function approach to solve fuzzy matrix games in a direct way abstract a general method of solving fuzzy matrix games is presented this method is suitable when players choose their fuzzy number ranking procedures in a wide class i e that which may be represented by means of a linear ranking functions in the first case described both players use the same criterion to rank fuzzy numbers and in the second case each player uses different criteria several situations of players knowledge are analyzed in the second case and game solutions are provided in all of them

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

duality in linear programming with fuzzy parameters and matrix games with fuzzy pay offs abstract a dual for linear programming problems with fuzzy parameters is introduced and it is shown that a two person zero sum matrix game with fuzzy pay offs is equivalent to a primal dual pair of such fuzzy linear programming problems further certain difficulties with similar studies reported in the literature are discussed

matrix games with payoffs of belief structures imprecise matrix games such as interval valued matrix games and fuzzy matrix games have attracted much interest for a long time most of the previous studies on imprecise matrix games mainly focus on the fuzzy uncertainty of payoffs however the uncertainties of nonspecificity and discord involved in payoffs are not well addressed so far the purpose of this paper is to study the matrix game with such types of uncertainties in order to achieve that purpose we present a matrix game model with payoffs of belief structures so as to integrate discord and nonspecificity the proposed model can be used to express more imprecise interactions between players in the reality besides as another main contribution of the study an effective method for solving matrix games with belief structures payoffs is developed to help us find the equilibrium points of the kind of games at last an example is given to illustrate the proposed model and method

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

games with incomplete information played by bayesian players i iii this article originally appeared in management science november 1967 volume 14 number 3 pp 159 182 published by the institute of management sciences the paper develops a new theory for the analysis of games with incomplete information where the players are uncertain about some important parameters of the game situation such as the payoff functions the strategies available to various players the information other players have about the game etc however each player has a subjective probability distribution over the alternative possibilities in most of the paper it is assumed that these probability distributions entertained by the different players are mutually consistent in the sense that they can be regarded as conditional probability distributions derived from a certain basic probability distribution over the parameters unknown to the various players but later the theory is extended also to cases where the different players subjective probability distributions fail to satisfy this consistency assumption in cases where the consistency assumption holds the original game can be replaced by a game where nature first conducts a lottery in accordance with the basic probability distribution and the outcome of this lottery will decide which particular subgame will be played i e what the actual values of the relevant parameters will be in the game yet each player will receive only partial information about the outcome of the lottery and about the values of these parameters however every player will know the basic probability distribution governing the lottery thus technically the resulting game will be a game with complete information it is called the bayes equivalent of the original game part i of the paper describes the basic model and discusses various intuitive interpretations for the latter part ii shows that the nash equilibrium points of the bayes equivalent game yield bayesian equilibrium points for the original game finally part iii considers the main properties of the basic probability distribution

non cooperative fuzzy games in normal form a survey in this paper we present a review of most of the approaches for solving non cooperative fuzzy games in normal form applications of these games are reviewed as well we also present a new class of fuzzy games in normal form the class of non cooperative games involving fuzzy parameters finally some potential directions of research are provided throughout the paper and in the conclusion

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

transparent boundary conditions for parabolic equation solutions of radiowave propagation problems perfectly transparent boundary conditions are derived for truncating the integration domain when solving radiowave propagation problems with a parabolic equation pe method the boundary conditions are nonlocal they are expressed as a convolution integral involving the field at all previous ranges the convolution kernel is matched to the refractive index vertical gradient at the boundary the boundary conditions include an incoming energy term which can model an arbitrary incident field in particular they may be used with plane wave incidence or with a point source located below or above the domain boundary if required the solution can be extended to heights above the boundary with a generalized horizontal pe method closed form solutions for the incoming energy term are given for plane wave incidence and for gaussian sources when the refractive index above the boundary is constant or linear the resulting finite difference algorithms provide efficient solutions to problems involving airborne sources numerical examples are given showing excellent agreement with a pure split step fourier pe algorithm

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

exact discrete nonlocal boundary conditions for high order pade parabolic equations the nonlocal boundary conditions nlbcs for high order finite difference parabolic equations pes are obtained by z transformation of the discrete pe in a homogeneous medium the considered nlbcs include the free space radiation condition possibly with a density jump at the nlbc interface the nlbc at an arbitrary impedance interface and the nlbcs for sources and the starting field beyond the nlbc interface the derivation is presented for the multiterm pade pe model owwe one way wave equation but the developed technique is applicable to a broad class of finite difference pes the obtained nlbcs are exact for the given finite difference scheme they are not limited by the order of pade approximation or by the pe steps in range and depth the nlbc convolution coefficients are calculated by the numerical inverse z transformation the accuracy and performance of the algorithm are analyzed for several benchmark problems the solution is robust for the range steps over 25 wavelengths and or the approximations up to the tenth order the nlbcs are faster and more accurate for large steps because fewer previous range steps contribute to the convolution precomputation of the nlbc coefficients may be required in time demanding applications the results are compared with earlier proposed nlbcs for high order pes

pareto optimal security strategies in matrix games with fuzzy payoffs we present a new methodology for the analysis of fuzzy payoff matrix games the main difficulty that appears in the study of these games is the comparison between the payoff values associated to the strategies of the players because these payoffs are fuzzy quantities our approach does not transform the fuzzy payoffs to crisp numbers via standard defuzzyfication but we use standard fuzzy orders which allows us to find solutions within the same space of fuzzy numbers moreover we provide a method to solve these games finding equivalent fuzzy linear programs whose maximal solutions give the solutions of the games

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

the cournot game under a fuzzy decision environment the conventional precision based decision analysis methodology is invalid for business decision analysis when precise assessment data seldom exist this paper considers the cournot game with fuzzy demand and fuzzy costs that are assumed to be triangular fuzzy numbers our model utilizes the weighted center of gravity wcog method to defuzzify the fuzzy profit function into a crisp value we derive the equilibrium cournot quantity of each firm by simultaneously solving the first order condition of each firm our model explicitly derives the necessary condition to avoid an unreasonable outcome of negative equilibrium quantities and lack of flexibility for modification of the ranking method in addition we examine the standard deviation of the fuzzy profit resulting from the fuzziness of each firm s cost and market demand functions we conduct sensitivity analysis to investigate the effect of parameter perturbations on firms outcomes the results indicate that the center of parameter plays an important role in sensitivity analysis and dominates over variations in equilibrium quantity due to a perturbation of fuzzy parameters

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

a complete complex hypersurface in the ball of c n in 1977 p yang asked whether there exist complete immersed complex submanifolds m k c n with bounded image a positive answer is known for holomorphic curves k 1 and partial answers are known for the case when k 1 the principal result of the present paper is a construction of a holomorphic function on the open unit ball bn of c n whose real part is unbounded on every path in bn of nite length that ends on bbn a consequence is the existence of a complete closed complex hypersurface in bn this gives a positive answer to yang s question in all dimensions k n 1 k n by providing properly embedded complete complex manifolds

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

two person zero sum game approach for fuzzy multiple attribute decision making problems the multiple attribute decision making madm problem deals with candidate priority alternatives with respect to various attributes madm techniques are popularly used in diverse fields such as engineering economics management science transportation planning etc several approaches have been developed for assessing the weights of madm problems e g the eigenvector method electre topsis etc in this paper we obtained weights of a madm problem with a fuzzy decision matrix by formulating it as a two person zero sum game with an uncertain payoff matrix moreover the equilibrium solution and the resolution method for the madm game have also been developed these results are validated by a product development example of nano materials our study is an innovative approach for applying the game theory on madm problems with management of technology mot

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

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

a generalized impedance method for application of the parabolic approximation to underwater acoustics the parabolic equation pe has become an important computational tool for approximating underwater acoustic path losses in inhomogeneous environments the numerical solution of this equation is performed on a grid over the propagation medium which includes the water column and has also included a homogeneous false bottom below the actual ocean bottom this situation is viewed as one in which the propagation medium can be divided into a horizontally inhomogeneous upper layer and a horizontally homogeneous lower layer the pressure field in the latter layer is found using standard techniques valid for homogeneous media and in the former layer is found using an implicit finite difference scheme these fields and their normal derivatives are matched along the interface between the layers the result is referred to as a generalized impedance boundary condition gibc which serves to eliminate the need for a false bottom predictions obtained using the standard parabolic equation and a completely homoge

analysis of an implicit finite difference solution to an underwater wave propagation problem abstract an implicit finite difference scheme approximating a third order partial differential equation is examined the scheme is derived shown to be consistent and its stability properties are analyzed the partial differential equation is a parabolic approximating equation to the reduced wave equation

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

horizontal parabolic equation solution of radiowave propagation problems on large domains the modeling of radiowave propagation in the troposphere often involves field strength calculations in very large domains for which the usual parabolic equation techniques become prohibitively expensive the horizontal parabolic equation method hpe provides a rigorous and efficient full wave solution for this type of problem taking advantage of the fact that refractive index perturbations in the troposphere are usually confined to a limited portion of the integration domain above the height where the medium becomes standard fourier and laplace transform techniques are used to compute the field on a given horizontal with convolution kernels based on exponential or airy functions the field on the initial horizontal may be obtained by any available method the environment below the initial height may be range dependent and include terrain variations substantial computing gains in both memory requirements and execution time are obtained the method has been validated by comparison to the standard vertical pe

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