classical to critical crossovers from field theory we extend our previous determinations of nonasymptotic critical behavior of phys rev b 32 7209 1985 and 35 3585 1987 to accurate expressions of the complete classical to critical crossover in three dimensional field theory in terms of the temperaturelike scaling field i e along the critical isochore for 1 the correlation length the susceptibility and the specific heat in the homogeneous phase for the n vector model n 1 to 3 and 2 the spontaneous magnetization coexistence curve the susceptibility and the specific heat in the inhomogeneous phase for the ising model n 1 the present calculations include the seventh loop order of murray and nickel and closely account for the up to date estimates of universal asymptotic critical quantities exponents and amplitude combinations provided by guida and zinn justin j phys a 31 8103 1998

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

25th order high temperature expansion results for three dimensional ising like systems on the simple cubic lattice 25th order high temperature series are computed for a general nearest neighbor three dimensional ising model with arbitrary potential on the simple cubic lattice in particular we consider three improved potentials characterized by suppressed leading scaling corrections critical exponents are extracted from high temperature series specialized to improved potentials obtaining gamma 1 2373 2 nu 0 63012 16 alpha 0 1096 5 eta 0 03639 15 beta 0 32653 10 delta 4 7893 8 moreover biased analyses of the 25th order series of the standard ising model provide the estimate delta 0 52 3 for the exponent associated with the leading scaling corrections by the same technique we study the small magnetization expansion of the helmholtz free energy the results are then applied to the construction of parametric representations of the critical equation of state using a systematic approach based on a global stationarity condition accurate estimates of several universal amplitude ratios are also presented

master crossover functions for one component fluids by introducing three well defined dimensionless numbers we establish the link between the scale dilatation method able to estimate master i e unique singular behaviors of the one component fluid subclass and the universal crossover functions recently estimated garrabos and bervillier phys rev e 74 021113 2006 from the bounded results of the massive renormalization scheme applied to the ensuremath phi d 4 n model of scalar order parameter n 1 and three dimensions d 3 representative of the ising like universality class the master i e rescaled crossover functions are then able to fit the singular behaviors of any one component fluid without adjustable parameter using only one critical energy scale factor one critical length scale factor and two dimensionless asymptotic scale factors which characterize the fluid critical interaction cell at its liquid gas critical point an additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature the effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short range molecular interaction

min and max operators for fuzzy intervals and their potential use in aggregation operators this paper aims at expressing min and max operations when triangular fuzzy intervals are taken as inputs that is when zadeh s extension principle is considered first presented approach consists in representing fuzzy intervals by means of their profiles in this context a computation algorithm can be easily derived for implementing the min and max operations another methodology based on interval relations is then proposed for determining a general analytical expression of the min and max operations the potential use of these expressions in the framework of uncertain aggregation operators is illustrated with the two additive choquet integral

fuzzy approaches to the game of chicken game theory deals with decision making processes involving two or more parties also known as players with partly or completely conflicting interests decision makers in a conflict must often make their decisions under risk and under unclear or fuzzy information in this paper two distinct fuzzy approaches are employed to investigate an extensively studied 2 spl times 2 game model the game of chicken the first approach uses a fuzzy multicriteria decision analysis method to obtain optimal strategies for the players it incorporates subjective factors into the decision makers objectives and aggregates objectives using a weight vector the second approach applies the theory of fuzzy moves tfm to the game of chicken the theory of moves tom is designed to bring a dynamic dimension to the classical theory of games by allowing decision makers to look ahead for one or several steps so that they can make a better decision tom is the crisp counterpart of tfm the approach we implement here to deal with games that include fuzzy and uncertain information the application of fuzzy approaches to the game of chicken demonstrates their effectiveness in manipulating subjective uncertain and fuzzy information and provides valuable insights into the strategic aspects of chicken

enumerating independent vertex sets in grid graphs abstract a set of vertices in a graph is called independent if no two vertices of the set are connected by an edge in this paper we use the state matrix recursion algorithm developed by oh to enumerate independent vertex sets in a grid graph and even further to provide the generating function with respect to the number of vertices we also enumerate bipartite independent vertex sets in a grid graph the asymptotic behavior of their growth rates is presented

critical crossover functions for simple fluids non analytical scaling determination of the ising like crossover parameter a non analytical scaling determination of the ising like crossover parameter is proposed considering the critical isochore of a simple fluid at finite distance from its critical temperature the mean crossover functions estimated from the bounded results of the massive renormalization scheme in field theory applied to the left phi 2 right d 2 left n right model in three dimensions d 3 and scalar order parameter n 1 are used to formulate the corresponding scaling equations valid in two well defined temperature ranges from the critical temperature the validity range and the ising like nature of the corresponding crossover description are discussed in terms of a single ising like scale factor characterizing the critical isochore the asymptotic value of this scale factor can be predicted within the ising like preasymptotic domain unfortunately the absence of precise experimental data in such a close vicinity of the critical point leads the direct testing impossible a contrario from our scaling equations and the use of precise measurements performed at finite distance from the critical point its local value can be estimated beyond the ising like preasymptotic domain this non analytical scaling determination only needs to make reference to the universal features estimated from the mean crossover functions and to introduce a single master dimensionless length common to all the simple fluids this latter parameter guaranties the uniqueness of the physical length unit used for the theoretical crossover functions and the fluid singular properties when the generalized critical coordinates of the vapor liquid critical point of each fluid are known xenon case along its critical isochore is considered as a typical example to demonstrate the singleness of the ising like crossover parameter with the measurements at finite temperature range of the effective singular behaviors of the isothermal compressibility in the homogeneous domain and the vapor liquid coexisting densities in the non homogeneous domain our scaling equations provide the local estimate of this crossover parameter as a function of the temperature distance from the critical temperature our results compare favorably with the single asymptotic value calculated only using four critical coordinates of xenon

uncertain coalition structure game with payoff of belief structure abstract the uncertain coalition structure game with payoff of belief structure ucs game is studied based on belief structures of d s theory this type of ucs games gives us the uncertainty by assigning the probability to the set composed of multiple risk situations for the solution of ucs game this ucs game is transferred into an interval valued coalition structure game by the two step method as the value for the interval valued ucs game the uncertain owen value is axiomatically characterized by hukuhara difference because the uncertain owen value does not exist the risk owen value is proposed for the general ucs games the risk owen value adopts a risk coefficient to represent the risk tolerance of players which is more realistic than the uncertain owen value also the payoff value of ucs game is decreasing with the increasing of risk coefficient and the allocation value for the ucs game is also decreasing with the increasing of risk coefficient the players can choose their allocation scheme according to their risk tolerance

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

master singular behavior for the sugden factor of one component fluids near their gas liquid critical point we present the master i e unique behavior of the squared capillary length the so called sugden factor as a function of the temperaturelike field along the critical isochore asymptotically close to the gas liquid critical point of about twenty one component fluids this master behavior is obtained using the scale dilatation of the relevant physical fields of the one component fluids the scale dilatation method introduces the fluid dependent scale factors in a manner analog to the linear relations between physical fields and scaling fields needed by the renormalization theory applied to any physical system belonging to the ising like universality class the master behavior for the sugden factor satisfies hyperscaling it can be asymptotically fitted by the leading terms of the theoretical crossover functions for the correlation length and the susceptibility in the homogeneous domain recently obtained from massive renormalization in field theory in the absence of corresponding estimation of the theoretical crossover functions for the interfacial tension we define the range of the temperaturelike field where the master leading power law can be practically used to predict the singular behavior of the sugden factor in conformity with the theoretical description provided by the massive renormalization scheme within the extended asymptotic domain of the one component fluid subclass

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

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

an extension of cooperative fuzzy games in this paper a generalized form of fuzzy game is proposed that can be seen as an extension of the cooperative fuzzy game players in the proposed fuzzy game do not need to know precise information about the payoff value or to form a crisp coalition based on the hukuhara difference a game with a fuzzy characteristic function is studied and the explicit form of a shapley function is shown furthermore we introduce and investigate a new class of fuzzy game with fuzzy coalitions and a fuzzy characteristic function based on the hukuhara difference and the choquet integral we give the explicit form of the shapley value for the new class of fuzzy game it has been seen that most of the properties of a crisp game hold well in the proposed fuzzy game a practical application of the proposed model in joint production problem is also provided

mean crossover functions for uniaxial three dimensional ising like systems we give simple expressions for the mean of the max and min bounds of the critical to classical crossover functions previously calculated bagnuls and bervillier phys rev e 65 066132 2002 within the massive renormalization scheme of the phi d 4 n model in three dimensions d 3 and scalar order parameter n 1 of the ising like universality class the mean functions are determined relying on the properties of the theoretical functions in the two limiting three dimensional 3d ising like and mean field like descriptions close to the wilson fisher fixed point and to the gaussian fixed point respectively such descriptions correspond to the preasymptotic domains near each fixed point where a wegner expansion restricted to two terms leading and first confluent terms is valid the ising like preasymptotic domain description includes the correlations between parameters due to the error bar determination of the exponents and amplitude combinations very close to the wilson fisher fixed point adding the equivalent description of the mean field preasymptotic domain close to the gaussian fixed point leads to define each mean crossover function with three calculated parameters fixing a unique value of one parameter whatever the selected mean crossover function we use this parameter as a relative sensor to estimate the dominant nature either ising like critical or mean field like classical of the crossover behavior finally we obtain an explicit criterion to measure the extension of the ising like preasymptotic domain which can then permit to coherently account for measurements performed in systems where the asymptotical approach to the critical point remains finite using a well controlled number of system dependent parameters like in the subclass of one component fluids

inequality relation between fuzzy numbers and its use in fuzzy optimization the inequality relation between two fuzzy numbers is investigated a certain type of such a relation motivated by practical interpretation is proposed and its correspondence with the usual lattice type relation generated by the extended maximum and minimum operators and its possible interpretation are discussed the concept of r l fuzzy number is introduced the class of all r l fuzzy numbers covering practically the whole set of normal convex fuzzy numbers comparing two r l fuzzy numbers of the same type the relation introduced in the paper may be replaced by four ordinary inequalities this fact may be taken advantage of in optimization problems with linear fuzzy constraints

critical exponents of the n vector model recently the series for two renormalization group functions corresponding to the anomalous dimensions of the fields and of the three dimensional field theory have been extended to next order seven loops by murray and nickel we examine the influence of these additional terms on the estimates of critical exponents of the n vector model using some new ideas in the context of the borel summation techniques the estimates have slightly changed but remain within the errors of the previous evaluation exponents such as related to the field anomalous dimension which were poorly determined in the previous evaluation of le guillou zinn justin have seen their apparent errors significantly decrease more importantly perhaps summation errors are better determined the change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values finally because an error has been discovered in the last order of the published expansions order we have also re analysed the determination of exponents from the expansion the conclusion is that the general agreement between expansion and three dimensional series has improved with respect to le guillou zinn justin

enhanced karnik mendel algorithms the karnik mendel km algorithms are iterative procedures widely used in fuzzy logic theory they are known to converge monotonically and superexponentially fast however several usually two to six iterations are still needed before convergence occurs methods to reduce their computational cost are proposed in this paper extensive simulations show that on average the enhanced km algorithms can save about two iterations which corresponds to more than a 39 reduction in computation time an additional at least 23 computational cost can be saved if no sorting of the inputs is needed

critical crossover functions for simple fluids towards the crossover modelling uniqueness based on a single non universal temperature scaling factor present in a simple fluid case a detailed analysis of non universal parameters involved in different critical to classical crossover models is given for the infinite limit of the cutoff wave number a set of three scaling parameters is defined for each model such that it shows all the shapes of the theoretical crossover functions overlap on the mean crossover function shapes close to the non trivial fixed point the analysis of corresponding links between their fluid dependent parameters opens a route to define a parametric model of crossover equation of state closely satisfying the universal features calculated from the ising like limit in the massive renormalization scheme

upper bounds on the growth rates of independent sets in two dimensions via corner transfer matrices abstract we devise an algorithm to calculate upper bounds on the growth rates of the number of independent sets on a variety of regular two dimensional lattices using an amalgamation of techniques from linear algebra combinatorics and statistical mechanics our method uses calkin and wilf s transfer matrix eigenvalue upper bound together with the collatz wielandt formula from linear algebra to obtain a good bound we need an approximate eigenvector which we find using baxter s corner transfer matrix ansatz and nishino and okunishi s corner transfer matrix renormalisation group method this results in an algorithm for computing upper bounds which is far faster in practice than all other known methods it is also the first algorithm for this problem with a polynomial rather than exponential memory requirement and it is extremely parallelisable this allows us to make dramatic improvements to the previous best known upper bounds we apply our algorithm to five models including independent sets on the square lattice also known as the hard squares lattice gas from statistical mechanics in all cases we extend the number of rigorously known digits of the growth rate by 4 6 digits

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

super exponential convergence of the karnik mendel algorithms for computing the centroid of an interval type 2 fuzzy set computing the centroid of an interval t2 fs is an important operation in a type 2 fuzzy logic system where it is called type reduction but it is also a potentially time consuming operation the karnik mendel km iterative algorithms are widely used for doing this in this paper we prove that these algorithms converge monotonically and super exponentially fast both properties are highly desirable for iterative algorithms and explain why in practice the km algorithms have been observed to converge very fast thereby making them very practical to use

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

linear programming problems and ranking of fuzzy numbers abstract in this paper linear programming problems with fuzzy constraints and fuzzy coefficients in both matrix and right hand side of the constraint set are considered because of fuzzy coefficients in both members of each constraint ranking methods for fuzzy numbers must be considered the diversity of such methods provides a lot of different models of conventional linear programming problems from which fuzzy solutions to the former problem can be obtained

fuzzy coalition structures the paper deals with a fuzzy cooperation model where the fuzziness reflects the vague expectation of achievable pay offs this vagueness implies the possibilities of the coalitions forming and results into the vague idea about possible partitions of the set of players into coalition structures

enumeration of structure sensitive graphical subsets calculations abstract numerical calculations are presented for all connected graphs on six and fewer vertices of the numbers of independent sets connected sets point and line covers externally stable sets kernels and irredundant sets with the exception of the number of kernels the numbers of such sets are all highly structure sensitive quantities

interval valued fuzzy multi criteria decision making based on simple additive weighting and relative preference relation abstract to encompass imprecise messages traditional multi criteria decision making mcdm was generalized into fuzzy multi criteria decision making fmcdm in solving decision making problems in numerous mcdm methods simple additive weighting saw is the simplest one but fuzzy multiplication for generalizing saw under fuzzy environment is still complicated especially interval valued fuzzy numbers in the past wang proposed a model based on saw and relative preference relation to resolve fuzzy multiplication tie practically wang s model is useful to fuzzy generalization of saw however the model is only used in triangular fuzzy numbers recently more and varied messages are obtained and processed for decision making problems triangular fuzzy numbers are insufficient to express the variance whereas interval valued fuzzy numbers are suitable therefore saw had to be generalized under interval valued fuzzy environment in this paper we combine saw with a relative preference relation into interval valued fmcdm to avoid fuzzy multiplication and grasp more messages our proposed relative preference relation improved from lee s fuzzy preference relation is similar to wang s relative preference relation the main difference is that the proposed relation is utilized in interval valued fuzzy numbers whereas wang s is used in triangular fuzzy numbers to sum up we provide the fmcdm to solve decision making problems with interval valued fuzzy numbers easily and quickly

crossover scaling in two dimensions we determine the scaling functions describing the crossover from ising like critical behavior to classical critical behavior in two dimensional systems with a variable interaction range since this crossover spans several decades in the reduced temperature as well as in the finite size crossover variable it has up to now largely evaded a satisfactory numerical determination using a dedicated monte carlo method we could obtain accurate results for sufficiently large interaction ranges our data cover the full crossover region both above and below the critical temperature and support the hypothesis that the crossover functions are universal also the so called effective exponents are discussed and we show that these can vary nonmonotonically in the crossover region