a simplified expression of the shapley function for fuzzy game abstract in this paper a simplified expression of the shapley function for games with fuzzy coalition is proposed which can be regarded as the generalization of shapley functions defined in some particular games with fuzzy coalition the simplified expression of the shapley function is compared with two definitions established by butnariu tsurumi et al a conclusion is drawn that the simplified expression of the shapley function is equivalent to butnariu s definition when characteristic function is a game with proportional values and is equivalent to tsurumi s definition when characteristic function is a game with choquet integral forms furthermore from an angle of interaction between two participation levels the properties of the two games defined by butnariu and tsurumi are respectively studied

kernel pca for novelty detection kernel principal component analysis kernel pca is a non linear extension of pca this study introduces and investigates the use of kernel pca for novelty detection training data are mapped into an infinite dimensional feature space in this space kernel pca extracts the principal components of the data distribution the squared distance to the corresponding principal subspace is the measure for novelty this new method demonstrated a competitive performance on two dimensional synthetic distributions and on two real world data sets handwritten digits and breast cancer cytology

principal component analysis based on l1 norm maximization a method of principal component analysis pca based on a new l1 norm optimization technique is proposed unlike conventional pca which is based on l2 norm the proposed method is robust to outliers because it utilizes l1 norm which is less sensitive to outliers it is invariant to rotations as well the proposed l1 norm optimization technique is intuitive simple and easy to implement it is also proven to find a locally maximal solution the proposed method is applied to several datasets and the performances are compared with those of other conventional methods

a boundary method for outlier detection based on support vector domain description the support vector domain description svdd is a popular kernel method for outlier detection which tries to fit a class of data with a sphere and uses a few target objects to support its decision boundary the problem is that even with a flexible gaussian kernel function the svdd could sometimes generate such a loose decision boundary that the discrimination ability becomes poor therefore a computationally intensive procedure called kernel whitening is often required to improve the performance in this paper we propose a simple post processing method which tries to modify the svdd boundary in order to achieve a tight data description with no need of kernel whitening with the derivation of the distance between an object and its nearest boundary point in input space the proposed method can efficiently construct a new decision boundary based on the svdd boundary the improvement from the proposed method is demonstrated with synthetic and real world datasets the results show that the proposed decision boundary can fit the shape of synthetic data distribution closely and achieves better or comparable classification performance on real world datasets

a banzhaf function for a fuzzy game in this paper another important solution for fuzzy games called the banzhaf function is investigated first a sim plified expression for the banzhaf function for games with fuzzy coalition is proposed the relationship between this simplified ex pression and two kinds of particular banzhaf functions are dis cussed in detail furthermore in the framework of games with fuzzy coalitions we give a definition of the potential function of fuzzy games and prove that the marginal values of the potential function are the components of the banzhaf function further more a new axiomatic characterization of the banzhaf function for games with fuzzy coalitions is provided

nested support vector machines one class and cost sensitive support vector machines svms are state of the art machine learning methods for estimating density level sets and solving weighted classification problems respectively however the solutions of these svms do not necessarily produce set estimates that are nested as the parameters controlling the density level or cost asymmetry are continuously varied such nesting not only reflects the true sets being estimated but is also desirable for applications requiring the simultaneous estimation of multiple sets including clustering anomaly detection and ranking we propose new quadratic programs whose solutions give rise to nested versions of one class and cost sensitive svms furthermore like conventional svms the solution paths in our construction are piecewise linear in the control parameters although here the number of breakpoints is directly controlled by the user we also describe decomposition algorithms to solve the quadratic programs these methods are compared to conventional non nested svms on synthetic and benchmark data sets and are shown to exhibit more stable rankings and decreased sensitivity to parameter settings

on cores and stable sets for fuzzy games in this paper cores and stable sets for games with fuzzy coalitions are introduced and their relations studied for convex fuzzy games it turns out that all cores coincide and that the core is the unique stable set also relations between cores and stable sets of fuzzy clan games are discussed

shapley mappings and the cumulative value for n person games with fuzzy coalitions abstract in this paper we prove existence and uniqueness of the so called shapley mapping which is a solution concept for a class of n person games with fuzzy coalitions whose elements are defined by the specific structure of their characteristic functions the shapley mapping when it exists associates to each fuzzy coalition in the game an allocation of the coalitional worth satisfying the efficiency the symmetry and the null player conditions it determines a cumulative value that is the sum of all coalitional allocations for whose computation we provide an explicit formula

h infty optimal fractional delay filters fractional delay filters are digital filters to delay discrete time signals by a fraction of the sampling period since the delay is fractional the intersample behavior of the original analog signal becomes crucial in contrast to the conventional designs based on the shannon sampling theorem with the band limiting hypothesis the present paper proposes a new approach based on the modern sampled data h optimization that aims at restoring the intersample behavior beyond the nyquist frequency by using the lifting transform or continuous time blocking the design problem is equivalently reduced to a discrete time h optimization which can be effectively solved by numerical computation softwares moreover a closed form solution is obtained under an assumption on the original analog signals design examples are given to illustrate the advantage of the proposed method

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

on the state space and frequency domain characterization of h norm of sampled data systems this paper studies the problem of characterization and computation of the h norm of sampled data systems using the time invariant function space model via lifting with the advantage of time invariance the treatment gives an eigenvalue type characterization first in the operator form in the frequency domain and then in the hamiltonian type finite dimensional form the form obtained can be adopted for use with the bisection algorithm for actual computation

shapley shubik and banzhaf indices revisited we provide a new axiomatization of the shapley shubik and the banzhaf power indices in the domain of simple superadditive games by means of transparent axioms only anonymity is shared with the former characterizations in the literature the rest of the axioms are substituted by more transparent ones in terms of power in collective decision making procedures in particular a clear restatement and a weaker alternative for the transfer axiom are proposed only one axiom differentiates the characterization of either index and these differentiating axioms provide a new point of comparison in a first step both indices are characterized up to a zero and a unit of scale then both indices are singled out by simple normalizing axioms

potential value and consistency let p be a real valued function defined on the space of cooperative games with transferable utility satisfying the following condition in every game the marginal contributions of all players are efficient it is proved that there exists just one such function p called the potential and moreover that the resulting payoff vector coincides with the shapley value

new mathematical properties of the banzhaf value abstract a new axiomatic characterization of the banzhaf value for a cooperative n person game with transferable utilities is given by using a new potential function in the space of all games with a fixed set of players a potential basis has been found which allows an explicit representation of all games with an apriori given banzhaf value

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

l1 norm based kpca for novelty detection novelty detection is a one class classification problem and it builds up the model with only normal samples based on which the novelty is detected though conventional kpca is an effective method of building one class classification models it is prone to being affected by the presence of outliers due to its inherent properties of l2 norm in this paper we propose a new optimization problem l1 norm based kpca which is robust to outliers correspondingly we present the algorithm and the measure of novelty the proposed method is applied to novelty detection and performs well on the simulation data sets

solutions of algebraic equations involving generalized fuzzy numbers abstract this paper deals with algebraic equations involving generalized fuzzy numbers with continuous membership functions the generalized fuzzy number defined in this paper is a general name for fuzzy numbers fuzzy intervals crisp numbers and interval numbers three important properties of the generalized fuzzy numbers with continuous membership functions are introduced as the basis for deriving the solvability criterion the sufficient and necessary condition for solving a x c is derived the sufficient and necessary condition for solving a x c and a x c when a and c are nonzero generalized fuzzy numbers is also derived in this paper instead of the inverse operation method which fails for fuzzy sets inverse operations on the boundary points of level set intervals for continuous membership functions are used when the derived criteria of solvability are satisfied a unique solution rather than a solution set is obtained

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

equations with fuzzy numbers abstract assuming that is any operation defined in the real number set it can be extended to the fuzzy sets by zadeh s extension principle in this paper we study which conditions have to be verified by the cuts of the fuzzy numbers f and g in order that the equation f x g has a solution by the way we study some properties of the function h g f considered by e sanchez

characterization and sampled data design of dual tree filter banks for hilbert transform pairs of wavelet bases characterization and design of dual tree filter banks for forming hilbert transform pairs of wavelet bases are studied the characterization extends the existing results for quadrature mirror filter banks to general prefect reconstruction filter banks that satisfy only a mild technical assumption regarding the ratio of determinants of the two filter banks we establish equivalent relationships of hilbert transform pairs on scaling filters wavelet filters or scaling functions the design of scaling filters of a dual filter bank is formulated as a sampled data hinfin optimization problem the wavelet filters are then determined using the relationship on the determinants of the filter banks we convert the sampled data problem into an equivalent discrete time hinfin control problem which can be solved by standard hinfin control theory an analytical solution to the sampled data design problem is obtained for a special case the sampled data design approach usually gives infinite impulse response filter in the case where the primal filter bank is of finite impulse response fir we may truncate the impulse responses to get fir approximations they also lead to approximate hilbert transform pairs design examples are presented

hilbert transform pairs of orthogonal wavelet bases necessary and sufficient conditions the condition on scaling filters of two orthogonal wavelet bases that render the corresponding wavelets as hilbert transform pairs is re examined in this note without making any pre assumption on the relationship between the two scaling filters the authors derive necessary and sufficient conditions for forming hilbert transform pairs they lead to new magnitude conditions and selesnick s phase condition unique solutions to these conditions are concluded it is shown that orthogonal wavelet bases form hilbert transform pairs if and only if the two scaling filters are offset from one another by half a sample

sdp approximation of a fractional delay and the design of dual tree complex wavelet transform we show that an hinfin optimization problem related to fractional delay approximation can be formulated as a semideflnite programming sdp problem and thus solved reliably particularly given the finite impulse response fir filter h z we find the fir filter g z of given degree such that g z z 1 2h z infin is minimum this half sample delay approximation problem is used in the design of filters generating orthogonal dual tree complex wavelet transforms since the solution does not conform to the orthogonality constraints exactly we propose their enforcement in a second stage of optimization in which an analyticity criterion is optimized the proposed designs compare favorably with previous ones

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

sampled data design of fir dual filter banks for dual tree complex wavelet transforms via lmi optimization starting from a given finite impulse response fir primal filter bank we design a dual filter bank such that the complex wavelets associated with the dual tree filter bank are almost analytic the dual filter bank is required to be fir and have a prescribed number of zeros at we formulate a sampled data optimization problem based on the half sample delay condition on scaling filters a discrete time filter is introduced in the formulation to specify the number of the zeros the optimization problem is converted into an equivalent discrete time control problem the latter is further reduced to an lmi optimization problem we then present a procedure for design of fir dual filter banks illustrative examples are provided the results compare favorably to early designs

fast support vector data descriptions for novelty detection support vector data description svdd has become a very attractive kernel method due to its good results in many novelty detection problems however the decision function of svdd is expressed in terms of the kernel expansion which results in a run time complexity linear in the number of support vectors for applications where fast real time response is needed how to speed up the decision function is crucial this paper aims at dealing with the issue of reducing the testing time complexity of svdd a method called fast svdd f svdd is proposed unlike the traditional methods which all try to compress a kernel expansion into one with fewer terms the proposed f svdd directly finds the preimage of a feature vector and then uses a simple relationship between this feature vector and the svdd sphere center to re express the center with a single vector the decision function of f svdd contains only one kernel term and thus the decision boundary of f svdd is only spherical in the original space hence the run time complexity of the f svdd decision function is no longer linear in the support vectors but is a constant no matter how large the training set size is in this paper we also propose a novel direct preimage finding method which is noniterative and involves no free parameters the unique preimage can be obtained in real time by the proposed direct method without taking trial and error for demonstration several real world data sets and a large scale data set the extended mit face data set are used in experiments in addition a practical industry example regarding liquid crystal display micro defect inspection is also used to compare the applicability of svdd and our proposed f svdd when faced with mass data input the results are very encouraging

fuzzy nash equilibriums in crisp and fuzzy games in this paper we introduce fuzzy nash equilibrium to determine a graded representation of nash equilibriums in crisp and fuzzy games this interpretation shows the distribution of equilibriums in the matrix form of a game and handles uncertainties in payoffs in addition a new method to rank fuzzy values with the user s viewpoint is investigated by this means the definition of satisfaction function which provides the result of comparison in the form of real value is developed when users have preferences regarding the payoffs

on the phase condition and its solution for hilbert transform pairs of wavelet bases in this paper the phase condition on the scaling filters of two wavelet bases that renders the corresponding wavelets as hilbert transform pairs is studied an alternative and equivalent phase condition is derived with the equivalent condition and using fourier series expansions we show that the solution for which the corresponding scaling filters are offset from one another by a half sample is the only solution satisfying the phase condition

a coalitional extension of generalized fuzzy games abstract in this paper we give a coalitional extension of generalized fuzzy games and introduce the notion of coalitional fuzzy equilibria we first prove the existence of coalitional fuzzy equilibria in our model as an application we further show the existence theorem of strong fuzzy equilibria for fuzzy games

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

hilbert transform pairs of biorthogonal wavelet bases the forming of hilbert transform pairs of biorthogonal wavelet bases of two band filter banks is studied in this paper we first derive necessary and sufficient conditions on the scaling filters that render two hilbert transform pairs one decomposition pair and one reconstruction pair we show that the hilbert transform pairs are achieved if and only if the decomposition scaling filter of one filter bank is half sample delayed from that of the other filter bank and the reconstruction scaling filter of the former is half sample advanced from that of the latter hilbert transform pairs of wavelet bases are also characterized by equivalent relationships on the wavelet filters and the scaling functions associated with the two filter banks an illustrative example is provided

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

the phaselet transform an integral redundancy nearly shift invariant wavelet transform this paper introduces an approximately shift invariant redundant dyadic wavelet transform the phaselet transform that includes the popular dual tree complex wavelet transform of kingsbury see phil r soc london a sept 1999 as a special case the main idea is to use a finite set of wavelets that are related to each other in a special way and hence called phaselets to achieve approximate shift redundancy the bigger the set the better the approximation a sufficient condition on the associated scaling filters to achieve this is that they are fractional shifts of each other algorithms for the design of phaselets with a fixed number vanishing moments is presented building on the work of selesnick see ieee trans signal processing for the design of wavelet pairs for kingsbury s dual tree complex wavelet transform construction of two dimensional 2 d directional bases from tensor products of one dimensional 1 d phaselets is also described phaselets as a new approach to redundant wavelet transforms and their construction are both novel and should be interesting to the reader independent of the approximate shift invariance property that this paper argues they possess

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

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

the design of approximate hilbert transform pairs of wavelet bases several authors have demonstrated that significant improvements can be obtained in wavelet based signal processing by utilizing a pair of wavelet transforms where the wavelets form a hilbert transform pair this paper describes design procedures based on spectral factorization for the design of pairs of dyadic wavelet bases where the two wavelets form an approximate hilbert transform pair both orthogonal and biorthogonal fir solutions are presented as well as iir solutions in each case the solution depends on an allpass filter having a flat delay response the design procedure allows for an arbitrary number of vanishing wavelet moments to be specified a matlab program for the procedure is given and examples are also given to illustrate the results

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

a fuzzy approach to strategic games a game is a decision making situation with many players each having objectives that conflict with each other the players involved in the game usually make their decisions under conditions of risk or uncertainty in the paper a fuzzy approach is proposed to solve the strategic game problem in which the pure strategy set for each player is already defined based on the concepts of fuzzy set theory the approach uses a multicriteria decision making method to obtain the optimal strategy in the game a method which shows more advantages than the classical game methods moreover with this approach some useful conclusions are reached concerning the famous prisoner s dilemma problem in game theory

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