on soft mappings in this paper an idea of soft mappings is given and some of their properties are studied images and inverse images of crisp sets and soft sets under soft mappings are also studied an application of soft mapping in medical diagnosis has been shown

application of fuzzy soft set in decision making problems based on grey theory there are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets however the basis of evaluation of the decision method is single and simple the same decision problem can obtain different results from using a different evaluation basis in this paper in order to obtain the right result we discuss fuzzy soft set decision problems a new algorithm based on grey relational analysis is presented the evaluation bases of the new algorithm are multiple there is more information in a decision result based on multiple evaluation bases which is more easily accepted and logical to one s thinking for the two cases examined the results show that the new algorithm is efficient for solving decision problems

face recognition using the discrete cosine transform an accurate and robust face recognition system was developed and tested this system exploits the feature extraction capabilities of the discrete cosine transform dct and invokes certain normalization techniques that increase its robustness to variations in facial geometry and illumination the method was tested on a variety of available face databases including one collected at mcgill university the system was shown to perform very well when compared to other approaches

soft sets and soft groups molodtsov introduced the concept of soft set theory which can be used as a generic mathematical tool for dealing with uncertainty in this paper we introduce the basic properties of soft sets and compare soft sets to the related concepts of fuzzy sets and rough sets we then give a definition of soft groups and derive their basic properties using molodtsov s definition of the soft sets

linear versus nonlinear dimensionality reduction of high dimensional dynamical systems two techniques for dimensionality reduction of high dimensional dynamical systems are presented the first is based on karhunen loeve k l analysis and the second on autoassociative neural networks anns first we analyze the dynamics of two partial differential equations namely the one dimensional 1 d kuramoto sivashinsky k s equation and the two dimensional 2 d navier stokes n s equations for the 1 d k s equation one particular dynamical behavior represented by a heteroclinic connection in phase space is investigated as for the 2 d n s equations a quasi periodic behavior is examined coherent structures of both dynamics were extracted spanning linear subspaces with minimum information loss then we obtain systems of ordinary differential equations based on sophisticated k l galerkin type approximation capturing the dynamics of the attractors of both regimes residing on linear manifolds using the k l data coefficients as inputs to autoassociative neural networks we are able to r

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

multi local task learning with global regularization for object tracking in this paper we propose a novel multi local task learning with global regularization gr mltl method for object tracking in our formulation the tracking task is decomposed into several local tasks by dividing the whole target into several fragments and the final tracking result is obtained by combining the local tasks specifically we propose a global regularization term and inject it into the objective function of the multi local task learning formulation and derive a closed form solution in our method both the local and the global properties are embedded into a unified framework which can not only retain the integral structure of the target by the global regularization but also address the occlusions effectively by the local tasks experimental results demonstrate that our method is robust and achieves comparable performance to many state of the art methods highlightsa multi local task learning with global regularization method is proposed tracking is formulated as a novel multi local task learning problem the closed form solution to the multi local task learning is derived the local tasks can assist in addressing the occlusion problem and guide the update the global regularization can constrain the relationship of the local tasks

incremental learning of 3d dct compact representations for robust visual tracking visual tracking usually requires an object appearance model that is robust to changing illumination pose and other factors encountered in video many recent trackers utilize appearance samples in previous frames to form the bases upon which the object appearance model is built this approach has the following limitations 1 the bases are data driven so they can be easily corrupted and 2 it is difficult to robustly update the bases in challenging situations in this paper we construct an appearance model using the 3d discrete cosine transform 3d dct the 3d dct is based on a set of cosine basis functions which are determined by the dimensions of the 3d signal and thus independent of the input video data in addition the 3d dct can generate a compact energy spectrum whose high frequency coefficients are sparse if the appearance samples are similar by discarding these high frequency coefficients we simultaneously obtain a compact 3d dct based object representation and a signal reconstruction based similarity measure reflecting the information loss from signal reconstruction to efficiently update the object representation we propose an incremental 3d dct algorithm which decomposes the 3d dct into successive operations of the 2d discrete cosine transform 2d dct and 1d discrete cosine transform 1d dct on the input video data as a result the incremental 3d dct algorithm only needs to compute the 2d dct for newly added frames as well as the 1d dct along the third dimension which significantly reduces the computational complexity based on this incremental 3d dct algorithm we design a discriminative criterion to evaluate the likelihood of a test sample belonging to the foreground object we then embed the discriminative criterion into a particle filtering framework for object state inference over time experimental results demonstrate the effectiveness and robustness of the proposed tracker

generalised fuzzy soft sets in this paper we define generalised fuzzy soft sets and study some of their properties application of generalised fuzzy soft sets in decision making problem and medical diagnosis problem has been shown

graph based transductive learning for robust visual tracking in object tracking problem most methods assume brightness constancy or subspace constancy which are violated in practice in this paper the object tracking problem is considered as a transductive learning problem and a robust tracking method is proposed under intrinsic and extrinsic varieties the object not only fits the object model but also has the same cluster with the previous objects which are the labeled data by constraining the global and local information the cost function is constructed firstly the solution for minimizing the cost function can be solved by a simple linear algebra with graph laplacian moreover a novel graph is constructed over the positive samples and candidate patches which can simultaneously learn the object s global appearance model and the local intrinsic geometric structure of all the patches furthermore a heuristic positive samples selection scheme is adopted to make the method more effective the proposed method is tested on different videos which undergo large pose expression illumination and partial occlusion and compared with state of the art algorithms experimental results and comparative studies are provided to demonstrate the efficiency of the proposed method

vague soft hemirings abstract xu et al introduced the concept of vague soft sets which is an extension to the soft set and the vague set in this paper we apply the concept of vague soft sets to hemiring theory the notion of q vague soft left h ideals of a hemiring is introduced and some related properties are investigated

the normal parameter reduction of soft sets and its algorithm this paper is concerned with the reduction of soft sets and fuzzy soft sets firstly the problems of suboptimal choice and added parameter set of soft sets are analyzed then we introduce the definition of normal parameter reduction in soft sets to overcome these problems in addition a heuristic algorithm of normal parameter reduction is presented two new definitions parameter important degree and decision partition are proposed for analyzing the algorithm of normal parameter reduction furthermore the normal parameter reduction is also investigated in fuzzy soft sets

a multi class classification strategy for fisher scores application to signer independent sign language recognition fisher kernels combine the powers of discriminative and generative classifiers by mapping the variable length sequences to a new fixed length feature space called the fisher score space the mapping is based on a single generative model and the classifier is intrinsically binary we propose a multi class classification strategy that applies a multi class classification on each fisher score space and combines the decisions of multi class classifiers we experimentally show that the fisher scores of one class provide discriminative information for the other classes as well we compare several multi class classification strategies for fisher scores generated from the hidden markov models of sign sequences the proposed multi class classification strategy increases the classification accuracy in comparison with the state of the art strategies based on combining binary classifiers to reduce the computational complexity of the fisher score extraction and the training phases we also propose a score space selection method and show that similar or even higher accuracies can be obtained by using only a subset of the score spaces based on the proposed score space selection method a signer adaptation technique is also presented that does not require any re training

kernels and closures of soft set relations and soft set relation mappings in this paper the notions of anti reflexive kernel symmetric kernel reflexive closure and symmetric closure of a soft set relation are first introduced respectively then their accurate calculation formulae and some properties are obtained finally soft set relation mappings and inverse soft set relation mappings are proposed and some related properties are discussed

effective viscosity in the simulation of spatially evolving shear flows with monotonic fct models abstract the global numerical diffusion of a model for the low mach number simulation of free mixing layers is investigated the numerical model solves the inviscid time dependent conservation equations for mass momentum and energy for ideal gases the equations are solved using an explicit flux corrected transport fct algorithm directional timestep splitting techniques on structured grids and appropriate inflow and outflow boundary conditions effective measurement of the numerical diffusion of the model in uniform grids is performed by comparison of the laminar spread of the simulated mixing layers with that predicted by boundary layer theory the results show that the residual numerical diffusion of the fct model can emulate physical viscosity for laminar shear flows at moderately high reynolds numbers the global numerical diffusion is not very sensitive to changes in free stream velocity ratio and can be reduced in a predictable way by refining the grid spacing

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

linearized proximal alternating minimization algorithm for motion deblurring by nonlocal regularization abstract non blind motion deblurring problems are highly ill posed and so it is quite difficult to find the original sharp and clean image to handle ill posedness of the motion deblurring problem we use nonlocal total variation abbreviated as tv regularization approaches nonlocal tv can restore periodic textures and local geometric information better than local tv but since nonlocal tv requires weighted difference between pixels in the whole image it demands much more computational resources than local tv by using the linearization of the fidelity term and the proximal function our proposed algorithm does not require any inversion of blurring operator and nonlocal operator therefore the proposed algorithm is very efficient for motion deblurring problems we compare the numerical performance of our proposed algorithm with that of several state of the art algorithms for deblurring problems our numerical results show that the proposed method is faster and more robust than state of the art algorithms on motion deblurring problems

large eddy simulation of high reynolds number free and wall bounded flows the ability to simulate complex unsteady flows is limited by the current state of the art of subgrid scale sgs modeling which invariably relies on the use of smagorinsky type isotropic eddy viscosity models turbulent flows of practical importance involve inherently three dimensional unsteady features often subjected to strong inhomogeneous effects and rapid deformation which cannot be captured by isotropic models although some available improved sgs models can outperform the isotropic eddy viscosity models their practical use is typically limited because of their complexity development of more sophisticated sgs models is actively pursued and it is desirable to also investigate alternative nonconventional approaches in ordinary large eddy simulation les approaches models are introduced for closure of the low pass filtered navier strokes equations nse a promising les approach is the monotonically integrated les miles which involves solving the unfiltered nse using high resolution monotone algorithms in this approach implicit sgs models provided by intrinsic nonlinear high frequeacy filters built into the convection discretization are coupled naturally to the resolvable scales of the flow formal properties of the effective sgs modeling using miles are documented using databases of simulated free and wall bounded inhomogeneous flows including isotropic decaying turbulence transitional jets and channel flows mathematical and physical aspects of implicit sgs modeling through the use of nonlinear flux limiters are addressed using a formalism based on the modified les equations

robust tracking via locally structured representation representation method is critical to visual tracking a robust representation describes the target accurately leading to good tracking performance in this work a novel representation is proposed which is designed to be simultaneously low rank and joint sparse for the local patches within a target region in this representation the subspace structure is exploited by the low rank constraint to reflect the global information of all the patches and the sparsity structure is captured by the joint sparsity restriction to describe the locally intimate relationship between the neighboring patches importantly to make the representation computationally applicable to visual tracking a novel fast algorithm based on greedy strategy is proposed and the performance analysis of this algorithm is also presented thus the tracking in this work is formulated as a locally low rank and joint sparse matching problem within particle filtering framework a large number of experimental results show that the tracking drift problem is effectively alleviated in various challenging situations by using the proposed representation method both qualitative and quantitative evaluations demonstrate that the proposed tracker performs favorably against many other state of the art trackers benefitting from the good adaptive capability of the representation all the parameters of the proposed tracking algorithm are fixed in all the experiments

a combined forecasting approach based on fuzzy soft sets forecasting the export and import volume in international trade is the prerequisite of a government s policy making and guidance for a healthier international trade development however an individual forecast may not always perform satisfactorily while combination of forecasts may result in a better forecast than component forecasts we believe the component forecasts employed in combined forecasts are a description of the actual time series which is fuzzy this paper attempts to use forecasting accuracy as the criterion of fuzzy membership function and proposes a combined forecasting approach based on fuzzy soft sets this paper also examines the method with data of international trade from 1993 to 2006 in the chongqing municipality of china and compares it with a combined forecasting approach based on rough sets and each individual forecast the experimental results show that the combined approach provided in this paper improves the forecasting performance of each individual forecast and is free from a rough sets approach s restrictions as well it is a promising forecasting approach and a new application of soft sets theory

reduced order structure of reacting rectangular jets the results of proper orthogonal decomposition analyses on co 2 number density and vorticity magnitude data from reacting rectangular jet simulations are presented the resulting proper orthogonal decomposition eigenfunctions are used to develop physical insight of the vortex formations and dynamics of these jets and their related mixing and spreading characteristics it is seen that different vortex structures are captured in the eigenfunctions and that co 2 and vorticity eigenfunctions are very similar indicating that vortex driven mixing dominates in these jets the eigenvalue spectra associated with these eigenfunctions are used to evaluate the information content of the eigenfunctions and the potential for reduced order models using subsets of eigenfunctions with high information content co 2 and vorticity magnitude distributions can be represented with relatively few eigenfunctions however as the flows develop downstream more eigenfunctions are needed to represent them to the same level of accuracy the potential for reduced order modeling of each field is approximately the same for the jets of aspect ratios 1 2 and 3 however there is stronger potential for reduced order modeling of the co 2 field than of the vorticity field

robust control based object tracking this correspondence presents a video tracking framework using control based observer design it unifies several kernel based approaches into a consistent theoretical framework by modeling tracking as a recursive inverse problem the framework relies on observability theory to handle the ldquosingularityrdquo problem and provides explicit criteria for kernel design and dynamics evaluation

application of level soft sets in decision making based on interval valued fuzzy soft sets molodtsov s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty research on fuzzy soft set based decision making has received much attention in recent years this paper aims to give deeper insights into decision making involving interval valued fuzzy soft sets a hybrid model combining soft sets with interval valued fuzzy sets the concept called reduct fuzzy soft sets of interval valued fuzzy soft sets is introduced using reduct fuzzy soft sets and level soft sets flexible schemes for decision making based on weighted interval valued fuzzy soft sets are proposed and some illustrative examples are employed to show that the proposals presented here are not only more reasonable but more efficient in practical applications

soft subsets and soft product operations molodtsov s soft set theory provides a general mathematical framework for dealing with uncertainty it is known that soft subsets and soft equal relations are of vital importance in soft set theory this paper aims to give a systematic study on several types of soft subsets and various soft equal relations induced by them we give some equivalent characterizations of different soft subsets and endeavor to ascertain the interrelations among these notions illustrated by a number of concrete examples we also consider ontology based soft sets and show that soft l subsets generalize both soft m subsets and ontology based soft subsets moreover by means of soft l subsets and some related notions we give a theoretical study concerning soft product operations such as products and products we consummate some incomplete results concerning soft product operations existing in the literature and investigate the algebraic properties of soft product operations in detail finally we consider free soft algebras associated with soft product operations it is shown that soft l equal relations are congruence relations over free soft algebras and the corresponding quotient structures form commutative semigroups

chemically reacting fluid flows weak solutions and global attractors abstract in this paper we present a model for incompressible chemically reacting flows where reactants enter the domain react and then leave the domain in the interior of the domain we have the navier stokes equations for the fluid flow coupled with reaction diffusion equations for the chemistry and temperature on the boundary we use mixed neumann and inhomogeneous robin boundary conditions for the chemistry and temperature equations which fix the amount of chemicals and heat flowing into the system for three dimensional domains we then show the existence of weak solutions which are physically reasonable i e which satisfy certain maximum principle properties these solutions are sufficient to provide the basis for a dynamical systems study of these reacting flows we do not show that the solutions are unique however we are able to show the existence of global attractors for the system

eigentracking robust matching and tracking of articulated objects using a view based representation this paper describes an approach for tracking rigid and articulated objects using a view based representation the approach builds on and extends work on eigenspace representations robust estimation techniques and parameterized optical flow estimation first we note that the least squares image reconstruction of standard eigenspace techniques has a number of problems and we reformulate the reconstruction problem as one of robust estimation second we define a subspace constancy assumption that allows us to exploit techniques for parameterized optical flow estimation to simultaneously solve for the view of an object and the affine transformation between the eigenspace and the image to account for large affine transformations between the eigenspace and the image we define a multi scale eigenspace representation and a coarse to fine matching strategy finally we use these techniques to track objects over long image sequences in which the objects simultaneously undergo both affine image motions and changes of view in particular we use this eigentracking technique to track and recognize the gestures of a moving hand

self expressive tracking target representation is critical to visual tracking a good representation usually exploits some inherent relationship and structures among the observed targets the candidates or both in this work we observe that the candidates are strongly correlated to each other and exhibit obvious clustering structure when they are densely sampled around possible target locations thus we propose a self expressive tracking set algorithm based on an accurate representation with good discriminative performance the interrelationship and the clustering structure among the observed targets and the candidates are exploited by using a self expressive scheme with a low rank constraint further we design a discriminative criterion of the likelihood for target location which simultaneously considers the target background and representation errors to appropriately capture the appearance changes of the target we develop an update strategy that adaptively switches different update rates during tracking extensive experiments demonstrate that our tracking algorithm outperforms many other state of the art methods highlightsan observation of the inherent relationship and structure among the candidates a structured representation with naturally discriminative power for target description an evaluation criterion of the likelihood of the candidates belonging to the target an update strategy with adaptive update rates for appearance model maintenance

soft ideals and soft filters of soft ordered semigroups it is shown that soft ordered semigroups over an ordered semigroup are actually soft ordered subsemigroups of s a soft idealistic semigroups over an ordered semigroup are soft ideals of soft ordered semigroup s a the concept of soft filters of a soft ordered semigroup is introduced it is shown that restricted complement of a soft filter is a soft prime ideal of s a

robust visual tracking with discriminative sparse learning recently sparse representation in the task of visual tracking has been obtained increasing attention and many algorithms are proposed based on it in these algorithms for visual tracking each candidate target is sparsely represented by a set of target templates however these algorithms fail to consider the structural information of the space of the target templates i e target template set in this paper we propose an algorithm named non local self similarity nlss based sparse coding algorithm nlssc to learn the sparse representations which considers the geometrical structure of the set of target candidates by using non local self similarity nlss as a smooth operator the proposed method can turn the tracking into sparse representations problems in which the information of the set of target candidates is exploited extensive experimental results on visual tracking have demonstrated the effectiveness of the proposed algorithm

eigenfunction analysis of turbulent mixing phenomena this paper has focused on the problem of mixing and mixing assessment the k l procedure applied to data collected from a jet in crossflow provides optimal bases for the analysis of the flow it is found that better mixed flows are characterized by the dominance of spatially complex eigenfunctions qualitative measures of the complexity are presented and it is anticipated that this technique will provide a sensitive metric of the mixedness of flows in a wide variety of applications

image super resolution via sparse representation this paper presents a new approach to single image superresolution based upon sparse signal representation research on image statistics suggests that image patches can be well represented as a sparse linear combination of elements from an appropriately chosen over complete dictionary inspired by this observation we seek a sparse representation for each patch of the low resolution input and then use the coefficients of this representation to generate the high resolution output theoretical results from compressed sensing suggest that under mild conditions the sparse representation can be correctly recovered from the downsampled signals by jointly training two dictionaries for the low and high resolution image patches we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries therefore the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch the learned dictionary pair is a more compact representation of the patch pairs compared to previous approaches which simply sample a large amount of image patch pairs reducing the computational cost substantially the effectiveness of such a sparsity prior is demonstrated for both general image super resolution sr and the special case of face hallucination in both cases our algorithm generates high resolution images that are competitive or even superior in quality to images produced by other similar sr methods in addition the local sparse modeling of our approach is naturally robust to noise and therefore the proposed algorithm can handle sr with noisy inputs in a more unified framework

pruning method for optimal solutions of intm intn decision making scheme abstract this paper aims to find a faster method for optimal solutions of feng et al s int m int n decision making scheme we first give theoretical characterizations of optimal decision sets then we develop a pruning method which filters out those objects that cannot be elements of any optimal decision sets in the beginning experimental results have shown that our method has higher efficiency in computing the optimal solutions of this scheme particularly when we are processing soft sets with a great quantity of data

letter to the editor comment on a fuzzy soft set theoretic approach to decision making problems the algorithm for identification of an object in a previous paper of a r roy et al a r roy p k maji a fuzzy soft set theoretic approach to decision making problems j comput appl math 203 2007 412 418 is incorrect using the algorithm the right choice cannot be obtained in general the problem is illustrated by a counter example

finite dimensional approximation and control of non linear parabolic pde systems this article proposes a rigorous and practical methodology for the derivation of accurate finite dimensional approximations and the synthesis of non linear output feedback controllers for non linear parabolic pde systems for which the manipulated inputs the controlled and measured outputs are distributed in space the method consists of three steps first the karhunen loeve expansion is used to derive empirical eigenfunctions of the non linear parabolic pde system then the empirical eigenfunctions are used as basis functions within a galerkin s and approximate inertial manifold model reduction framework to derive low order ode systems that accurately describe the dominant dynamics of the pde system and finally these ode systems are used for the synthesis of non linear output feedback controllers that guarantee stability and enforce output tracking in the closed loop system the proposed method is used to perform model reduction and synthesize a non linear dynamic output feedback controller for a rapi