reasonable properties for the ordering of fuzzy quantities ii as a continuation of the first part related to the first and second class of ordering approaches this paper deals with the fulfilment of reasonable properties in the third class of ordering approaches to do so we briefly introduce fuzzy relations on which the third class of approaches is based then we recall some transitivity related concepts and an ordering procedure based on a acyclic fuzzy relation acyclicity is a very weak restriction on a fuzzy relation we prove that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity so we give a widely applicable formulation to derive a total ranking order from a fuzzy relation with our formulation we examine all the ordering indices in the third class with respect to the proposed axioms in part i

classification of hyperspectral images by tensor modeling and additive morphological decomposition pixel wise classification in high dimensional multivariate images is investigated the proposed method deals with the joint use of spectral and spatial information provided in hyperspectral images additive morphological decomposition amd based on morphological operators is proposed amd defines a scale space decomposition for multivariate images without any loss of information amd is modeled as a tensor structure and tensor principal components analysis is compared as dimensional reduction algorithm versus classic approach experimental comparison shows that the proposed algorithm can provide better performance for the pixel classification of hyperspectral image than many other well known techniques highlights additive morphological decomposition without any loss of information is proposed decomposition is modeled as a tensor structure tensor pca is compared versus pca proposed workflow performs better than other techniques in hsi classification

higher genus wall crossing in the gauged linear sigma model we introduce a technique for proving all genus wall crossing formulas in the gauged linear sigma model as the stability parameter varies without assuming factorization properties of the virtual class implementing this technique to the gauged linear sigma model associated to a complete intersection in weighted projective space we obtain a uniform proof of the wall crossing formula in both the geometric and the landau ginzburg phase

a new approach to morphological color image processing this paper presents a new approach to the generalization of the concepts of grayscale morphology to color images a new vector ordering scheme is proposed infimum and supremum operators are defined and the fundamental vector morphological operations are extracted the basic properties of the presented vector morphology are described and its similarities to grayscale morphological operators are pointed out the main advantages of the proposed methodology are that is vector preserving and provides improved results in many morphological applications furthermore experimental results demonstrate the applicability of the proposed technique in a number of image processing and analysis problems such as noise removal edge detection and skeleton extraction

landau ginzburg calabi yau correspondence for quintic three folds via symplectic transformations we compute the recently introduced fan jarvis ruan witten theory of w curves in genus zero for quintic polynomials in five variables and we show that it matches the gromov witten genus zero theory of the quintic three fold via a symplectic transformation more specifically we show that the j function encoding the fan jarvis ruan witten theory on the a side equals via a mirror map the i function embodying the period integrals at the gepner point on the b side this identification inscribes the physical landau ginzburg calabi yau correspondence within the enumerative geometry of moduli of curves matches the genus zero invariants computed by the physicists huang klemm and quackenbush at the gepner point and yields via givental s quantization a prediction on the relation between the full higher genus potential of the quintic three fold and that of fan jarvis ruan witten theory

fuzzy mathematical morphology for color images defined by fuzzy preference relations nowadays the representation and the treatment of color images are still open problems mathematical morphology is the natural area for a rigorous formulation of many problems in image analysis moreover it comprises powerful non linear techniques for filtering texture analysis shape analysis edge detection or segmentation a large number of morphological operators have been widely defined and tested to process binary and gray scale images however the extension of mathematical morphology operators to multi valued functions and in particular to color images is neither direct nor general due to the vectorial nature of the data in this paper basic morphological operators erosion and dilation are extended to color images from a new vector ordering scheme based on a fuzzy order in the rgb color space experimental results show that the proposed color operators can be efficiently used for color image processing highlightsfuzzy mathematical morphology for color images erosion and dilation operators avoid false colors proposed order considers all the components with the same weight

construction of d m splines in l 2 m 0 1 space by sobolev method abstract in the present paper using s l sobolev s method interpolation d m splines that minimizes the expression 0 1 m x 2 dx in the l 2 m 0 1 space are constructed explicit formulas for the coefficients of the interpolation splines are obtained the obtained interpolation spline is exact for polynomials of degree m 1 some numerical experiments are presented moreover the connection between the obtained interpolation splines and the optimal quadrature formulas are shown

perturbed kernel approximation on homogeneous manifolds current methods for interpolation and approximation within a native space rely heavily on the strict positive definiteness of the underlying kernels if the domains of approximation are the unit spheres in euclidean spaces then zonal kernels kernels that are invariant under the orthogonal group action are strongly favoured in the implementation of these methods to handle real world problems however some or all of the symmetries and positive definiteness may be lost in digitalization due to small random errors that occur unpredictably during various stages of the execution perturbation analysis is therefore needed to address the stability problem encountered in this paper we study two kinds of perturbations of positive definite kernels small random perturbations and perturbations by dunkl s intertwining operators c dunkl y xu orthogonal polynomials of several variables encyclopedia of mathematics and its applications vol 81 cambridge university press cambridge 2001 we show that with some reasonable assumptions a small random perturbation of a strictly positive definite kernel can still provide vehicles for interpolation and enjoy the same error estimates we examine the actions of the dunkl intertwining operators on zonal strictly positive definite kernels on spheres we show that the resulted kernels are strictly positive definite on spheres of lower dimensions

landau ginzburg calabi yau correspondence for the complete intersections x3 3 and x2 2 2 2 abstract we define a generalization of fan jarvis ruan witten theory a hybrid model associated to a collection of quasihomogeneous polynomials of the same weights and degree which is expected to match the gromov witten theory of the calabi yau complete intersection cut out by the polynomials in genus zero we prove that the correspondence holds for any such complete intersection of dimension three in ordinary rather than weighted projective space these results generalize those of chiodo ruan for the quintic threefold and as in that setting givental s quantization can be used to yield a conjectural relation between the full higher genus theories

a new method toward the landau ginzburg calabi yau correspondence via quasi maps the landau ginzburg calabi yau correspondence claims that the gromov witten invariant of the quintic calabi yau 3 fold should be related to the fan jarvis ruan witten invariant of the associated landau ginzburg model via wall crossings in this paper we consider the stack of quasi maps with a cosection and introduce sequences of stability conditions which enable us to interpolate between the moduli stack for gromov witten invariants and the moduli stack for fan jarvis ruan witten invariants

witten s top chern class via cosection localization for a landau ginzburg space mathbb c n g w we construct witten s top chern class as an algebraic cycle using cosection localized virtual cycles in the case where all sectors are narrow verify all axioms of this class and derive an explicit formula for it in the free case we prove that this construction is equivalent to the constructions of polishchuk vaintrob chiodo and fan jarvis ruan

fast and accurate interpolation of large scattered data sets on the sphere in this paper a new efficient algorithm for spherical interpolation of large scattered data sets is presented the solution method is local and involves a modified spherical shepard s interpolant which uses zonal basis functions as local approximants the associated algorithm is implemented and optimized by applying a nearest neighbour searching procedure on the sphere specifically this technique is mainly based on the partition of the sphere in a suitable number of spherical zones the construction of spherical caps as local neighbourhoods for each node and finally the employment of a spherical zone searching procedure computational cost and storage requirements of the spherical algorithm are analyzed moreover several numerical results show the good accuracy of the method and the high efficiency of the proposed algorithm

integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations abstract the purpose of this paper is to study a fuzzy multipurpose decision making problem where the information about the alternatives provided by the experts can be of a diverse nature the information can be represented by means of preference orderings utility functions and fuzzy preference relations and our objective is to establish a general model which cover all possible representations firstly we must make the information uniform using fuzzy preference relations as uniform preference context secondly we present some selection processes for multiple preference relations based on the concept of fuzzy majority fuzzy majority is represented by a fuzzy quantifier and applied in the aggregation by means of an owa operator whose weights are calculated by the fuzzy quantifier we use two quantifier guided choice degrees of alternatives a dominance degree used to quantify the dominance that one alternative has over all the others in a fuzzy majority sense and a non dominance degree that generalises orlovski s non dominated alternative concept the application of the two above choice degrees can be carried out according to two different selection processes a sequential selection process and a conjunction selection process

probabilistic pseudo morphology for grayscale and color images mathematical morphology offers popular image processing tools successfully used for binary and grayscale images recently its extension to color images has become of interest and several approaches were proposed due to various issues arising from the vectorial nature of the data none of them imposed as a generally valid solution we propose a probabilistic pseudo morphological approach by estimating two pseudo extrema based on chebyshev inequality the framework embeds a parameter which allows controlling the linear versus non linear behavior of the probabilistic pseudo morphological operators we compare our approach for grayscale images with the classical morphology and we emphasize the impact of this parameter on the results then we extend the approach to color images using principal component analysis as validation criteria we use the estimation of the color fractal dimension color textured image segmentation and color texture classification furthermore we compare our proposed method against two widely used approaches one morphological and one pseudo morphological we propose a pseudo morphology based on probabilistic tools we use chebyshev inequality and pca for estimating pseudo extrema of a set our operators are linear or non linear depending on the choice of a parameter we extend the approach to multivariate images particularly for the color domain validation is performed through texture feature extraction

group invariant colour morphology based on frames mathematical morphology is a very popular framework for processing binary or grayscale images one of the key problems in applying this framework to color images is the notorious false color problem we discuss the nature of this problem and its origins in doing so it becomes apparent that the lack of invariance of operators to certain transformations forming a group plays an important role the main culprits are the basic join and meet operations and the associated lattice structure that forms the theoretical basis for mathematical morphology we show how a lattice that is not group invariant can be related to another lattice that is when all transformations in a group are linear these lattices can be related to one another via the theory of frames this provides all the machinery to let us transform any grayscale or color morphological filter into a group invariant filter on grayscale or color images we then demonstrate the potential for both subjective and objective improvement in selected tasks

spherical spline interpolation basic theory and computational aspects abstract the purpose of the paper is to adapt to the spherical case the basic theory and the computational method known from surface spline interpolation in euclidean spaces spline functions are defined on the sphere the solution process is made simple and efficient for numerical computation in addition the convergence of the solution obtained by spherical spline interpolation is developed using estimates for legendre polynomials

geometry and analysis of spin equations we introduce w spin structures on a riemann surface and give a precise definition to the corresponding w spin equations for any quasi homogeneous polynomial w then we construct examples of nonzero solutions of spin equations in the presence of ramond marked points the main result of the paper is a compactness theorem for the moduli space of the solutions of w spin equations when w w x1 xt is a non degenerate quasi homogeneous polynomial with fractional degrees or weights qi 1 2 for all i in particular the compactness theorem holds for the superpotentials e6 e7 e8 or an 1 dn 1 for n 3

computing genus zero twisted gromov witten invariants twisted gromov witten invariants are intersection numbers in moduli spaces of stable maps to a manifold or orbifold x which depend in addition on a vector bundle over x and an invertible multiplicative characteristic class special cases are closely related to local gromov witten invariants of the bundle and to genus zero one point invariants of complete intersections in x we develop tools for computing genus zero twisted gromov witten invariants of orbifolds and apply them to several examples we prove a quantum lefschetz theorem that expresses genus zero one point gromov witten invariants of a complete intersection in terms of those of the ambient orbifold x we determine the genus zero gromov witten potential of the type a surface singularity c2 zn we also compute some genus zero invariants of c3 z3 verifying predictions of aganagic bouchard and klemm 3 in a self contained appendix we determine the relationship between the quantum cohomology of the an surface singularity and that of its crepant resolution thereby proving the crepant resolution conjectures of ruan and of bryan and graber 12 in this case

the witten equation mirror symmetry and quantum singularity theory for any nondegenerate quasi homogeneous hypersurface singularity we describe a family of moduli spaces a virtual cycle and a corresponding cohomological eld theory associated to the singularity this theory is analogous to gromov witten theory and generalizes the theory of r spin curves which corresponds to the simple singularity ar 1 we also resolve two outstanding conjectures of witten the rst conjecture is that ade singularities are self dual and the second conjecture is that the total potential functions of ade singularities satisfy corresponding ade integrable hierarchies other cases of integrable hierarchies are also discussed

torus localization and wall crossing for cosection localized virtual cycles abstract the theory of virtual fundamental class defines important invariants such as the gromov witten and the donaldson thomas invariants it has been generalized to the cosection localized virtual cycle which has applications in seiberg witten fan jarvis ruan witten and other invariants in this paper we prove the formulas of virtual pullback torus localization and wall crossing for cosection localized virtual cycles

multi factorial risk assessment the main purpose of this paper is to develop a new method to aggregate the information given by several experts or criteria about different alternatives in order to obtain the preferred alternative or alternatives this method has to take into account the interaction of the different alternatives and a parameter modelling the flexibility of this method has to be introduced more precisely this method uses fuzzy preference relations aggregated by means of weighted ordered weighted averaging aggregation operators wowa for the exploitation phase the extended weighted voting algorithm is introduced and studied in detail finally the goodness of this approach is analyzed using it to combine different points of view people environment assets and reputation impact for the company in the assessment of risk associated with human reliability