logic based fuzzy networks a study in system modeling with triangular norms and uninorms the ultimate challenges of system modeling concern designing accurate yet highly transparent and user centric models we have witnessed a plethora of neurofuzzy architectures which are aimed at addressing these two highly conflicting requirements this study is concerned with the design and the development of transparent logic networks realized with the aid of fuzzy neurons and fuzzy unineurons the construction of networks of this form requires a formation of efficient interfaces that constitute a conceptually appealing bridge between the model and the real world experimental environment in which the model is to be used in general the interfaces are constructed by invoking some form of granulation of information and binary boolean discretization in particular we introduce a new discretization environment that is realized by means of particle swarm optimization pso and data clustering implemented by the k means algorithm the underlying structure of the network is optimized by invoking a combination of the pso and the mechanisms of conventional gradient based learning we discuss various optimization strategies by considering boolean as well as fuzzy data coming as the result of discretization of original experimental data and then involving several learning strategies we elaborate on the interpretation aspects of the network and show how those could be strengthened through efficient pruning we also show how the interpreted network leads to a simpler and more accurate logic description of the experimental data a number of experimental studies are included

fast algorithms for close to toeplitz plus hankel systems and two sided linear prediction the low displacement rank definition of close to toeplitz ct matrices is extended to close to toeplitz plus hankel ctph matrices fast algorithms for solving ctph systems of equations are presented a matrix is defined as ctph if the sum of a ct matrix and a second ct matrix postmultiplied by an exchange matrix an equivalent definition in terms of uv rank is also given this definition is motivated by the application of the algorithms to two sided linear prediction tsp autocorrelation and covariance forms of tsp analogous to those for one sided linear prediction osp are defined the covariance form of tsp is solved using the ctph fast algorithms just as the covariance form of osp is solved using ct fast algorithms numerical examples show that tsp produces smaller residuals than osp and resolves sharp spectral peaks better than osp and that covariance tsp produces smaller residuals than autocorrelation tsp

new analogs of split algorithms for arbitrary toeplitz plus hankel matrices fast algorithms for solving arbitrary toeplitz plus hankel systems of equations are presented the algorithms are analogs of the split levinson and schur algorithms although the more general toeplitz plus hankel structure requires that the algorithms be based on a four term recurrence relations with the previous split algorithms are considered the algorithms require roughly half as many multiplications as previous fast algorithms for toeplitz plus hankel systems

maximum entropy and spectral estimation a review the method of maximum entropy is reviewed with emphasis on its relationship to entropy rate wiener filters autoregressive processes extrapolation the levinson algorithm lattice all pole and all pass filters and stability

signatures definitions operators and applications to fuzzy modelling this paper presents a new framework for the symbolic representation of data which is referred to as signatures the definitions of signatures and of signature trees are first given original operators on signatures are next presented i e contraction extension pruning addition multiplication and grafting attractive applications of signatures related to the modelling of fuzzy inference systems are suggested and discussed an example is included to accompany the theoretical results

quadratic wavefront and traveltime approximations in inhomogeneous layered media with curved interfaces a quadratic approximation for the square of the traveltime from a source region to a receiver region is given for a three dimensional 3 d medium consisting of inhomogeneous layers with curved interfaces the square of the traveltime being a function of source and receiver coordinates is developed in a taylor series around a reference source and receiver point the relationships of the traveltime parameters to the ray parameters and the wavefront curvature matrices are shown using midpoint half offset coordinates gives a simplified traveltime function compared to using source receiver coordinates only in the case that the reference source point and the reference receiver point coincide zero offset approximation for a medium consisting of homogeneous layers with plane dipping interfaces the traveltime approximation is further simplified the derived traveltime approximation is shown to be exact for a reflection from a plane dipping interface in a homogeneous medium explicit expressions for the tr

lattice valued f transforms and similarity relations abstract the relationships between lattice valued f transforms and similarity relations are investigated several similarity relations are naturally associated with f transforms three types of such similarity relations related to lattice valued f transforms are investigated namely similarity relationships that are related to spaces with fuzzy partitions as ground structures of the f transform relationships between extensional hulls with respect to similarity relations and f transforms and relationships between similarities of pairs of functions on the one hand and similarities of the f transforms of these functions on the other some examples of possible applications are also presented

normal moveout revisited inhomogeneous media and curved interfaces the equation of normal moveout t2 t02 x2 va2 is valid for a reflection from the base of a single homogeneous and isotropic bed but is only an approximation in the real world of multilayered inhomogeneous media and curved interfaces using the theory of geometrical optics we can find another second order equation which represents hyperbolas that are also symmetrical about the time axis however the centers of these hyperbolas do not coincide with the center of coordinates but are shifted along the time axis the equation describing this second type of hyperbola is t tp t0 2 tp2 x2 v12 where tp is the time of focusing depth and v1 the velocity of the input medium this equation is not only more accurate than the usual normal moveout but its use is more economical on a vector computer because the traditional dynamic correction is a static correction in the tp analysis this procedure makes it possible to compute velocities for all the samples of all the stacked traces and produces a velocity secti

a color image reduction based on fuzzy transforms we present a new method for color image reduction based on the concept of fuzzy transform any image in a single band can be considered as a fuzzy matrix which is subdivided into submatrices called blocks each block is compressed with various compression rates by means of a fuzzy transform in two variables we compare our method with recent three algorithms due to g beliakov h bustince and d paternain based on the minimizing penalty functions defined over a discrete lattice the quality of the reduced image is measured by the mean square error mse and penalty function pen obtained by comparing both magnified and original images we also point out a threshold of the compression rate beyond which the mse follows a linear trend and the corresponding loss of information is still acceptable

toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic there are three basic concepts that underlie human cognition granulation organization and causation informally granulation involves decomposition of whole into parts organization involves integration of parts into whole and causation involves association of causes with effects granulation of an object a leads to a collection of granules of a with a granule being a clump of points objects drawn together by indistinguishability similarity proximity or functionality for example the granules of a human head are the forehead nose cheeks ears eyes etc in general granulation is hierarchical in nature a familiar example is the granulation of time into years months days hours minutes etc modes of information granulation ig in which the granules are crisp c granular play important roles in a wide variety of methods approaches and techniques crisp ig however does not reflect the fact that in almost all of human reasoning and concept formation the granules are fuzzy f granular the granules of a human head for example are fuzzy in the sense that the boundaries between cheeks nose forehead ears etc are not sharply defined furthermore the attributes of fuzzy granules e g length of nose are fuzzy as are their values long short very long etc the fuzziness of granules their attributes and their values is characteristic of ways in which humans granulate and manipulate information

traveltime approximations for a layered transversely isotropic medium we consider multiple transmitted reflected and converted qp qsv waves or multiple transmitted and reflected sh waves in a horizontally layered medium that is transversely isotropic with a vertical symmetry axis vti traveltime and offset horizontal distance between a source and receiver not necessarily in the same layer are expressed as functions of horizontal slowness these functions are given in terms of a taylor series in slowness in exactly the same form as for a layered isotropic medium the coefficients depend on the parameters of the anisotropic layers through which the wave has passed and there is no weak anisotropy assumption using classical formulas the traveltime or traveltime squared can then be expressed as a taylor series in even powers of offset these taylor series give rise to a shifted hyperbola traveltime approximation and a new continued fraction approximation described by four parameters that match the taylor series up to the sixth power in offset further approximations give several simplified continued fraction approximations all of which depend on three parameters zero offset traveltime nmo velocity and a heterogeneity coefficient the approximations break down when there is a cusp in the group velocity for the qsv wave numerical studies indicate that approximations of traveltime squared are generally better than those for traveltime a new continued fraction approximation that depends on three parameters is more accurate than the commonly used continued fraction approximation and the shifted hyperbola

construction of image reduction operators using averaging aggregation functions in this work we present an image reduction algorithm based on averaging aggregation functions we axiomatically define the concepts of image reduction operator and local reduction operator we study the construction of the latter by means of averaging functions and we propose an image reduction algorithm image reduction operator we analyze the properties of several averaging functions and their effect on the image reduction algorithm finally we present experimental results where we apply our algorithm in two different applications analyzing the best operators for each concrete application

fuzzy transforms for compression and decompression of color videos we use fuzzy transforms for coding decoding color frames of videos and we compare the results with the same frames reconstructed with the standard jpeg method we classify all the frames in intra frames and predictive frames by adopting a similarity measure based on the lukasiewicz t norm and a pre processing phase which determines the best similarity threshold value the compression is made on particular frames called d frames obtained from a suitable difference defined on the values of the pixels of an intra frame and a predictive frame under high compression rates we see that the peak signal to noise ratio of the frames obtained with the fuzzy transforms is averagely close to the psnr obtained with the jpeg method we use the videos at url sampl eng ohiostate edu sampl database htm

efficient solution of a toeplitz plus hankel coefficient matrix system of equations there are well known fast algorithms such as the levinson recursion for solving linear equations with a toeplitz or hankel coefficient matrix this paper extends the saving obtained by the levinson recursion for inversion of a toeplitz matrix to problems involving the inversion of matrices which are the sum of toeplitz and hankel matrices

f transform with parametric generalized fuzzy partitions the fuzzy transform f transform has some interesting properties that allow its use in curve fitting and smoothing we suggest the following a a generalization of fuzzy partitions for the f transform to control and improve the smoothing effect and b a parametrization of the fuzzy numbers constituting the basic functions related to the fuzzy partitions an optimization criterion is then suggested to obtain the f transform with best approximation properties by estimating the basic functions from a family of parametric fuzzy numbers the generalized fuzzy partitions are characterized by the number of subintervals the bandwidth of the partition forming the core of each basic function and we suggest two procedures for bandwidth selection one based on taut string variation and a second based on generalized cross validation some illustrative examples are included

similarities and differences between one sided and two sided linear prediction provides a comparison between one sided linear prediction osp and two sided linear prediction tsp with respect to prediction error relationships to ar modeling and to two sided ar modeling and the application to time series interpolation linear phase filter design and spectral estimation although some of these results have appeared previously in scattered references the authors present a unified framework for deriving all of these results as well as new additional results new contributions of the paper include i proof that tsp produces smaller nonwhite residuals than osp extending previous results ii specification of the frequency domain error criterion minimized by tsp and comparison with the analogous osp criterion iii demonstration that tsp and two sided ar modeling are different problems unlike osp iv interpretation of performance of tsp interference rejection filters

general approximation of fuzzy numbers by f transform in this paper we will prove that in most of the cases the extended inverse fuzzy transform preserves the quasi concavity of a fuzzy number and hence it can be used to generate fuzzy numbers by approximating the restriction of the membership function to its support in the case of continuous fuzzy numbers with cores containing more than one element the rate of uniform convergence is of linear type and the same holds when we approximate the important characteristics of a fuzzy number such as the value or the ambiguity moreover we have the preservation of the support and the convergence of the core which in addition can be determined precisely in the case of continuous fuzzy numbers with one element core it is in general necessary to normalize the approximation but the support is preserved again and the core can be determined exactly in this case too moreover the approximations have again linear rate of uniform convergence

development of autofocusing algorithm based on fuzzy transforms in this paper we propose a new passive auto focusing algorithm to acquire images with enhanced quality through a digital camera the focus measure operations play a key role in a passive auto focusing method the proposed focus measure operation is based on a localized version of image variance method the localization of the image variance focus measure operation can be implemented with the use of fuzzy partition and fuzzy transform in order to validate our approach experimental comparative studies are conducted on test images with the use of different focus measure operators the selected operators have been chosen from an extensive review of the state of the art approaches a comparative analysis demonstrates that the proposed algorithm is superior to the conventional methods

fuzzy transforms of monotone functions with application to image compression this paper is focused on the special properties of functions monotonicity lipschitz continuity that are invariant with fuzzy transform on the basis of the monotonicity invariance we propose an efficient algorithm for improved image compression and reconstruction based on fuzzy transform

a new autoregressive method for high performance spectrum analysis in this paper a new method of autoregressive ar spectrum estimation is presented it shall be called two sided autoregressive spectrum estimation because an interpolative or smoothing model is postulated as opposed to the predictive one sided model used in ar modeling the matrix equations arising in the estimation procedures proposed in this paper exhibit a special structure the exploitation of these structures leads to fast solutions that reduce the total number of computations by an order of magnitude compared with straightforward approaches also special attention is directed to the constrained two sided ar model simulation examples show higher resolution capability of the proposed method relative to the least squares ar method

fuzzy transforms theory and applications the technique of direct and inverse fuzzy f transforms of three different types is introduced and approximating properties of the inverse f transforms are described all three types of the direct f transform are transformations from a function space to a finite dimensional vector space the first ordinary f transform is constructed on the basis of the ordinary algebra of reals while the other two types of the f transform are constructed on the basis of residuated lattice the core idea of the technique of f transforms is a fuzzy partition of a universe into fuzzy subsets factors clusters granules etc we claim that for a sufficient representation of a function defined on this universe we may consider its average values over fuzzy subsets from the partition thus a function can be associated with a mapping from a set of fuzzy subsets to the set of its thus obtained average values a number of theorems establishing best approximation properties of the inverse f transforms are proved in fact three types of the inverse f transform are the best approximations in average from below and from above respectively as one of many possible applications we present a method of image compression and reconstruction on the basis of the f transform