a two channel overlapped block transform for image compression in this correspondence a new two channel overlapped block transform is introduced by prefiltering the haar transform the prefiltering employs plane rotations with one single rotation angle to achieve high computational efficiency the resulting transform is equivalent to a periodically time varying ptv filter bank the proposed transform or ptv filter bank has several advantages for image coding first symmetric extension is very easily performed at the boundaries in spite of the fact that the filters are asymmetric second arithmetic complexity can be reduced to simple shifts and adds finally the performance for image compression is shown to be high both in terms of visual quality and psnr as a result the proposed transform is a competitive alternative to the 5 3 and the 9 7 filters which are currently popular for subband wavelet image coders

nonparametric fuzzy regression k nn and kernel smoothing techniques abstract fuzzy regression without predefined functional form or nonparametric fuzzy regression is investigated the two most basic nonparametric regression techniques in statistics namely k nearest neighbor smoothing and kernel smoothing are fuzzified and analyzed algorithms are proposed to obtain the best smoothing parameters based on the minimization of cross validation criteria

fuzzy stage characteristic preserving product life cycle modeling abstract stage concerns have been important in product life cycles plc such concerns are stage identification stage related strategies and here newly introduced stage modeling stage modeling is concerned with not only modeling but also aggregation of individual stages in an overall influencing manner it not only preserves the respective characteristics of the stages but also may be explored for the stage related strategy issue later to date this aspect of plc modeling has not yet been explored in this paper a fuzzy plc modeling capable of preserving the fuzzy individual characteristics of the stages is proposed the various concepts such as boundary identification fuzzy stages modeling and stages inter influence functions are introduced and discussed finally to illustrate and support the approach a numerical example and a comparison with classical data analytic procedures segmented polynomial regression and autoregressive integrated moving average is provided

new perspectives and improvements on the symmetric extension filter bank for subband wavelet image compression in subband wavelet image coding size limited subband decompositions are ordinarily used to avoid increasing the number of samples that need to be coded to reduce coding distortions that can occur at the borders the symmetric extension filter bank is typically employed this paper introduces some new perspectives and improvements to that decomposition the symmetric extension filter bank is couched in the cyclic frequency domain providing a framework that accommodates fir and iir filters in a natural way all with perfect reconstruction iir filters with both rational and irrational transfer functions can be implemented and in the context of symmetric extension can accommodate iirs that effectively have perfect stopband suppression enhancements to the filter bank at a tree structured system level are also presented and include the application of spectral reversal correction and a transition band normalization approach to designing the constituent filters of the symmetric extension wavelet packet transform

continuous location of dimensional structures abstract a natural extension of point facility location problems are those problems in which facilities are extensive i e those that cannot be represented by isolated points but as some dimensional structures such as straight lines line segments polygonal curves or circles in this paper a review of the existing work on the location of extensive facilities in continuous spaces is given gaps in the knowledge are identified and suggestions for further research are made

fuzzy nonparametric regression based on local linear smoothing technique in a great deal of literature on fuzzy regression analysis most of research has focused on some predefined parametric forms of fuzzy regression relationships especially on the fuzzy linear regression models in many practical situations it may be unrealistic to predetermine a fuzzy parametric regression relationship in this paper a fuzzy nonparametric model with crisp input and lr fuzzy output is considered and based on the distance measure for fuzzy numbers suggested by diamond p diamond fuzzy least squares information sciences 46 1988 141 157 the local linear smoothing technique in statistics with the cross validation procedure for selecting the optimal value of the smoothing parameter is fuzzified to fit this model some simulation experiments are conducted to examine the performance of the proposed method and three real world datasets are analyzed to illustrate the application of the proposed method the results demonstrate that the proposed method works quite well not only in producing satisfactory estimate of the fuzzy regression function but also in reducing the boundary effect significantly

fuzzy linear regression and its applications to forecasting in uncertain environment abstract linear regression has been used for many years in developing mathematical models for application in marketing management and sales forecasting in this paper two different sales forecasting techniques are discussed the first technique involves non fuzzy abstract methods of linear regression and econometrics a study of the international market sales of cameras done in 1968 by john scott armstrong utilized these non fuzzy forecasting techniques the second sales forecasting technique uses fuzzy linear regression introduced by h tanaka s uejima and k asai in 1980 in this paper a study of the computer and peripheral equipment sales in the united states is discussed using fuzzy linear regression moreover fuzzy linear regression is applied to forecasting in an uncertain environment finally some possible improvements and suggestions for further study are mentioned

a fuzzy varying coefficient model and its estimation the fuzzy linear regression model has been a useful tool for analyzing relationships between a set of variables in a fuzzy environment and has been extensively studied in the literature however this model may fail to reflect the more complicated regression relationships that are usually found in practice because of its simple and predefined linear structure in order to enhance the feasibility and adaptability of the fuzzy linear models we propose in this paper a fuzzy varying coefficient model in which the fuzzy coefficients in the fuzzy linear models are allowed to vary with a covariate a restricted weighted least squares estimation is suggested for locally fitting the model furthermore some real world datasets are analyzed in order to evaluate the performance of the proposed method and the results show that the proposed model with its estimation approach performs satisfactorily in predicting the fuzzy response even in the case where the regression relationship is complicated

parallel projection methods and the resolution of ill posed problems abstract in this paper we consider a modification of the parallel projection method for solving overdetermined nonlinear systems of equations introduced recently by diniz ehrhardt and martinez 1 this method is based on the classical cimmino s algorithm for solving linear systems the components of the function are divided into small blocks as an attempt to correct the intrinsic ill conditioning of the system and the new iteration is a convex combination of the projections onto the linear manifolds defined by different blocks the modification suggested here was motivated by the application of the method to the resolution of a nonlinear fredholm first kind integral equation we prove convergence results and we report numerical experiments

a simultaneous projections method for linear inequalities abstract an iterative method for solving general systems of linear inequalities is considered the method a relaxed generalization of cimmino s scheme for solving linear systems was first suggested by censor and elfving each iterate is obtained as a convex combination of the orthogonal projections of the previous iterate on the half spaces defined by the linear inequalities the algorithm is particularly suitable for implementation on computers with parallel processors we prove convergence from any starting point for both consistent and nonconsistent systems to a feasible point in the first case and to a weighted least squares type solutions in the second

developing a fuzzy bicluster regression to estimate heat tolerance in plants by chlorophyll fluorescence this paper presents a straightforward and useful fuzzy regression approach to estimate heat tolerance of plants by chlorophyll fluorescence measurement the chlorophyll fluorescence measurement is an indicator of functional change of photosynthesis and is sensitive to temperature using the fluorescence temperature curves the experimenter may determine the heat tolerance tc of plants by intersections of two linear regression lines however as traditional statistical regression analysis shows the experiment may contain uncertain factors or phenomena such as leaf nature and growth environment which concludes that data may vary among individual plants and different species this research presents a fuzzy bicluster regression fbcr analysis with genetic algorithms which helps derive a fuzzy intersection set and fuzzy heat tolerance of plants in addition to the traditional statistical regression analysis a fuzzy clustering concept and simultaneously optimal determination of data clusters is also developed especially when there are nonlinear inflections in data curves due to the imperative use of linear regression models the traditional regression analysis may become unable to sufficiently model the uncertainties exhibited the fbcr analysis can resolve this problem effectively due to the nonlinear tolerance of the system even in a linear model to demonstrate the fbcr analysis it was applied to estimate the heat tolerance of five plant species the results derived appeared to be more suitable than that of the conventional method the approach may provide a useful means for the experimenters to derive more credible results from their chlorophyll fluorescence temperature data

ranking of fuzzy sets based on the concept of existence abstract various approaches have been proposed for the comparison or ranking of fuzzy sets however due to the complexity of the problem a general method which can be used for any situation still does not exist this paper formalizes the concept of existence for the ranking of fuzzy sets many of the existing fuzzy ranking methods are shown to be some application of this concept an improved fuzzy ranking method is then introduced based on this concept this newly introduced method is expanded for treating both normal and nonnormal convex and nonconvex fuzzy sets emphasis is placed on the use of the subjectivity of the decision maker such as the optimistic or the pessimistic view points an improved procedure for obtaining linguistic conclusions is also developed finally some numerical examples are given to illustrate the approach

fuzzy regression analysis using neural networks abstract in this paper we propose simple but powerful methods for fuzzy regression analysis using neural networks since neural networks have high capability as an approximator of nonlinear mappings the proposed methods can be applied to more complex systems than the existing lp based methods first we propose learning algorithms of neural networks for determining a nonlinear interval model from the given input output patterns a nonlinear interval model whose outputs approximately include all the given patterns can be determined by two neural networks next we show two methods for deriving nonlinear fuzzy models from the interval model determined by the proposed algorithms nonlinear fuzzy models whose h level sets approximately include all the given patterns can be derived last we show an application of the proposed methods to a real problem

a robust varying coefficient approach to fuzzy multiple regression model abstract the varying coefficient models are powerful tools for exploring the dynamic pattern between a response and a group of predictors in multiple regression models in addition robust regression is another solid approach in the regression analyses for cases whose data are contaminated with outliers or influential observations this paper proposed a novel varying coefficient model with exact predictors and fuzzy responses which can be used in cases where outliers occur in the data set for this purpose a locally weighted approximation idea and a popular m estimator were combined to estimate unknown fuzzy nonparametric varying coefficients some common goodness of fit criteria including an outlier detection criterion were also applied to examine the performance of the proposed method the effectiveness of the presented method was then illustrated through two numerical examples including a simulation study it was also compared with several common fuzzy multiple regression models the numerical results clearly indicate that the proposed method is not sensitive to the outliers moreover compared to the available fuzzy multiple regressions with constant coefficients the proposed fuzzy varying coefficient model managed to provide more accurate results

ranking function based solutions of fully fuzzified minimal cost flow problem the aim of minimal cost flow problem mcfp is to find the least transportation cost of a single commodity through a capacitated network this paper presents a model to deal with one particular group of such problems in which the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers for easier reference hereafter we refer to this group of problems as fully fuzzified mcfp to represent our model hukuhara s difference and approximated multiplication are used thereafter we sort fuzzy numbers by an order using a ranking function and show that it is a total order i e a reflexive anti symmetric transitive and complete binary relation utilizing the proposed ranking function we transform the fully fuzzified mcfp into three crisp problems solvable in polynomial time from this standpoint combinatorial algorithms are provided to solve the above mentioned problem and find the fuzzy optimal flow furthermore the proposed order is related to the importance weights of the center the left spread and the right spread of each fuzzy number thus this method is capable of handling the decision maker s risk taking by comparing some previous ranking function based works with our method the efficiency of the latter is revealed finally an application of our proposed method to petroleum industry is presented

fuzzy linear regression with spreads unrestricted in sign abstract by the use of actual examples it is shown that when the two trends namely the fuzzy spread trend and the center line or modal trend are in conflict or inconsistent the results of the fuzzy linear regression flr model based on the approach of tanaka and coworkers frequently misinterprets the data to avoid this misinterpretation a modification of the flr procedure by allowing the spreads of the parameter to be unrestricted in sign is proposed it is shown that by the use of this unrestricted fuzzy linear regression uflr model correct prediction of the trends are obtained

a partial robust ridge based regression model with fuzzy predictors responses abstract this paper extends the conventional semi parametric partial linear regression model with fuzzy predictors and fuzzy response in cases where 1 outliers occur in data set 2 multicollinearity exists in predictors for this purpose the classical kernel fitting method is first extended for estimating unknown fuzzy smooth function then inspired by the conventional local linear smoothing method a kernel based weighted criterion is suggested for determining the exact coefficients on the basis of ridge methodology some common goodness of fit criteria are also used to examine the performance of the proposed method the effectiveness of the proposed method is then illustrated through two numerical examples including a simulation study the proposed method is also compared with some common fuzzy multiple regression models with fuzzy predictors and fuzzy responses the numerical results clearly indicate that 1 the proposed method is not sensitive to the outliers 2 the proposed method provides sufficiently accurate results in cases where multicollinearity happens among predictors and 3 comparing to existing fuzzy multiple regressions the proposed model provides more efficient predictions

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

extended fuzzy linear models and least squares estimates least squares regression of the fuzzy linear model is extended to overcome and interpret the occurrence of negative spreads 1 the idea is to introduce best fit difference models which exploit both the hukuhara difference and the l2 metric distance the fuzzy models use lr fuzzy numbers fitted models are compared by using the coefficient of determination in a similar way to its use in classical statistical least squares fitting the non lr fuzzy case is also considered

least squares model fitting to fuzzy vector data abstract we consider model fitting problems in which the mathematical model of an observed event is a system of equations involving model parameters and observables and in which the data are fuzzy vectors such problems naturally arise in applications when data are scarce and information is vague about distributions of variances that are contained in the observations then it may only be possible to obtain estimates of membership functions of the data a model can be fitted to such data by maximizing the membership values of the adjusted observations we achieve this by minimizing the sum of squares of the deviations of the membership values from one the optimization problem simplifies significantly if the membership functions of the fuzzy vectors belong to a class of conical functions which are defined in terms of an elliptic norm properties of these functions are discussed and a membership propagation formula derived which component wise obeys the extension principle the least squares model fitting to the described fuzzy vector data deviates in important aspects from ordinary least squares one obtains as a solution a fuzzy model parameter vector and a number of indicators which describe the quality of the fit viz the grade of compatibility between data and model their discord and dilators of model and data membership functions these new concepts are illustrated and discussed in the context of an example from a terminal ballistics problem

fuzzy least absolute deviations regression and the conflicting trends in fuzzy parameters a general fuzzy linear model for fuzzy regression analysis was first formulated based on both this general model and a fuzzy difference ranking method 1 2 approaches for fuzzy least squares regression and fuzzy least absolute value deviations regression were proposed the former approach resulted in a nonlinear programming problem while the latter resulted linear numerical examples were solved by using the absolute deviations approach to illustrate the problems of conflicting trends and ways to at least partially overcome these problems furthermore these examples showed that the absolute deviations formulation forms an effective computational tool

development of a cost function for wastewater treatment systems with fuzzy regression abstract a fuzzy linear regression analysis is performed to study the cost function of wastewater that is developed by using a pool of data from 26 municipal wastewater treatment systems in taiwan the choice of a primary or more higher wastewater treatment process is intimately related to financial land availability effluent standards and managerial factors especially financial consideration plays an important role in the planning stage in addition cost estimation is difficult to precisely evaluate in an uncertain environment in the conventional regression model deviations between the observed values and the estimated values are supposed to be due to measurement errors here taking a different perspective these deviations are regarded as the fuzziness of the system s parameters thus these deviations are reflected in a linear function with fuzzy parameters using linear programming algorithm this fuzzy linear regression model might be very convenient and useful for finding a fuzzy structure in an evaluation system in this paper the details of the fuzzy linear regression concept and its applications to the cost function in an uncertain environment are shown and discussed

spectrum decomposition for image signal coding in conventional subband wavelet image coding the subband decomposition is performed on the spatial domain image here we introduce a novel decomposition where the subband decomposition is performed on the global dct spectrum of the image that is the two dimensional spectrum rather than the image is represented by a sum of basis functions each weighted by the transform coefficients the distinct features of this decomposition are analyzed from a transform perspective this spectral subband decomposition is then used as the basis for a new image coder building on the condensed wavelet packet cwp algorithm ironically this new method is shown to have lower arithmetic complexity than conventional subband wavelet coders that directly decompose a time or spatial domain signal comparisons of the new method against conventional subband wavelet coders that use the popular 9 7 dyadic decomposition condensed wavelet packets and generalized lapped orthogonal transforms show that the new method has lower complexity and higher compression performance

the genlot generalized linear phase lapped orthogonal transform the general factorization of a linear phase paraunitary filter bank lppufb is revisited from this new perspective a class of lapped orthogonal transforms with extended overlap generalized linear phase lapped orthogonal transforms genlots is developed as a subclass of the general class of lppufb in this formulation the discrete cosine transform dct is the order 1 genlot the lapped orthogonal transform is the order 2 genlot and so on for any filter length that is an integer multiple of the block size the genlots are based on the dct and have fast implementation algorithms the implementation of genlots is explained including the method to process finite length signals the degrees of freedom in the design of genlots are described and design examples are presented along with image compression tests

finknn a fuzzy interval number k nearest neighbor classifier for prediction of sugar production from populations of samples this work introduces finknn a k nearest neighbor classifier operating over the metric lattice of conventional interval supported convex fuzzy sets we show that for problems involving populations of measurements data can be represented by fuzzy interval numbers fins and we present an algorithm for constructing fins from such populations we then present a lattice theoretic metric distance between fins with arbitrary shaped membership functions which forms the basis for finknn s similarity measurements we apply finknn to the task of predicting annual sugar production based on populations of measurements supplied by hellenic sugar industry we show that finknn improves prediction accuracy on this task and discuss the broader scope and potential utility of these techniques

extended lapped transform in image coding a modulated lapped transform with extended overlap elt is investigated in image coding with the objective of verifying its potential to replace the discrete cosine transform dct in specific applications some of the criteria utilized for the performance comparison are reconstructed image quality both objective and subjective reduction of blocking artifacts robustness against transmission errors and filtering for scalability also a fast implementation algorithm for finite length signals using symmetric extensions is developed specially for the elt with overlap factor 2 elt 2 this comparison shows that elt 2 is superior to both dct and the lapped orthogonal transform lot

on the choice of the regularization parameter in nonlinear inverse problems this paper focuses on regularization techniques for nonlinear ill posed inverse problems tikhonov regularization and regularization due to the use of norm constraints are analyzed a model function technique is proposed to iteratively determine an optimal regularization parameter or the parameter characterizing the norm constraint and to estimate the error in the data if it is not known a priori

fuzzy seasonality forecasting abstract in this paper a fuzzy forecasting technique for seasonality in the time series data is presented using the following procedure first with the fuzzy regression analysis the fuzzy trend of a time series is analyzed then the fuzzy seasonality is defined by realizing the membership grades of the seasons to the fuzzy regression model both making fuzzy forecast and crisp forecast are investigated seasonal fuzziness and trends are analyzed the method is applied to the sales forecasting problem of a food distribution company

fuzzy spline univariate regression with exact predictors and fuzzy responses abstract spline smoothing is a form of nonlinear regression when there is reason to believe that relationship between the predictor and the response is curvilinear in such cases the spline smoothing is an effective method to improve the performances of the conventional polynomial based regression models this paper proposed a fuzzy spline method based on a weighted absolute error distance measure with exact predictors and fuzzy responses unknown fuzzy coefficients tuning parameter were selected according to a hybrid optimization algorithm the effectiveness of the proposed method was also examined and compared with some well established fuzzy nonlinear regression models through some numerical examples including a simulation study for this purpose several common goodness of fit criteria were employed the numerical results clearly indicated that our prediction estimation gives more accurate results compared to other methods

possibilistic linear regression analysis for fuzzy data abstract fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined recently it has become important to deal with fuzzy data in connection with expert knowledge three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data since our formulations can be reduced to linear programming problems the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters this approach can be regarded as a fuzzy interval analysis in a fuzzy environment

using block norms for location modeling in formulating a continuous location model with facilities represented as points in rn e g typically in the plane one must characterize the distance between two points as a function of their coordinates two criteria in selecting a distance function are 1 to obtain good approximations of actual distances and 2 to obtain a mathematical model of the location problem that is easy to solve in this paper we show how a class of norms with polygonal contours called block norms can yield attractive choices as distance functions with respect to these criteria in particular we consider the following relevant properties of block norms they generalize the concepts of rectilinear or city block travel they are dense in the set of all norms they have interesting travel interpretations in the plane they can be expressed as a sum of the absolute values of linear functions they often give better approximations to actual highway distances than the most frequently used family of norms the lp norms and finally they yield linear programming formulations of certain facility location problems i e the weber problem and the rawls problem

estimating the circle closest to a set of points by maximum likelihood using the bhhh algorithm abstract the purpose of this paper is to exploit the idea that in linear models the least squares estimators and the maximum likelihood estimators based on the normality assumption are often identical in particular we wish to add the normality assumption to the problem of finding the best fitting circle the addition of the normality assumption will allow the use of the bhhh algorithm to estimate the model by maximum likelihood although the bhhh algorithm is not especially fast its virtue is that it only requires the first derivatives of the loglikelihood function and is therefore easier to program than the newton raphson algorithm as we will show the likelihood framework also allows for easy testing of several important hypotheses and construction of an r 2 measure from regression analysis

a parallel subgradient projections method for the convex feasibility problem abstract an iterative method to solve the convex feasibility problem for a finite family of convex sets is presented the algorithm consists in the application of a generalization of an acceleration procedure introduced by de pierro in a parallel version of the subgradient projections method proposed by censor and lent the generated sequence is shown to converge for any starting point some numerical results are presented

gbsss the generalized big square small square method for planar single facility location abstract big square small square is a geometrical branch and bound algorithm devised by p hansen et al or 33 1251 1265 for the solution of constrained planar minisum single facility location problems with l p norms and continuous non decreasing costfunctions the method basically works by splitting the studied planar region into squares and either rejecting or further processing these squares by the evaluation of a lower bound we present a modified version of this algorithm aimed at correcting a small failure to converge accelerating the calculations minimising the information to be stored and most importantly determining a region of near optimality furthermore the method is applicable to any planar single facility problem with distances measured by mixed norms and as an objective any continuous function of the distances this includes nearly all the models which have been proposed in the literature

extended support vector interval regression networks for interval input output data in many applications it is natural to use interval data because of uncertainty existence in the measurements variability in defining terms such as the temperature during a given day description for extremely behavior such as the maximum wind speed in a given area etc in order to handle such interval data a novel approach called the interval support vector interval regression networks isvirns is proposed the isvirns is extended from our previous work the support vector interval regression networks svirns it is easy to find that svirns can handle interval output data but for input data they must be crisp in this study the hausdorff distance is employed as the distance measure of interval data and is incorporated into the kernel functions of svirns to determine the initial structure of isvirns because the proposed approach can provide a better initial structure for isvirns it can have a faster convergent speed the experimental results with real data sets show the validity of the proposed isvirns

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

lapped transform via time domain pre and post filtering this paper presents a general framework of constructing a large family of lapped transforms with symmetric basis functions by adding simple time domain pre and post processing modules onto existing block discrete cosine transform dct based infrastructures a subset of the resulting solutions is closed form fast computable modular near optimal in the energy compaction sense and leads to an elegant boundary handling of finite length data starting from these solutions a general framework for block based signal decomposition with a high degree of flexibility and adaptivity is developed several simplified models are also introduced to approximate the optimal solutions these models are based on cascades of plane rotation operators and lifting steps respectively despite tremendous savings in computational complexity the optimized results of these simplified models are virtually identical to that of the complete solution the multiplierless versions of these pre and post filters when combined with an appropriate multiplierless block transform such as the bindct which is described in an earlier paper by liang and tran see ieee trans signal processing vol 49 p 3032 44 dec 2001 generate a family of very large scale integration vlsi friendly fast lapped transforms with reversible integer to integer mapping numerous design examples with arbitrary number of channels and arbitrary number of borrowed samples are presented

an architecture of neural networks with interval weights and its application to fuzzy regression analysis abstract in this paper we first propose an architecture of neural networks that have interval weights and interval biases a neural network with the proposed architecture maps an input vector of real numbers to an output interval the target output is also given as an interval next we define a cost function using the interval output from the neural network and the corresponding target output a learning algorithm is derived from the cost function in a similar manner as the bp back propagation algorithm we also show two variations of the learning algorithm for the proposed architecture which lead to the inclusion relation between the interval output and the interval target last we apply the learning algorithms to fuzzy regression analysis where target outputs are given as fuzzy numbers

fuzzy linear regression using rank transform method in regression analysis the rank transform rt method is known to be neither dependent on the shape of the error distribution nor sensitive to outliers in this paper we construct a so called level fuzzy regression model based on the resolution identity theorem and apply rt method to this model fuzzy regression models with crisp input fuzzy output and fuzzy input fuzzy output are investigated to show the effectiveness of the proposed method to compare its effectiveness with existing methods we introduce a new performance measure in addition we propose a method to obtain a predicted output with respect to a specific target value and show that our model is more robust compared with other methods when the data contain some outliers

the minimax center estimation problem for automated roundness inspection abstract significant advances in computer technology sensing devices pattern recognition and image processing techniques have made the on line inspection of all production parts a feasible option in modern manufacturing systems this study is concerned with the development of efficient algorithms to determine the out of roundness error for automated inspection of circular production parts the out of roundness error is defined as the maximum deviation of a given sey of sample points taken from the boundary of the part from the so called minimax circle

asymptotic properties of least squares estimation with fuzzy observations this paper deals with the asymptotic properties of the least squares estimators for fuzzy linear regression models with fuzzy triangular input output and random error terms the asymptotic normality and strong consistency of the fuzzy least squares estimator flse are investigated a confidence region based on a class of flses is proposed the asymptotic relative efficiency of flses with respect to the crisp least squares estimators is also provided and a numerical example is given some simulation results are also presented to illustrate the behavior of flses

a constrained least squares regularization method for nonlinear ill posed problems this paper deals with a method for solving ill posed nonlinear hilbert space operator equations f x y regularization is obtained by solving a constrained least squares regularization problem min f x y 2 quad text subject to j x leqq beta 2 beta serves as a regularization parameter and j x is a quadratic penalty functional to robustly and efficiently solve this regularization problem we apply a trust region method at each iteration the quadratic penalty constraint is retained a gauss newton approximation to the objective functional is taken and we add a quadratic trust region constraint the resulting quadratic subproblem is then reformulated as a nonlinear complementarily problem and solved using newton s method this paper applies methods to find approximate solutions to a severely ill posed nonlinear first kind integral equation arising in geophysics the method of generalized cross validation gcv is used to pick the regularization parameter when random er

identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters abstract we have already discussed several models of the possibilities linear regression analysis under the assumption that probabilitioes parameters in the models are non interactive i e the possibilistic distribution of parameters is defined by minimum operators in this paper quadratic membership functions as defined by a celmi s are considered to propose an identification method of interactive fuzzy parameters in possibilistic linear systems our method can be reduced to linear programming so that it is very easy to obtain the posssibilistic distribution of parameters

fuzzy regression methods a comparative assessment abstract the fundamental differences between fuzzy regression and ordinary regression are identified in this paper fuzzy regression can be used to fit fuzzy data and crisp data into a regression model whereas ordinary regression can only fit crisp data through a comprehensive literature review three approaches of fuzzy regression are summarized the first approach of fuzzy regression is based on minimizing fuzziness as an optimal criterion the second approach uses least squares of errors as a fitting criterion and two methods are summarized in this paper the third approach can be described as an interval regression analysis for each fuzzy regression method numerical examples and graphical presentations are used to evaluate their characteristic and differences with ordinary least squares regression based on the comparative assessment the fundamental differences between ordinary least squares regression and conventional fuzzy regression are concluded that is ordinary least squares regression modeling data with randomness type of uncertainty and conventional fuzzy regression modeling data with fuzziness type of uncertainty in order to integrate both randomness and fuzziness types of uncertainty into one regression model the concept of hybrid fuzzy least squares regression analysis is proposed in this paper and the details of its method are derived in the accompanying paper

evaluation of fuzzy linear regression models abstract fuzzy linear regression provides means for tackling regression problems lacking a significant amount of data for determining regression models and with vague relationships between the dependent variable and independent variables in the paper a two stage construction of a linear regression model is proposed using an enhancement of a minimal vagueness criterion already discussed in fuzzy regression analysis two different experiments are set up and used for evaluating both models the choice of the fuzzy regression model should be made in the context of a practical application

a progressive transmission image coder using linear phase uniform filterbanks as block transforms this paper presents a novel image coding scheme using m channel linear phase perfect reconstruction filterbanks lpprfbs in the embedded zerotree wavelet ezw framework introduced by shapiro 1993 the innovation here is to replace the ezws dyadic wavelet transform by m channel uniform band maximally decimated lpprfbs which offer finer frequency spectrum partitioning and higher energy compaction the transform stage can now be implemented as a block transform which supports parallel processing and facilitates region of interest coding decoding for hardware implementation the transform boasts efficient lattice structures which employ a minimal number of delay elements and are robust under the quantization of lattice coefficients the resulting compression algorithm also retains all the attractive properties of the ezw coder and its variations such as progressive image transmission embedded quantization exact bit rate control and idempotency despite its simplicity our new coder outperforms some of the best image coders published previously in the literature for almost all test images especially natural hard to code ones at almost all bit rates

resolution of fuzzy regression model abstract fuzzy linear regression was originally introduced by tanaka et al to cope with different types of input output information several approaches to fuzzy linear regression have been proposed in this paper a type of problem with crisp input and fuzzy output described by tanaka is considered of which a modified fuzzy least square method was proposed for solution it shows that with such an approach the predictability in the new model is better than tanaka s and its computation efficiency is better than the conventional fuzzy least square method

the solution and duality of imprecise network problems duality properties have been investigated by many researchers in the recent literature they are introduced in this paper for a fully fuzzified version of the minimal cost flow problem which is a basic model in network flow theory this model illustrates the least cost of the shipment of a commodity through a capacitated network in terms of the imprecisely known available supplies at certain nodes which should be transmitted to fulfil uncertain demands at other nodes first we review on the most valuable results on fuzzy duality concepts to facilitate the discussion of this paper by applying hukuhara s difference approximated and exact multiplication and wu s scalar production we exhibit the flow in network models then we use combinatorial algorithms on a reduced problem which is derived from fully fuzzified mcfp to acquire fuzzy optimal flows to give duality theorems we utilize a total order on fuzzy numbers due to the level of risk and realize optimality conditions for providing some efficient combinatorial algorithms finally we compare our results with the previous worthwhile works to demonstrate the efficiency and power of our scheme and the reasonability of our solutions in actual decision making problems

nonparametric kernel estimation based on fuzzy random variables this paper extends the classical nonparametric curve fitting methods for fuzzy random variables the study was conducted in two parts 1 fuzzy density estimation and 2 nonparametric regression the classical nonparametric density estimation was first developed based on the kernel method for a given fuzzy random sample at crisp and or fuzzy point based on crisp or fuzzy bandwidth the classical bandwidth selection was also extended when the underlying population was normal with known or unknown fuzzy variance moreover the classical nonparametric kernel based regression model with crisp and or input or output is extended whenever a given bandwidth is a crisp or fuzzy number the cross validation procedure for selecting the optimal value of the crisp smoothing parameter is also extended to fit the proposed nonparametric regression model the large sample properties of the proposed fuzzy estimators were also investigated by some theorems several numerical examples including that of real life data are used to illustrate the proposed methods in curve fitting estimation with crisp and or fuzzy information moreover the proposed methods were examined in comparison with some other existing methods and their effectiveness were clarified via some numerical examples and simulation studies both theatrical and numerical results indicated that the nonparametric curve fitting methods significantly reduced the sum of square errors as well as the spreads of the fuzzy curve fitting estimation

algorithms for computerized inspection of rectangular and square shapes abstract vision systems are increasingly being considered and implemented as an alternative to manual inspection and manual gauging in manufacturing systems inspection for geometric shape and size is essential in automated quality monitoring the techniques used to perform this inspection need to be practical to satisfy time and equipment constraints and make the system cost effective this paper presents practical and useful techniques based on the euclidean least squares method to inspect production parts with rectangular and square shapes the techniques determine the optimal parameters of the straight lines that define the four edges of the object being inspected

locating objects in the plane using global optimization techniques we address the problem of locating objects in the plane such as segments arcs of circumferences arbitrary convex sets their complements or their boundaries given a set of points we seek the rotation and translation for such an object optimizing a very general performance measure which includes as a particular case the classical objectives in semi obnoxious facility location in general the above mentioned model yields a global optimization problem whose resolution is dealt with using difference of convex dc techniques such as outer approximation or branch and bound

row action methods for huge and sparse systems and their applications this paper brings together and discusses theory and applications of methods identified and labelled as row action methods for linear feasibility problems find x in bf r n such that ax leqq b linearly constrained optimization problems minimize f x subject to ax leqq b and some interval convex programming problems minimize f x subject to c leqq ax leqq b the main feature of row action methods is that they are iterative procedures which without making any changes to the original matrix a use the rows of a one row at a time such methods are important and have demonstrated effectiveness for problems with large or huge matrices which do not enjoy any detectable or usable structural pattern apart from a high degree of sparaseness fields of application where row action methods are used in various ways include image reconstruction from projection operations research and game theory learning theory pattern recognition and transportation theory a row action method for the

fuzzy regression wiht radial basis function network radial basis function network is used in fuzzy regression analysis without predefined functional relationship between the input and the output the proposed approach is a fuzzification of the connection weights between the hidden and the output layers this fuzzy network is trained by a hybrid learning algorithm where self organized learning is used for training the parameters of the hidden units and supervised learning is used for updating the weights between the hidden and the output layers the c mean clustering method and the k nearest neighbor heuristics are used for the self organized learning the supervised learning is carried out by solving a linear possibilistic programming problem techniques for the generalization of the network are also proposed numerical examples are used to illustrate and to test the performances of the approach

fixed point quasi newton methods this article studies iterative methods defined by x k 1 phi x k e k where x k in mathbb r n and e k lie on a space of parameters sufficient conditions are established for local convergence and for convergence at an ideal linear or superlinear rate a theory of least change secant update methods for this class of processes is developed several examples are given showing a wide range of applications of the new theory key words quasi

efficient algorithms for the weighted minimum circle problem the weighted minimum covering circle problem is a well known single facility location problem used in emergency facility models this paper introduces a classification scheme based on fundamental mathematical programming concepts for algorithms which solve both weighted and unweighted versions one result of this classification is proof that a recently developed method is identical to one developed in the nineteenth century also within the classification scheme efficient new algorithms are given for the weighted problem the results of some extensive computational tests identify the empirically fastest methods