fuzzy versus statistical linear regression abstract statistical linear regression and fuzzy linear regression have been developed from different perspectives and thus there exist several conceptual and methodological differences between the two approaches the characteristics of both methods in terms of basic assumptions parameter estimation and application are described and contrasted their descriptive and predictive capabilities are also compared via a simulation experiment to identify the conditions under which one outperforms the other it turns out that statistical linear regression is superior to fuzzy linear regression in terms of predictive capability whereas their comparative descriptive performance depends on various factors associated with the data set size quality and proper specificity of the model aptness of the model heteroscedasticity autocorrelation nonrandomness of error terms specifically fuzzy linear regression performance becomes relatively better vis a vis statistical linear regression as the size of the data set diminishes and the aptness of the regression model deteriorates fuzzy linear regression may thus be used as a viable alternative to statistical linear regression in estimating regression parameters when the data set is insufficient to support statistical regression analysis and or the aptness of the regression model is poor e g due to vague relationship among variables and poor model specification

two dimensional local moment surface fitting and their fast computation abstract it is proved that local moments are related to their surface fitting coefficients by a linear transform and by this the surface fitting based feature extraction is converted into the computation of 2d local moments a npt recursive method is proposed to compute 2d local moments quickly and then to efficiently implement surface fitting the new method has a novel advantage that its computational complexity for both 2d local moment computation and surface fitting is independent of the mask size which much efficiently speed up the feature extraction

subpixel edge detection of color images by principal axis analysis and moment preserving principle this paper discusses a new approach for detecting edges with sub pixel accuracy in color images using the principal axis analysis and the moment preserving principle first the principal axis of the color vectors in a three dimensional space is obtained analytically for each image block based on the projection scores the direction of the line edge is obtained by analyzing the three dimensional principal axis of a color image block next by preserving some spatial color moments of the pixels of each square block analytic formulas are derived to extract the edge feature experiments on both synthetic and real images show that the accuracy of the proposed method is comparable to other color edge detectors the proposed algorithm can be performed very fast for real time applications with no need for special hardware

an observation of quadratic algebra dual family of nonlinear coherent states and their non classical properties in the generalized isotonic oscillator in this paper we construct nonlinear coherent states for the generalized isotonic oscillator and study their non classical properties in detail by transforming the deformed ladder operators suitably which generate the quadratic algebra we obtain heisenberg algebra from the algebra we define two non unitary and one unitary displacement type operators while the action of one of the non unitary type operators reproduces the original nonlinear coherent states the other one fails to produce a new set of nonlinear coherent states dual pair we show that these dual states are not normalizable for the nonlinear coherent states we evaluate the parameter a3 and examine the non classical nature of the states through quadratic and amplitude squared squeezing effect further we derive analytical formula for the p function q function and the wigner function for the nonlinear coherent states all of them confirm the non classicality of the nonlinear coherent states in addition to the above we obtain the

competence set expansion using an efficient 0 1 programming model abstract competence set expansion is an application of habitual domain through which a decision maker acquires the skills required to make satisfactory decisions the methods of li operations research 47 1999 209 220 and li et al european journal of operational research 120 2000 511 524 use numerous 0 1 and integer variables this study presents a more compact model for the competence set expansion problem which is as effective as the two methods yet more efficient

susan a new approach to low level image processing this paper describes a new approach to low level image processing in particular edge and corner detection and structure preserving noise reduction non linear filtering is used to define which parts of the image are closely related to each individual pixel each pixel has associated with it a local image region which is of similar brightness to that pixel the new feature detectors are based on the minimization of this local image region and the noise reduction method uses this region as the smoothing neighbourhood the resulting methods are accurate noise resistant and fast details of the new feature detectors and of the new noise reduction method are described along with test results

normally ordering some multimode exponential operators by virtue of the iwop technique the author shows that the technique of integration within an ordered product iwop provides one with a very simple approach to deriving the normal product form of some multimode exponential operators which greatly simplifies the calculations of normalising some state vectors in hilbert space

an improved corner detection algorithm based on chain coded plane curves abstract one possible measure of corners on chain coded plane curves is the product of the length of the uniform chain sections to either side the forward and backward arms of a point times the angle of discontinuity of that particular point this paper describes a corner detection algorithm which performs close to humans expectations the improved algorithm is based on previous work done by freeman and davis the algorithm uses an approach of averaging multiple s values to avoid the selection of spurious corners the algorithm also uses a maximum cut off value a certain fraction of the entire chain to determine the length of the forward and backward arms of each point and hence eliminates the detection of spurious corners the improved algorithm was tested with results close to humans expectations the results of the improved algorithm are shown by way of examples

image compression by moment preserving edge detection abstract a new image compression algorithm based on a new edge detection technique is proposed a given image is compressed by dividing the image into non overlapping square blocks and coding the edge information in each non uniform block the edge feature in a given window is detected by applying the moment preserving principle to the image data the edge directions are approximated by multiples of 45 to speed up the direction process without introducing obvious distortion for a larger block size a more accurate model of a two step edge is employed in the detection process the proposed algorithm offers excellent reconstructed image quality agreeing with human perception high compression ratios and greatly reduced coding complexity the solution to the edge detection problem in a given block is also analytic the algorithm can be performed very fast for real time applications with no need for special hardware

using competence sets to analyze the consumer decision problem abstract this study is intended to provide a different approach to complement the existing consumer decision models cdms based on the concept of habitual domains and competence sets we supply a framework for helping a firm in expanding the benefits of its products to fully address the consumer s needs according to the features of consumers decision making we use challenging problem types to explore extensive problem solving fuzzy problem types for limited problem solving and routine and mixed routine problem types for routine problem solving in addition several useful indexes are established using fuzzy measures in this study including the possibility of successfully appealing to consumers the degree of consumer satisfaction the degree of compatibility and the degree of uniqueness these indexes can be a decision support for implementing competence set analysis in practical applications finally an empirical study on children s apparel was conducted to show the applicability and feasibility of our proposed method in practice

statistical properties of a generalized photon modulated thermal state in this paper we introduce a new kind of quantum state generalized photon modulated thermal states gpmts which are obtained by repeatedly acting the superposed operation a coherent superposition of photon subtraction and addition on the thermal state it is found that the normalization factor of gpmts is a legendre polynomial moreover we present the analytical expressions of several quasi probability distributions for gpmts and calculate the corresponding tomogram and photocount distribution as well

grey relational analysis and radial basis function network for determining costs in learning sequences there is a competence set consisting of ideas knowledge information and skills for solving a decision problem in order to effectively acquire the needed skills in the competence set to solve the problem finding appropriate learning sequences of the needed skills for decision makers should be taken into account however how to determine the learning cost of learning one skill to another skill plays a critical role for generating learning sequences for this the paper aims to propose an effective method to estimate the learning cost between any two skills by using the grey relational analysis and a radial basis function network a computer simulation with an integer programming method is employed to demonstrate that it is possible to facilitate the acquisition of single skills by considering a set of useful compound skills this indicates the effectiveness of the proposed method

an enhanced logarithmic method for signomial programming with discrete variables abstract signomial programming problems with discrete variables spd appear widely in real life applications but they are hard to solve this paper proposes an enhanced logarithmic method to reformulate the spd problem as a mixed 0 1 linear program milp with a minimum number of binary variables and inequality constraints both of the theoretical analysis and numerical results strongly support its superior performance to other state of the art linearization methods we also extend the proposed method to linearize some more complicated problems involving product and fractional terms in discrete and continuous variables

interval regression analysis by quadratic programming approach when we use linear programming in possibilistic regression analysis some coefficients tend to become crisp because of the characteristic of linear programming on the other hand a quadratic programming approach gives more diverse spread coefficients than a linear programming one therefore to overcome the crisp characteristic of linear programming we propose interval regression analysis based on a quadratic programming approach another advantage of adopting a quadratic programming approach is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression by changing the weights of the quadratic function we can analyze the given data from different viewpoints for data with crisp inputs and interval outputs the possibility and necessity models can be considered therefore the unified quadratic programming approach obtaining the possibility and necessity regression models simultaneously is proposed even though there always exist possibility estimation models the existence of necessity estimation models is not guaranteed if we fail to assume a proper function fitting to the given data as a regression model thus we consider polynomials as regression models since any curve can be represented by the polynomial approximation using polynomials we discuss how to obtain approximation models which fit well to the given data where the measure of fitness is newly defined to gauge the similarity between the possibility and the necessity models furthermore from the obtained possibility and necessity regression models a trapezoidal fuzzy output can be constructed

color image processing by using binary quaternion moment preserving thresholding technique this paper presents a new moment preserving thresholding technique called the binary quaternion moment preserving bqmp thresholding for color image data based on representing color data by the quaternions the statistical parameters of color data can be expressed through the definition of quaternion moments analytical formulas of the bqmp thresholding can thus be determined by using the algebra of the quaternions the computation time for the bqmp thresholding is of order of the data size by using the bqmp thresholding quaternion moment based operators are designed for the application of color image processing such as color image compression multiclass clustering of color data and subpixel color edge detection the experimental results show that the proposed operator for color image compression can have output picture quality acceptable to human eyes in addition the proposed edge operator can detect the color edge at the subpixel level therefore the proposed bqmp thresholding can be used as a tool for color image processing

filtered projections as an aid in corner detection corners are very useful features for such purposes as image matching or shape analysis but corner detection is a relatively expensive operation this paper uses filtered x and y projections applied to an image containing an object that has not been explicitly segmented from its background to determine possible positions of corners so that corner detection can be applied only in the vicinity of these positions even in cases where the object would be hard to segment unimodal histogram this approach yields a good set of possible corner positions

multiobjective fuzzy competence set expansion problem by multistage decision based hybrid genetic algorithms the problem of competence set expansion involves determining the optimal expansion path under the minimum cost and has been widely used for the problem of process planning as we know the conventional competence set model only considers the problems of the single objective and the static situations in practice however the multiobjective and the dynamic situations usually occur in the optimal expansion path problems furthermore due to the subjective judgment and the restriction of information the degree of uncertainty should also be considered in this paper a multiobjective and multistage fuzzy competence set model is proposed to overcome the problems above simultaneously in order to efficiently obtain the optimal expansion path hybrid genetic algorithms hga are employed here in addition a particular job shop scheduling example is used to demonstrate the proposed method on the basis of the numerical results we can conclude that the proposed method can provide a sound fuzzy competence set model by considering the multiobjective and the multistage situations simultaneously

expanding competence sets for the consumer decision problem abstract the framework of competence set analysis provides a new approach to complement the existing models for the consumer decision problem since it is essential for the firm to improve the competence set of its product or service to fully address the consumer s truly needed benefits the effective expansion of competence sets plays an important role in marketing reality the previous studies regarding competence set expansion have thrown light on the tree expansion processes but forest learning is more suitable for the acquisition of product benefits than tree learning thus this study looses the assumption of tree learning and conducts forest learning to design an effective expansion program in addition this study explores a more general problem involving intermediate attributes compound benefits and experiential effects an algorithm is also provided for effective expansion of competence sets in consumer decision analysis

moment preserving corner detection abstract a new corner detection method based on the principle of preserving gray and mass moments is proposed for each circular region in a digital image bilevel thresholding based on gray moment preserving is used first to transform the blurred subimage in the region into a binary picture two approximate boundary points on the circumference of the thresholded circular region are obtained next by simple traversal an approximate corner point is estimated from the geometric relation between the centroid and the three vertices of the triangular lamina formed by the corner pattern within the circular region these points are then used as an initial guess for solving a system of nonlinear equations that are constructed by preserving the area and the three mass moments of the partial object lamina within the circular region more accurate corner boundary points can finally be determined from which not only the location but also the orientation as well as the angle of the corner can be computed experimental results show the effectiveness of the proposed method

incorporation competence sets of decision makers by deduction graphs this paper proposes an optimization model of incorporating competence sets of group decision makers to maximize the total benefit of the whole group such an incorporation model is formulated as finding a deduction graph linked from the nodes of existing competencies to the nodes of desired competencies compared with other methods treating competence set problems yu and zhang 1991 li and yu 1994 and shi and yu 1996 the proposed model can solve problems involving multiple decision makers in addition it allows the network to be cyclic and to contain compound nodes

a parametric approach to fuzzy linear programming in this paper we discuss how to deal with decision problems that are described with lp models and formulated with elements of imprecision and uncertainty more precisely we will study lp models in which the parameters are not fully known but only with some degree of precision even with incomplete information the model builder or model user is normally able to give a realistic interval for the parameters of an lp model for the constraint vector this is combined with some wishes or some leeway on the constraints even with ambiquity in the objective function there is normally some preference ordering to be found among alternative ways of action we will demonstrate that these modelling complications can be handled with the help of some results developed in the theory of fuzzy sets after an overview of some central contributions to fuzzy linear programming we will develop an lp model in which the parameters are not fully known only with some degree of precision and show that the model can be parametrised in such a way that the optimal solution becomes a function of the degree of precision the fuzzy lp model derived in this way appears to be fairly easy to handle computationally which is demonstrated with a numerical example

a milp formulation for generalized geometric programming using piecewise linear approximations abstract generalized geometric programming ggp problems are converted to mixed integer linear programming milp problems using piecewise linear approximations our approach is to approximate a multiple term log sum function of the form log x 1 x 2 x n in terms of a set of linear equalities or inequalities of log x 1 log x 2 and log x n where x 1 x n are strictly positive the advantage of this approach is its simplicity and readiness to implement and solve using commercial milp solvers while milp problems in general are no easier than ggp problems this approach is justified by the phenomenal progress of computing power of both personal computers and commercial milp solvers the limitation of this approach is discussed along with numerical tests

global optimization of signomial geometric programming problems abstract this paper presents a global optimization approach for solving signomial geometric programming problems in most cases nonconvex optimization problems with signomial parts are difficult np hard problems to solve for global optimality but some transformation and convexification strategies can be used to convert the original signomial geometric programming problem into a series of standard geometric programming problems that can be solved to reach a global solution the tractability and effectiveness of the proposed successive convexification framework is demonstrated by seven numerical experiments some considerations are also presented to investigate the convergence properties of the algorithm and to give a performance comparison of our proposed approach and the current methods in terms of both computational efficiency and solution quality

an effective genetic algorithm approach to multiobjective resource allocation problems moraps dynamic programming dp is a mathematical procedure designed primarily to improve the computational efficiency of solving select mathematical programming problems by decomposing them into smaller and hence computationally simpler subproblems in solving multiple objectives dynamic programming problem modp classical approaches reduce the multiple objectives into a single objective of minimizing a weighted sum of objectives the determination of these weights indicate the relative importance of the various objective also if the problem scale increases it become difficult to be dealt with even in the case of single objective because of the rapid expansion of the number of states to be considered in this paper we investigated the possibility of using genetic algorithms gas to solve multiobjective resource allocation problems moraps this procedure eliminates the need of any user defined weight factor for each objective also the proposed approach is developed to deal with the problems with both single or multiple objectives the simulation results for multiobjective resource allocation problems morap shows that genetic algorithms gas may hopefully be a new approach for such kinds of problems

deriving two stage learning sequences from knowledge in fuzzy sequential pattern mining a fuzzy sequential pattern consisting of several fuzzy sets represents a frequently occurring behavior related to time and can be discovered from transaction bases an example is that large purchase amounts of one product were bought by customers after these consumers had bought small purchase amounts of another product recently hu et al 2003 proposed a fuzzy data mining method to discover fuzzy sequential patterns in this method consumers products preferences and consumers product buying orders related to purchase behaviors can be found in the fuzzy sequential pattern mining since for each decision problem there is a competence set consisting of ideas knowledge information and skills for solving that problem we consider knowledge found in fuzzy sequential pattern mining as a needed competence set for solving one decision problem this paper uses a known competence set expansion method the minimum spanning table method to find appropriate two stage learning sequences that can effectively acquire individual fuzzy knowledge sets found in the fuzzy sequential pattern mining a numerical example is used to show the usefulness of the proposed method

optimal multiple stage expansion of competence set abstract in this paper we consider the expansion processes of competence sets which have asymmetric cost functions intermediate skills and compound skills among the skills cyclic connections are possible we introduce the concept of the stage expansion process sep of the competence set and provide mathematical programming methods to find a minimal cost sep and the ordering of expansion

range reduction techniques for improving computational efficiency in global optimization of signomial geometric programming problems many global optimization approaches for solving signomial geometric programming problems are based on transformation techniques and piecewise linear approximations of the inverse transformations since using numerous break points in the linearization process leads to a significant increase in the computational burden for solving the reformulated problem this study integrates the range reduction techniques in a global optimization algorithm for signomial geometric programming to improve computational efficiency in the proposed algorithm the non convex geometric programming problem is first converted into a convex mixed integer nonlinear programming problem by convexification and piecewise linearization techniques then an optimization based approach is used to reduce the range of each variable tightening variable bounds iteratively allows the proposed method to reach an approximate solution within an acceptable error by using fewer break points in the linearization process therefore decreasing the required cpu time several numerical experiments are presented to demonstrate the advantages of the proposed method in terms of both computational efficiency and solution quality

global optimization for generalized geometric programs with mixed free sign variables many optimization problems are formulated as generalized geometric programming ggp containing signomial terms f x g y where x and y are continuous and discrete free sign vectors respectively by effectively convexifying f x and linearizing g y this study globally solves a ggp with a lower number of binary variables than are used in current ggp methods numerical experiments demonstrate the computational efficiency of the proposed method

base 2 expansions for linearizing products of functions of discrete variables this paper presents an approach for representing functions of discrete variables and their products using logarithmic numbers of binary variables given a univariate function whose domain consists of n distinct values it begins by employing a base 2 expansion to express the function in terms of the ceiling of log2n binary and n continuous variables using linear restrictions to equate the functional values with the possible binary realizations the representation of the product of such a function with a nonnegative variable is handled via an appropriate scaling of the linear restrictions products of m functions are treated in an inductive manner from i 2 to m where each step i uses such a scaling to express the product of function i and a nonnegative variable denoting a translated version of the product of functions 1 through i 1 as a newly defined variable the resulting representations both in terms of one function and many are important for reformulating general discrete variables as binary and also for linearizing mixed integer generalized geometric and discrete nonlinear programs where it is desired to economize on the number of binary variables the approach provides insight into improves upon and subsumes related linearization methods for products of functions of discrete variables

multicriteria multistage planning for the optimal path selection using hybrid genetic algorithms the problem of the competence set expansion involves determining the optimal expansion path under the minimum cost and time as we know the conventional competence set model only considers the problems of the static situation and the single objective however the dynamic situation and the multicriteria should also be simultaneously considered in practice in this paper a multicriteria and multistage competence set model is proposed in order to efficiently obtain an optimal expansion path hybrid genetic algorithms hga are employed in addition a numerical example is used to demonstrate the proposed method on the basis of the numerical results we can conclude that the proposed method can provide a sound competence set model by simultaneously considering the multicriteria and multistage situations

a rotationally invariant two phase scheme for corner detection a rotationally invariant two phase scheme is proposed for the detection of corners in the first phase the curvature of each point on the curve is calculated based on the coordinates of five consecutive skipped points and the assumption that thes five points form a b spline curve the points with significant curvatures are collected as candidate corners during the second phase the candidate corners are verified for deviations in the global trend of the curve and the candidate corners due to quantization are removed using a self adjusting dot product window application of the propsed method on the examples given in the literature shows that it is both minimal in computation time and accurate and stable in the detected position of corners with the proposed method recognition of an object can be convenient since the corners detected are rotationally invariant