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

linear programming in linear time when the dimension is fixed it is demonstrated that the linear programming problem in d variables and n constraints can be solved in o n time when d is fixed this bound follows from a multidimensional search technique which is applicable for quadratic programming as well there is also developed an algorithm that is polynomial in both n and d provided d is bounded by a certain slowly growing function of n

annealed and quenched inhomogeneous cellular automata inca a probabilistic one dimensional cellular automaton model by domany and kinzel is mapped into an inhomogeneous cellular automaton with the boolean functions xor and and as transition rules wolfram s classification is recovered by varying the frequency of these two simple rules and by quenching or annealing the inhomogeneity in particular class 4 is related to critical behavior in directed percolation also the critical slowing down of second order phase transitions is related to a stochastic version of the classical halting problem of computation theory

grid anisotropy reduction for simulation of growth processes with cellular automaton abstract growth processes simulated on a regular cellular automaton grid with simple capture rules are considerably influenced by the structure of the grid some of the growth directions are favored over others leading to highly anisotropic or at least orientation dependent growth pattern a new method is proposed for significant reduction of artificial grid anisotropy in 2d and 3d cellular automata with continuous state variable the method employs additional diffusion process controlling the growth rate and allows for isotropic or anisotropic growth where the anisotropy is decoupled from the grid structure verification of the method is provided in the case of isotropic circular growth isotropic growth of various shapes in uniform and spatially varying fields and anisotropic growth with respect to orientation and symmetry of the pattern finally the reduction of grid anisotropy is demonstrated in 2d simulation of dendritic grain growth in pure metal the shape of the grain is shown to be virtually independent of the orientation an example growth of a grain with six fold symmetry is also included

on the quasi isometries of harmonic quasiconformal mappings abstract we prove versions of the ahlfors schwarz lemma for quasiconformal euclidean harmonic functions and harmonic mappings with respect to the poincare metric

projection based polygonality measurement measuring the degree to which a shape resembles a polygon referred to as polygonality is a difficult problem due to the intrinsic diversity in the form and distortion of shapes caused by digitization and similarity transformation this paper proposes a generic approach for this problem by performing the measurement in the projection space where the radon image of some primitive shapes which compose the shape becomes apparent the obtained measures take value in 0 1 with 1 corresponding to analytical polygons they are robust to additive noise and boundary distortion and is invariant to similarity transformation the new framework generalizes existing polygonal measures such as triangularity and quadrangularity in addition the ability to estimate polygon s geometric quantities in the projection space allows approximating a shape by analytical polygons the efficiency of the proposed approach is demonstrated through a number of experiments on both synthetic and real data sets

on certain quasiconformal and elliptic mappings abstract let d be the closure of the unit disk d in the complex plane c and g be a continuous function in d in this paper we discuss some characterizations of elliptic mappings f satisfying the poisson s equation f g in d and then establish some sharp distortion theorems on elliptic mappings with the finite perimeter and the finite radial length respectively the obtained results are the extension of the corresponding classical results

quasiconformal and harmonic mappings between jordan domains let and 1 be jordan domains let 0 1 and let f omega mapsto omega 1 be a harmonic homeomorphism the object of the paper is to prove the following results a if f is q c and 1 c 1 then f is lipschitz b if f is q c 1 c 1 and 1 is convex then f is bi lipschitz and c if is the unit disk 1 is convex and 1 c 1 then f is quasiconformal if and only if its boundary function is bi lipschitz and the hilbert transform of its derivative is in l these extend the results of pavlovic ann acad sci fenn 27 365 372 2002

lebesgue and saks decompositions of b decomposable measures abstract the properties of decomposable measures are investigated for t conorms which are more general than archimedean t conorms the continuity of such set functions with respect to suitably chosen submeasures is proved as an important consequence a lebesgue type decomposition theorem is obtained a version of saks decomposition for order continuous decomposable measures with respect to arbitrary t conorms is proved

linear time algorithms for linear programming in r 3 and related problems linear time algorithms for linear programming in r 2 and r 3 are presented the methods used are applicable for other graphic and geometric problems as well as quadratic programming for exam

muckenhoupt weights and lindelof theorem for harmonic mappings abstract we extend the result of lavrentiev which asserts that the harmonic measure and the arc length measure are a equivalent in a chord arc jordan domain by using this result we extend the classical result of lindelof to the class of quasiconformal q c harmonic mappings by proving the following assertion assume that f is a quasiconformal harmonic mapping of the unit disk u onto a jordan domain then the function a z arg f z z where z r e i is well defined and smooth in u z 0 z 1 and has a continuous extension to the boundary of the unit disk if and only if the image domain has c 1 boundary

an algorithm for identification of fuzzy measure in the paper the connection between fuzzy measures and lebesgue measure is discussed special attention is focused on fuzzy measures which satisfy the so called l rule a relation between such measures and probability measures is given basing on this relation a simple and fast algorithm for identification of a sugeno fuzzy measure is presented

isotropic growth on a grid abstract isotropic growth from a single point on a two dimensional square grid should generate an increasing sequence of discretized discs we present a simple probabilistic model for growth on a grid and discuss a class of parameterizations of the model called kernels which was conjectured s thompson and a rosenfeld discrete stochastic growth models for two dimensional shapes in shape in picture mathematical descriptions of shape in grey level images y l o a toet d h foster and p meer eds 301 318 springer verlag heidelberg 1993 to produce isotropic growth we disprove this conjecture but we claim that these kernels produce growth that can be decomposed into isotropic and nonisotropic other probabilistic growth processes on grids and describe qualitative and quantitative properties of the models we also consider a deterministic growth model based on the diffusion equation and show empirically that discretization of this model leads to a steady state configuration that appears to be polygonal

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

measure of circularity for parts of digital boundaries and its fast computation this paper focuses on the design of an effective method that computes the measure of circularity of a part of a digital boundary an existing circularity measure of a set of discrete points which is used in computational metrology is extended to the case of parts of digital boundaries from a single digital boundary two sets of points are extracted so that the circularity measure computed from these sets is representative of the circularity of the digital boundary therefore the computation consists of two steps first the inner and outer sets of points are extracted from the input part of a digital boundary using digital geometry tools next the circularity measure of these sets is computed using classical tools of computational geometry it is proved that the algorithm is linear in time in the case of convex parts thanks to the specificity of digital data and is in o nlogn otherwise experiments done on synthetic and real images illustrate the interest of the properties of the circularity measure

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

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

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

separating point sets by circles and the recognition of digital disks given two sets a and b of points in the plane we give a polynomial time algorithm to find the set s of points which are centers of circles that contain all the members of a and none of b a consequence of the algorithm is that s is polygonal another application is an o n2 time and o n2 space algorithm for the recognition of digital disks

on two dimensional directed percolation extended series expansions for the mean size and the first and second moments of the pair connectedness for both bond and site percolation on the directed square and triangular lattices have been obtained analysis based on differential approximants allows the critical percolation probabilities and exponents to be estimated and as a result the critical exponents are conjectured to be gamma 41 18 nu perpendicular to 79 72 and nu sub 26 15 scaling then gives beta 199 720 alpha 299 360 and delta 1839 199

fuzzy integrals and conditional fuzzy measures we introduce a fuzzy integral for fuzzy events with respect to l additive fuzzy measures this integral is the canonical generalization of the lehesgue integral a radon nikodym like theorem is used to give the definition of the conditional fuzziness

growth processes based on 8 neighbor time delays abstract unconstrained uniform growth on a regular grid of cells starting from a single cell results in a simple centrally symmetric shape on a square grid for example the resulting clusters of cells would be diamonds rotated squares using 4 neighbor growth or squares using 8 neighbor growth in order to model growth that is directed and focused in some directions and resisted in others we formulate growth in terms of a kernel which associates a time delay with each direction on a square grid a time delay kernel tdk consists of eight elements one for each of the eight directions we give a closed form characterization of the clusters that result from tdk based growth processes specifically we show that tdks give rise to convex octagons we also show that a much richer class of cluster shapes results from the composition of tdk based growth processes where activated cells synchronously cycle through sequences of tdks lastly we provide a recovery algorithm that outputs the sequence of tdks that when composed can produce a given shape

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 note on λ additive fuzzy measures abstract a relation between additive fuzzy measures and measures is given this relation is used to prove some properties of additive fuzzy measures

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

cellular automata for contour dynamics abstract the dynamics of deterministic partially permutive cellular automata in two dimensions is considered in particular we lay out the design principles and analyze the dynamics of generalized voter type rules they provide a two parameter model class of cellular automata which exhibit annealing diffusive and critical domain behavior we analyze the dynamics rigorously in certain cases and also show that all types of behavior are very close to their ideal counterparts observed in probabilistic models based on strong independence assumptions this is further evidence that the statistical mechanics extends to cover also classes of purely deterministic dynamics

critical growth phenomena in cellular automata abstract we study a one parameter family of probabilistic cullular automata on square and triagular lattices above a critical parameter value a new dominant invariant phase appears resulting in domain growth in the growth regime a second critical threshold is found above which domains grow at a maximal rate and facet this phenomenon is shown to be equivalent to a certain one dimensional directed percolation problem studied by domany and kinzel 1984 tight bounds are given to the critical probabilities which depend on the lattice these models are of special interest since their behavior corresponds extremely closely to that of certain simple purely deterministic cellular automata

on quasiconformal self mappings of the unit disk satisfying poisson s equation let qc k g be a family of k quasiconformal mappings of the open unit disk onto itself satisfying the pde w g g c u w 0 0 it is proved that qc k g is a uniformly lipschitz family moreover if g is small enough then the family is uniformly bi lipschitz the estimations are asymptotically sharp as k 1 and g 0 so w qc k g behaves almost like a rotation for sufficiently small k and g

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

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

sequential compactness for sets of sugeno fuzzy measures abstract pointwise sequential compactness for families of sugeno measures is studied and a sufficient condition is proved for the equivalence between equiabsolute continuity uniform order continuity and sequential compactness a group valued measure interpretation for additive fuzzy measures is also showed

identification of λ fuzzy measures using sampling design and genetic algorithms the data collection and identification of fuzzy measures are fundamental tasks to be capable of using them in practice although several studies have been made on fuzzy measure identification their methods require the knowledge of subjective estimates for all subsets of an attribute set or the corresponding computation process is rather complicated since little attention has been given to the issue of data collection this study designed a sampling procedure of attribute subsets to capture the most useful information and thus reduce the original information demand in solving fuzzy measures then this study developed an identification procedure for fuzzy measures using genetic algorithms several experiments were implemented to show the applicability and feasibility of the proposed methods

the critical contact process dies out by producing a finite box criterion for survival in a slab we show that the critical contact process dies out and that in two and more dimensions the critical parameter value coincides with the limit of slab thresholds using the techniques developed in this paper one may obtain the complete convergence and shape theorems for contact processes in all dimensions and for all infection rates our results apply also to the discrete time analogue of the contact process viz oriented percolation

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

surface structure and anisotropy of eden clusters the simple eden model is simulated with clusters which are orders of magnitude larger than those of some previous work the surface perimeter is slightly anisotropic and feels the underlying structure of the square lattice even for 17 million cluster sites the width of the surface layer increases with increasing cluster mass with an effective exponent presumably larger than 1 4 for averages over the whole circumference and perhaps equal to 1 4 for flat surfaces width averages over a small angle are compared with the recent prediction of plischke and racz 1985 even 17 million sites are not enough to see directly the asymptotic behaviour

out of roundness problem revisited the properties and computation of the minimum radial separation mrs standard for out of roundness are discussed another standard out of roundness measurement called the minimum area difference mad center is introduced although the two centers have different characteristics the approach to finding both centers shares many commonalities an o n log n k time algorithm which is used to compute the mrs center is presented it also computes the mad center of a simple polygon g where n is the number of vertices of g and k is the number of intersection points of the medial axis and the farthest neighbor voronoi diagram of g the relationship between mrs and mad is discussed

digitized circular arcs characterization and parameter estimation the digitization of a circular arc causes an inherent loss of geometrical information arcs with slightly different local curvature or position may lead to exactly the same digital pattern in this paper the authors give a characterization of all centers and radii of circular arcs yielding the same digitization pattern the radius of the arcs varies over the set however only one curvature or radius estimate can be assigned to the digital pattern the authors derive an optimal estimator and give expressions for the bound on the precision of estimation this bound due to digitization is the deterministic equivalent of the cramer rao bound known from parameter estimation theory consider the estimation of the local curvature and local radius of a smooth object typically such parameters are estimated by moving a window along the digital boundary methods in literature show a poor precision in estimating curvature values relative errors of over 40 are often found from the definition of curvature it follows that locally the curve can be considered a circular arc and hence the method presented in this paper can be applied to the pattern in the window giving estimates with optimal precision and a measure for the remaining error on the practical side the authors present examples of the residual error due to the discrete grid the estimation of the radius or curvature of a circular arc at random position with an estimation window containing 10 points coded with nine freemancodes has a relative deviation exceeding 2 for a full disk the deviation is below 1 when the radius r exceeds four grid units the presented method is particularly useful for problems where some prior knowledge on the distribution of radii is known and where there is a noise free sampling