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 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

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

lenses in arrangements of pseudo circles and their applications a collection of simple closed jordan curves in the plane is called a family of pseudo circles if any two of its members intersect at most twice a closed curve composed of two subarcs of distinct pseudo circles is said to be an empty lens if the closed jordan region that it bounds does not intersect any other member of the family we establish a linear upper bound on the number of empty lenses in an arrangement of n pseudo circles with the property that any two curves intersect precisely twice we use this bound to show that any collection of n x monotone pseudo circles can be cut into o n8 5 arcs so that any two intersect at most once this improves a previous bound of o n5 3 due to tamaki and tokuyama if in addition the given collection admits an algebraic representation by three real parameters that satisfies some simple conditions then the number of cuts can be further reduced to o n3 2 log n o s n where n is the inverse ackermann function and s is a constant that depends on the the representation of the pseudo circles for arbitrary collections of pseudo circles any two of which intersect exactly twice the number of necessary cuts reduces still further to o n4 3 as applications we obtain improved bounds for the number of incidences the complexity of a single level and the complexity of many faces in arrangements of circles of pairwise intersecting pseudo circles of arbitrary x monotone pseudo circles of parabolas and of homothetic copies of any fixed simply shaped convex curve we also obtain a variant of the gallai sylvester theorem for arrangements of pairwise intersecting pseudo circles and a new lower bound on the number of distinct distances under any well behaved norm

on the selection of poles in the single input pole placement problem abstract it is well known that the single input pole placement problem can be quite sensitive to perturbations in the data recent results by mehrmann and xu show how this sensitivity depends on the location of the poles in many applications it suffices to prescribe a set k in the complex plane that contains the poles mehrmann and xu formulated a minimization problem for allocating the poles in a given set k so that the sensitivity to perturbations is reduced the present paper uses methods of potential theory to derive simple algorithms that yield approximate solutions of this minimization problem

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 generalized adi iterative method the adi iterative method for the solution of sylvester s equationax xb c proceeds by strictly alternating between the solution of the two equations begin gathered left a delta k 1 i right x 2k 1 x 2k left b delta k 1 i right c hfill x 2k 2 left b tau k 1 i right left a tau k 1 i right x 2k 1 c hfill end gathered fork 0 1 2 herex o is a given initial approximate solution and the k and k are real or complex parameters chosen so that the computed approximate solutionsx k converge rapidly to the solutionx of the sylvester equation ask increases this paper discusses the possibility of solving one of the equations in the adi iterative method more often than the other one i e relaxing the strict alternation requirement in order to achieve a higher rate of convergence our analysis based on potential theory shows that this generalization of the adi iterative method can give faster convergence than when strict alternation is required

an algorithm to assign eigenvalues in a hessenberg matrix single input case we propose a conceptually simple algorithm to assign eigenvalues in a hessenberg matrix the method is based on the evaluation of a simple recursive relation and it is extremely easy to program on a computer numerical experiments compare favorably to those of other methods recently proposed for the problem

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

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

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

on the erdős distinct distances problem in the plane in this paper we prove that a set of n points in r 2 has at least c n log n distinct distances thus obtaining the sharp exponent in a problem of erd os we follow the setup of elekes and sharir which in the spirit of the erlangen program allows us to study the problem in the group of rigid motions of the plane this converts the problem to one of point line incidences in space we introduce two new ideas in our proof in order to control points where many lines are incident we create a cell decomposition using the polynomial ham sandwich theorem this creates a dichotomy either most of the points are in the interiors of the cells in which case we immediately get sharp results or alternatively the points lie on the walls of the cells in which case they are in the zero set of a polynomial of suprisingly low degree and we may apply the algebraic method in order to control points incident to only two lines we use the ecnode polynomial of the rev george salmon to conclude that most of the lines lie on a ruled surface then we use the geometry of ruled surfaces to complete the proof

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

pole placement preconditioning the partial pole placement problem has received considerable attention in control theory where it is applied to stabilize time invariant linear control systems this paper discusses application of the partial pole placement problem to the construction of preconditioners for linear systems of equations numerical examples show that these preconditioners can improve the rate of convergence of the restarted gmres methods significantly

the condition number of equivalence transformations that block diagonalize matrix pencils how ill conditioned must a matrix s be if its columns are constrained to span certain subspaces we answer this question in order to find nearly best conditioned matrices sr and sl that block diagonalize a given matrix pencil t a b i e s l 1 tsr is bloc diagonal we show that the best conditioned sr has a condition number approximately equal to the cosecant of the smallest angle between right subspaces belonging to different diagonal blocks of thus the more nearly the right subspaces overlap the more ill conditioned sr must be the same is true of sl and the left subspaces for the standard eigenproblem t a i sl sr and the cosecant of the angle between subspaces turns out equal to an earlier estimate of the smallest condition number namely the norm of the projection matrix associated with one of the subspaces we apply this result to bound the error in an algorithm to compute analytic functions of matrices for instance exp t

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

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

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

numerical methods in control we study classical control problems like pole assignment stabilization linear quadratic control and h control from a numerical analysis point of view we present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework we also discuss some new algorithmic approaches

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

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

on distinct sums and distinct distances abstract the paper discrete comput geom 25 2001 629 of solymosi and toth implicitly raised the following arithmetic problem consider n pairwise disjoint s element sets and form all s 2 n sums of pairs of elements of the same set what is the minimum number of distinct sums one can get this way this paper proves that the number of distinct sums is at least n d s where d s 1 c s 2 is defined in the paper and tends to e 1 as s goes to infinity here e is the base of the natural logarithm as an application we improve the solymosi toth bound on an old erdos problem we prove that n distinct points in the plane determine n 4e 5e 1 e distinct distances where e 0 is arbitrary our bound also finds applications in other related results in discrete geometry our bounds are proven through an involved calculation of entropies of several random variables