on a class of fuzzy classification maximum likelihood procedures classification maximum likelihood cml procedure is a remarkable mixture of maximum likelihood approach to clustering this has been well documented in the book of mclachlan and basford in this paper we make the fuzzy extension of the cml procedure based on this class of fuzzy cml procedures we extend the fuzzy clustering algorithms of trauwaert kaufman and rousseeuw by adding a penalty term especially we derive a generalized type of fuzzy c means fcm clustering algorithms called the penalized fcm clustering algorithms then we create some asymptotic behaviors of these penalized fcm procedures by doing some numerical examples we find that the penalized fcm is more meaningful and effective than fcm

approximation of functional relationships to fuzzy observations abstract for approximating functional relationships to fuzzy observations there exist several approaches joining some communities the functional relationship is still kept a fuzzy function even if the observations are crisp the case of crisp observations often requires specific considerations in this paper an approximation method using hausdorff like distances is proposed naturally containing the crisp observation case and leading to a crisp function for crisp observations additional the proposed method leads to well known approximation principles from classical theory and can be realized by standard computer software a simple example completes the considerations

strongly pseudoconvex cr structures over small balls part iii an embedding theorem the purpose of the present paper is to prove that any germ of strongly pseudoconvex cr structure on a manifold of real dimension 9 is realized by an embedding in the complex euclidean space of real codimension 1 it is well known that the above is true as formal power series hence we find an embedding such that the induced structure is very close to the given one on a small neighborhood of the reference point we correct our embedding by newton s method we then apply the moser nash procedure cf 4 to prove that the sequence of embeddings obtained by the successive correction converges on a sufficiently small neighborhood of the reference point to an embedding which realizes the given structure to explain how the correction is made let d be the differential operator in the complex associated with the given structure when f f f is an approximating embedding defined on u we set ox dfx if we can find gx such that dga on and f g is still an embedding f is completely corrected unfortunately we do not know how to find such a g however the neumann boundary value problem in parts i and ii for the differential operator df which is associated with the induced structure is a tool to handle such question by newton s method we mean that we make the best correction using df instead of d this is done as follows oa is not a differential form in the complex of df hence we replace 01 oj by its projection o on to the complex of df note that 0a may no longer be in the kernel of df and our domain may not be distinguished we first construct a distinguished distance function tf on u and consider a ball u tf r

reduction to least squares estimates in multiple fuzzy regression analysis in this paper we deal with the problem of least squares multiple regression with fuzzy data the regression coefficients are assumed to be real crisp a formula for solving the regression coefficients in one variable models is derived if each independent variable is effective i e its corresponding regression coefficient is nonzero the multiple regression problem can be replaced with a 0 1 programming problem its optimal solution is easily computed finally we also propose effective algorithms to compute the regression coefficients in a general case

strongly pseudoconvex cr structures over small balls part i an a priori estimate the purpose of the present series of papers is to develop the theory of harmonic integrals on strongly pseudoconvex cr structures over small balls along the line developed by d c spencer c b morrey j j kohn and l nirenberg 5 6 7 8 for strongly pseudoconvex complex manifolds we consider a strongly pseudoconvex cr structure on a manifold of real dimension 2n 1 in part i we establish the a priori estimate for the neumann boundary value problem on the complex associated with the structure in the case the structure is induced by an embedding in c and restricted to a small ball of special type provided i c q c n 3 where q is the degree of differential forms we consider in part ii we derive the regularity theorem of solutions of the neumann boundary value problem based on the a priori estimate of part i as an application we prove in part il that when n 5 the structure is realized on a neighborhood of a reference point by an embedding in cn we note here that l nirenberg gave an example of a strongly pseudoconvex cr structure which cannot be induced by such an embedding when n 2 9 l boutet de monvel proved that in the case of such structures over a compact manifold we can find such an embedding when n 3 1 there are two major differences between the cases of strongly pseudoconvex integrable almost complex structures and cr structures firstly the principal parts of the associated laplacians in cr structures are no longer elliptic secondly we have characteristic points on the boundary as a result when we follow over the predecessor s calculation in our case we end up with terms which may not be absorbed in the main non negative terms fortunately these leftover terms depend mostly on the levi form of the cr structure and the hessian form with respect to the cr structure of the equation of the boundary of our

multiobjective fuzzy linear regression analysis for fuzzy input output data abstract fuzzy linear regression models where both input data and output data are fuzzy numbers are introduced by using three indices for equalities between fuzzy numbers by considering the conflict between the fuzzy threshold for the three indices and the fuzziness of the fuzzy linear regression model three types of multiobjective programming problems for obtaining fuzzy linear regression models are formulated corresponding to the three indices then a linear programming based interactive decision making method to derive the satisficing solution of the decision maker for the formulated multiobjective programming problems is developed a numerical example demonstrates the appropriateness and efficiency of the proposed method

on fuzzy clustering of directional data abstract in this paper we propose fuzzy clustering algorithms for directional data it is a new type of classification maximum likelihood procedure for mixtures of von mises distributions these iterative clustering algorithms give us a new method for analysis of grouped directional data in the plane the procedure which embeds the fuzzy c partitions in the model of mixtures of von mises regressions is derived this is used as analysis of mixtures of directional regression models some numerical examples are given

an enhanced fuzzy linear regression model with more flexible spreads one of the deficiencies of previous fuzzy linear regression models is that with the increase of the magnitudes of independent variables the spreads of estimated fuzzy dependent variables are increasing even though the spreads of observed dependent variables actually decrease or remain unchanged some solutions have been proposed to solve this spreads increasing problem however those solutions still cannot model a decreasing trend in the spreads of the observed dependent variables as the magnitudes of the independent variables increase in this paper we propose an enhanced fuzzy linear regression model model flr f s in which the spreads of the estimated dependent variables are able to fit the spreads of the observed dependent variables no matter the spreads of the observed dependent variables are increased decreased or unchanged as the magnitudes and spreads of the independent variables change four numerical examples are used to demonstrate the effectiveness of model flr f s

strongly pseudoconvex cr structures over small balls part ii a regularity theorem the purpose of the present paper is to prove the regularity theorem for the solution of the generalized neumann boundary value problem for a strongly pseudoconvex cr structure say t over a small ball this will be based on the a priori estimate established in i namely we take an admissible distance function t to a reference point cf 2 12 in i and consider a sufficiently small ball ur t r denote by d the differential operator in the complex associated with 0t and consider the metric given by a levi form set b dt which is a function of u we consider the hilbert space of l2 norm with weight factor b2a 11 11 a and a denoting its norm and inner product respectively let ad be the adjoint of d set qa u v du dv a ad u ad v a for 0t q forms u v the generalized neumann boundary value problem is to solve the following equation for a given 0t q form a and an unknown 0t q form u withuldt 0

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

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

robust clustering methods a unified view clustering methods need to be robust if they are to be useful in practice in this paper we analyze several popular robust clustering methods and show that they have much in common we also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least squares technique the m estimator the minimum volume ellipsoid algorithm cooperative robust estimation minimization of probability of randomness and the epsilon contamination model by gleaning the common principles upon which the methods proposed in the literature are based we arrive at a unified view of robust clustering methods we define several general concepts that are useful in robust clustering state the robust clustering problem in terms of the defined concepts and propose generic algorithms and guidelines for clustering noisy data we also discuss why the generalized hough transform is a suboptimal solution to the robust clustering problem

fuzzy least squares algorithms for interactive fuzzy linear regression models fuzzy regression analysis can be thought of as a fuzzy variation of classical regression analysis it has been widely studied and applied in diverse areas in general the analysis of fuzzy regression models can be roughly divided into two categories the first is based on tanaka s linear programming approach the second category is based on the fuzzy least squares approach in this paper new types of fuzzy least squares algorithms with a noise cluster for interactive fuzzy linear regression models are proposed these algorithms are robust for the estimation of fuzzy linear regression models especially when outliers are present numerical examples are given to detail the effectiveness of this approach

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 least squares linear regression analysis for fuzzy input output data a fuzzy regression model is used in evaluating the functional relationship between the dependent and independent variables in a fuzzy environment most fuzzy regression models are considered to be fuzzy outputs and parameters but non fuzzy crisp inputs in general there are two approaches in the analysis of fuzzy regression models linear programming based methods and fuzzy least squares methods in 1992 sakawa and yano considered fuzzy linear regression models with fuzzy outputs fuzzy parameters and also fuzzy inputs they formulated multiobjective programming methods for the model estimation along with a linear programming based approach in this paper two estimation methods along with a fuzzy least squares approach are proposed these proposed methods can be effectively used for the parameter estimation comparisons are also made between them

global analytic hypoellipticity of the neumann problem on circular domains in this paper we show that if d subseteq mathbb c n n geqq 2 is a smooth bounded pseudoconvex circular domain with real analytic defining functionr z such that sum limits k 1 n z k frac partial r partial z k ne 0 for allz near the boundary then the solutionu to the bar partial neumann problem square u bar partial bar partial bar partial bar partial u f is real analytic up to the boundary if the given formf is real analytic up to the boundary in particular if d subseteq mathbb c n n geqq 2 is a smooth bounded complete reinhardt pseudoconvex domain with real analytic boundary then is analytic hypoelliptic

exponential possibility regression analysis abstract this paper aims at giving the application of possibility theory based on exponential distributions to regression analysis a general outline of the possibility theory is illustrated by exponential possibility distributions it is shown that possibility analysis is well corresponding to statistical analysis using exponential possibility analysis we propose possibility regression analysis which is suitable for rough phenomena arising from social and economic systems the spread of the given data can be directly transferred into the exponential possibility distribution of coefficients in the regression model by the proposed method

finitistic dimension conjecture and relative hereditary algebras abstract we introduce the notion of relative hereditary artin algebras as a generalization of algebras with representation dimension at most 3 we prove the following results 1 the relative hereditariness of an artin algebra is left right symmetric and is inherited by endomorphism algebras of projective modules 2 the finitistic dimensions of a relative hereditary algebra and its opposite algebra are finite as a consequence the finitistic projective dimension conjecture the finitistic injective dimension conjecture the gorenstein symmetry conjecture the wakamatsu tilting conjecture and the generalized nakayama conjecture hold for relative hereditary artin algebras and endomorphism algebras of projective modules over them in particular over algebras with representation dimension at most 3 we also show that the torsionless finiteness of an artin algebra is inherited by endomorphism algebras of projective modules and consequently give a partial answer to the question if the representation dimension of the endomorphism algebra of any projective module over an artin algebra a is bounded by the representation dimension of a