the alexander transform of a spirallike function abstract we show that the alexander transform of a spirallike function is univalent when cos 1 2 which settles the problem posed by robertson we also solved a problem considered by y j kim and merkes

statistical inference based on the possibility and belief measures in statistical inference we infer the population parameter based on the realization of sample statistics this can be considered in the framework of inductive inference we showed in chen 1993 that if we measure a parameter by the possibility or belief measure we can have an inductive inference similar to the bayesian inference in belief update in this article we apply this inference to statistical estimation and hypotheses evaluation testing for some parametric models and compare them to the classical statistical inferences for both onesample and two sample problems

vertex method for computing functions of fuzzy variables abstract this paper is to introduce a new approach the vertex method for computing functions of fuzzy variables the method is based on the cut concept and interval analysis the vertex method can avoid abnormality due to the discretization technique on the variables domain and the widening of the resulting function value set due to multi occurrence of variables in the functional expression by conventional interval analysis methods the algorithm is very easy to implement and can be applied to many practical problems some examples are given to illustrate the applications

an efficient configuration for probabilistic fuzzy logic system a novel inference configuration is proposed to improve the computational efficiency and information loss in the probabilistic fuzzy inference process the probabilistic inference and the fuzzy inference are unified in one operation based on the continuous form of the probabilistic fuzzy set besides the faster inference operation it is able to produce fuzzy outputs in a complete probabilistic distribution that in turn will provide information about the approximation bound the computational analyses of six different fuzzy systems demonstrate the inference efficiency of the proposed method its effectiveness can be further demonstrated on the application to modeling of an industrial curing process the robust modeling performance discloses its potential in process modeling under complex environment

extracting invariants of isolated hypersurface singularities from their moduli algebras we use classical invariant theory to construct invariants of complex graded gorenstein algebras of finite vector space dimension as a consequence we obtain a way of extracting certain numerical invariants of quasi homogeneous isolated hypersurface singularities from their moduli algebras which extends an earlier result due to the first author furthermore we conjecture that the invariants so constructed solve the biholomorphic equivalence problem in the homogeneous case the conjecture is easily verified for binary quartics and ternary cubics we show that it also holds for binary quintics and sextics in the latter cases the proofs are much more involved in particular we provide a complete list of canonical forms of binary sextics which is a result of independent interest

fuzzy analysis of statistical evidence bayesian classifiers are effective methods for pattern classification although their assumptions on the belief structure among attributes are not always justified in this paper we introduce a new classification method based on the possibility measure which does not require a precise belief model and in a sense it includes the bayesian classifiers as special cases this new classification method uses the fuzzy operators to aggregate attributes information evidence and it is referred to as fuzzy analysis of statistical evidence fase fase has several nice properties it is noise tolerant it can handle missing values with ease and it can extract statistical patterns from the data and represent them by knowledge of beliefs which in turn are propositions for an expert system thus from pattern classification to expert systems fase provides a linkage from inductive reasoning to deductive reasoning

fuzzy weighted averages and implementation of the extension principle abstract this paper addresses the computational aspect of the extension principle when the principle is applied to algebraic mappings and in particular to weighted average operations in risk and decision analysis a computational algorithm based on the cut representation of fuzzy sets and interval analysis is described the method provides a discrete but exact solution to extended algebraic operations in a very efficient and simple manner examples are given to illustrate the method and its relation to other discrete methods and the exact approach by non linear programming the algorithm has been implemented in a computer program which can handle very general extended algebraic operations on fuzzy numbers

on using a cuts to evaluate fuzzy equations abstract consider an equation y f x1 xn where the extension principle is used to find y f x 1 x n when we subtitute fuzzy numbers x i for the xi 1 i n if x i denotes an cut of x i then we argue that for only certain simple equations will one obtain y equal to f x 1 x n where f is evaluated using interval arithmetic

bernoulli trials from a fuzzy measure point of view abstract bernoulli ars conjectandi basle 1713 proved the first limit theorem of law of large numbers which provided the foundation of probability and statistical theory however the problem of bernoulli trials is still unsettled e g see hacking the emergence of probability cambridge univ press cambridge 1975 it is from different interpretations of the relationship between the bernoulli trials and relative frequency that we have different schools of probability theories e g see cox amer j phys 14 no 1 1946 1 13 and fine ieee trans inform theoryit 16 no 3 1970 251 257 in this paper we give a new treatment of the bernoulli trials based on fuzzy measure and we interpret the bernoulli trials through the interaction of probability and possibility measures

mapping properties of nonlinear integral operators and pre schwarzian derivatives in this paper nonlinear integral operators on normalized analytic functions in the unit disk are investigated in connection with the pre schwarzian derivative and the hornich operation in particular several nontrivial relations between these operators and the class of strongly starlike functions will be deduced

feedback stabilization using two hidden layer nets the representational capabilities of one hidden layer and two hidden layer nets consisting of feedforward interconnections of linear threshold units are compared it is remarked that for certain problems two hidden layers are required contrary to what might be in principle expected from the known approximation theorems the differences are not based on numerical accuracy or number of units needed nor on capabilities for feature extraction but rather on a much more basic classification into direct and inverse problems the former correspond to the approximation of continuous functions while the latter are concerned with approximating one sided inverses of continuous functions and are often encountered in the context of inverse kinematics determination or in control questions a general result is given showing that nonlinear control systems can be stabilized using two hidden layers but not in general using just one

norm of the pre schwarzian derivative bloch s constant and coefficient bounds in some classes of harmonic mappings abstract the aim of the paper is a study of a family of sense preserving complex valued harmonic functions f that are normalized in the open unit disk and such that its analytic part is convex in one direction we prove the univalence and establish estimates on pre schwarzian derivative and the bloch constant for co analytic part of harmonic mapping the bounds of the coefficients of co analytic part are also given

incorporating fuzzy membership functions into the perceptron algorithm the perceptron algorithm one of the class of gradient descent techniques has been widely used in pattern recognition to determine linear decision boundaries while this algorithm is guaranteed to converge to a separating hyperplane if the data are linearly separable it exhibits erratic behavior if the data are not linearly separable fuzzy set theory is introduced into the perceptron algorithm to produce a fuzzy algorithm which ameliorates the convergence problem in the nonseparable case it is shown that the fuzzy perceptron like its crisp counterpart converges in the separable case a method of generating membership functions is developed and experimental results comparing the crisp to the fuzzy perceptron are presented

a characteristic point based fuzzy inference classifier by a closeness matrix in this paper a characteristic point based fuzzy inference classifier cpfic is proposed to perform two class classification through fuzzy interpolation a subset of classified samples can be taken as representatives of all samples they are called characteristic points cps a closeness matrix representing the closeness of two samples in a same class is proposed in selecting cps by solving a number of constrained minimizations the cpfic is systematically built experiments were conducted on four classification problems with known bayes errors two benchmark classification problems and a real world application used in our research the cpfic performs well in accuracy evaluations in all the seven experiments the summarizing abilities from the cps into the linguistic descriptions of the fuzzy rule bases were also demonstrated in these examples

a neural network architecture for classification of fuzzy inputs abstract a neural network for classification problems with fuzzy inputs is proposed a fuzzy input is represented as an lr type fuzzy set a generalized pocket algorithm called fuzzy pocket algorithm that uses lr type fuzzy sets operations and defuzzification method is proposed to train a linear threshold unit ltu this ltu node will classify as many fuzzy input instances as possible afterward fv nodes that represent fuzzy vectors will then be generated and expanded by proposed fvge learning algorithm to classify those fuzzy input instances that cannot be classified by the ltu node the similarity degree between fv nodes and fuzzy inputs is measured by the fuzzy subsethood degree the network structure is automatically generated the number of hidden nodes generated depends on the overlapping degree of training instances besides on line learning is supplied and parameters used are few and insensitive the relationship between proposed model and hyperbox based classifiers e g fuzzy art series and fuzzy min max series is also discussed two sample problems heart disease and knowledge based evaluator are considered to illustrate the working of the proposed model the experimental results are very encouraging

norm estimates for convolution transforms of certain classes of analytic functions abstract for normalized analytic functions f in the unit disk we consider the class f f re 1 z f z f z 3 2 z where 2 3 1 and s a b f z f z f z 1 a z 1 b z z where 1 b a 1 and denotes the subordination set k a b f z f s a b for 0 b c define j b c f by j b c f z z f 1 b c z f z where f a b c z is the gauss hypergeometric function and denotes the convolution or hadamard product for a locally univalent analytic function f defined on we consider the pre schwarzian norm by f sup z 1 z 2 f z f z in this paper we find sharp norm estimates for functions in f and in k a b in addition we also present sharp norm estimates for j b c f z when f ranges over the classes f and k a b respectively

norm estimates for the alexander transforms of convex functions of order alpha abstract the hyperbolic sup norm of the pre schwarzian derivative of a locally univalent function on the unit disk measures the deviation of the function from similarities we present sharp norm estimates for the alexander transforms of convex functions of order 0 1

associated forms in classical invariant theory and their applications to hypersurface singularities it was conjectured in the recent article by eastwood and isaev that all absolute classical invariants of forms of degree m ge 3 on mathbb c n can be extracted in a canonical way from those of forms of degree n m 2 by means of assigning every form with non vanishing discriminant the so called associated form this surprising conjecture was confirmed for binary forms of degree m le 6 and ternary cubics in the present paper we settle the conjecture in full generality in addition we propose a stronger version of this statement and obtain evidence supporting it

associated forms and hypersurface singularities the binary case in the recent articles ei and ai it was conjectured that all rational gln invariant functions of forms of degree d 3 on cn can be extracted in a canonical way from those of forms of degree n d 2 by means of assigning to every form with nonvanishing discriminant the so called associated form the conjecture was confirmed in ei for binary forms of degree d 6 as well as for ternary cubics furthermore a weaker version of it was settled in ai for arbitrary n and d in the present paper we focus on the case n 2 and establish the conjecture in a rather explicit way for binary forms of an arbitrary degree

region of variability of two subclasses of univalent functions abstract let f 1 f 2 respectively denote the class of analytic functions f in the unit disk z 1 with f 0 0 f 0 1 satisfying the condition re p f z 3 2 re p f z 1 2 respectively in z 1 where p f z 1 z f z f z for any fixed z 0 in the unit disk and 0 1 we shall determine the region of variability for log f z 0 when f ranges over the class f f 1 f 0 and f f 2 f 0 3 respectively

fuzzy sets in pattern recognition accomplishments and challenges abstract we identify and discuss a role that fuzzy sets play in pattern recognition the main conceptual and algorithmic challenges are outlined highlighted are also some future trends

the dilworth number of artin gorenstein rings 1let a be an artin local ring the dilworth number of a is defined to be the supremum of p z for ideals z in a where p is the minimal number of generators in my paper 4 i developed some methods to compute this number when a is homogeneously graded over a field k and especially if a is gorenstein and ch k 0 i showed that it is the dominating case that the dilworth number is attained by a power of the maximal ideal in such a case we shall say that a has the sperner property in the present paper we consider artin rings a m not necessarily graded and compare the dilworth number of a and that of gr a and it will be shown that the main result of 4 is valid without the assumption that the rings are homogeneous our main result is theorem 7 where we prove that most artin gorenstein rings have the sperner property actually we prove a stronger result which says that it has the weak stanley property to explain the term most we represent an artin gorenstein ring a in the

git semistability of hilbert points of milnor algebras we study git semistability of hilbert points of milnor algebras of homogeneous forms our first result is that a homogeneous form f in n variables is git semistable with respect to the natural mathrm sl n action if and only if the gradient point of f which is the first non trivial hilbert point of the milnor algebra of f is semistable we also prove that the induced morphism on the git quotients is finite and injective on the locus of stable forms our second result is that the associated form of f also known as the macaulay inverse system of the milnor algebra of f and which is apolar to the last non trivial hilbert point of the milnor algebra is git semistable whenever f is a smooth form these two results answer questions of alper and isaev