particle lattices and fuzzy particle lattices abstract this paper introduces several new concepts a particle in a lattice which is a generalization of an atom in a distributive lattice by weakening the minimality property of atom a particle lattice which is a generalization of distributive complete atomic lattices by replacing atoms by particles a fuzzy particle lattice a particle lattice with an order reversing involution a particulate boolean algebra a fuzzy particle lattice whose involution is a complementation operator and other related concepts points fuzzy points boundary points and boundary quasi points the paper establishes representation theorems for fomse of these concepts establishes connections between others and some well established lattice theoretic concepts and provides some elementary properties for some of the new concepts

shrinkage estimators applied to prediction of french winter wheat yield summary the paper shows that it is possible to pool departmental information to predict regional wheat yield in an msep mean squared error of prediction context shrinkage estimation in linear agrometeorological models improves regional prediction cross validation is not precise enough to enable comparison between models the authors calculate the msep using the hypothesis of a multinormal distribution in simple cases the distribution parameters are estimated with data input and simulations are used for complex cases stein like estimators are shown to be a superior alternative to the conventional estimators usually applied for prediction

fuzzy nets and their application fuzzy net theory is enriched by the introduction of the fuzzy net of fuzzy sets the limsup liminf and limit of a fuzzy net of fuzzy sets are defined and their various properties are discussed alternative characterizations based on the notion of a fuzzy net are provided for several fuzzy topological concepts including open and closed fuzzy sets fuzzy continuity maps with closed fuzzy graph open fuzzy mapping etc thus the net theoretic approach is shown to be a promising tool in fuzzy topology

bootstrapping regression models the regression and correlation models are considered it is shown that the bootstrap approximation to the distribution of the least squares estimates is valid and some error bounds are given

fµ strongly semiopen sets fµ strong semicontinuity and fµ strongly semiretracts throughout the literature if x d is an f ts and y x the induced f topological subspace y d y is defined so that d y n g y n d macho stadler and de prada vicente fuzzy sets and systems 58 1993 365 introduced a new concept of f topological subspaces which coincides with the usual definition in the case that m g y also they introduced the concepts of f m open sets and f m continuity in this paper using the previous concepts we introduce weaker forms of f m open sets and f m continuity the notion of an f retract was introduced by rodabough j math anal appl 79 1981 273 here we introduce the notion of a f m retract and weaker forms of it the basic properties of these notions are given many results are obtained

some results on fuzzy supratopological spaces abstract in this note we study some results on the concepts of supracompactness and supracompactness in a fuzzy supratopological space we introduce the notions of hausdorffnessand lindelofness in a fuzzy supratopological space and characterize their properties interms of supracompactness we also introduce and study the concept of fuzzy supra regular space

connectedness on fuzzy topological spaces in this paper properties of connectedness on completely distributive topological lattices definition 2 1 and fuzzy topological spaces 1 are studied some equivalent propositions on the concepts of functions in completely distributive lattices and connected elements in completely distributive lattices and fuzzy topological spaces are proved specially connectedness is characterized both by the r neighborhoods of molecules and c separations for any family li i i i of fuzzy topological spaces the product 1 is connected iff every li i is connected a continuous function maps connected elements onto connected ones the connectedness on the fuzzy real line r l is discussed in the last section as an important example the intervals defined here definition 4 1 must be connected in the fuzzy real line r l and so the intervals defined by rodabaugh in 13 are too any connected element is connected in the fuzzy real line r l if and only if r l r

on fuzzy t1 topological spaces on etudie diverses relations entre les differentes definitions des espaces topologiques t 1 flous

mean squared error of prediction in models for studying ecological and agronomic systems the mean squared error of prediction msep as a criterion for evaluating models used for studying ecological and agronomic systems is considered it is shown that the different sources of error that have been discussed in the literature for such models can be rigorously defined in terms of the msep a situation that occurs frequently for such models is that the model parameters are determined independently of data used to test the model and the population of interest is structured in subpopulations it is shown that in this case obtaining estimators of msep and of the individual error contributions can be reduced to the classic problem of estimating components of variance in a oneway random model for comparison the case where the parameters are estimated from the same data used to test the model is also addressed here

on inductive dimensions for fuzzy topological spaces an approach to the dimension theory for fuzzy topological spaces is being developed the appropriate context for this theory is not the category cft of chang fuzzy topological spaces or some of its modifications but the category hut introduced in the paper this category is a slight extension of the category h of hutton fuzzy topological spaces hutton 1980 the frames of this category allow us to make exposition simple and uniform and on the other hand to make it applicable in quite a general setting

on induced fuzzy topological spaces the concept of induced fuzzy topological spaces was introduced by weiss 11 subsequently lowen 2 31 defined two mappings o and i which established the relationship between fuzzy topological spaces and topological spaces and proved some deeper results on induced fuzzy topological spaces since then several other authors continued the investigation of such spaces in this paper we will use the decomposition theorem for fuzzy sets to simplify the proofs of some theorems due to lowen and discuss the closure and interior operators separability ci c and separation properties of induced fuzzy topological spaces

two nonparametric methods for identifying the impulse response of linear systems this paper addresses the problem of impulse response identification using nonparametric methods although the techniques developed herein apply to the truncated untruncated and circulant models we focus on the truncated model which is useful in certain applications two methods of impulse response identification will be presented the first is based on the minimization of the c l statistic which is an estimate of the mean square prediction error the second is a bayesian approach for both of these methods we consider the effects of using both the identity matrix and the laplacian matrix as weights on the energy in the impulse response in addition we present a method for estimating the effective length of the impulse response estimating the length is particularly important in the truncated case finally we develop a method for estimating the noise variance at the output which is needed in the approach involving the c l statistic often prior information on the noise variance is not available and a good estimate is crucial to the success of estimating the impulse response with a nonparametric technique

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

estimators of the mean squared error of prediction in linear regression if a linear regression model is used for prediction the mean squared error of prediction msep measures the performance of the model the msep is a function of unknown parameters and good estimates of it are of interest this article derives a best unbiased estimator and a minimum mse estimator under the assumption of a normal distribution it compares the bias and the mse of these estimators and some others similar results are presented for the case in which the model is used to estimate values of the response function

estimating the error rate of a prediction rule improvement on cross validation abstract we construct a prediction rule on the basis of some data and then wish to estimate the error rate of this rule in classifying future observations cross validation provides a nearly unbiased estimate using only the original data cross validation turns out to be related closely to the bootstrap estimate of the error rate this article has two purposes to understand better the theoretical basis of the prediction problem and to investigate some related estimators which seem to offer considerably improved estimation in small samples

on fuzzy topological spaces abstract in this paper a few separation properties and some aspects of subspace fuzzy topology have been studied where both the crisp and the fuzzy elements have been taken into consideration since the conventional definition of compactness is not quite meaningful in hausdorff fuzzy spaces as introduced by us a new more natural definition of proper compactness is given and a few properties resulting from this are established

a very singular solution for the slow diffusion equation with nonlinear convection abstract we here investigate an existence and uniqueness of the nontrivial nonnegative solution of a nonlinear ordinary differential equation f m r f f f q 0 satisfying a specific decay rate lim r r f r 0 with 1 2 q m 1 and q m 2 q m 1 here m 1 m q m 1 and 1 or 1 such a solution arises naturally when we study a very singular solution for a slow diffusion equation with nonlinear convection u t u m x x u q x defined either on the whole real line or on the half line 0

a comparison of some hausdorff notions in fuzzy topological spaces abstract several different notions of the hausdorff separation property for fuzzy topological spaces have appeared in the literature this paper is a study of the relationships between 12 of these concepts

representation theorem of fuzzy lattices and its applications in fuzzy topology abstract a fuzzy lattice is expressed as a direct product of all its minimal fuzzy sublattices and a pointwise characterization of fuzzy complete regularity is proved

functions and as closedness in fuzzy topological spaces abstract in this paper we discuss s closedness in fuzzy topological spaces and we give some characterizations of s closedness also we investigate the image and the inverse image of s closed spaces under some types of functions and we improve and generalize some results on s closed spaces in fuzzy setting

on the goodness of some types of fuzzy paracompactness abstract we introduce in fuzzy topological spaces definitions of paracompactness almost paracompactness and nearly paracompactness all of which turn out to be good extensions of their classical topological counterparts fuzzy semi paracompact para s closed weakly compact and rs paracompact spaces are treated to a similar approach

fuzzy path and fuzzy connectedness abstract this paper discusses fuzzy connectedness in fuzzy topology zadeh s classical paper 1 has introduced the fundamental concept of a fuzzy set upon which the foundation of fuzzy mathematics rests the theory of fuzzy topology is a branch of such mathematics our purpose is to introduce some basic concepts as fuzzy path fuzzy path connected set locally fuzzy path connected set in the fuzzy topological spaces and to prove some fundamental properties related to fuzzy connectedness

on decomposition of proper compactness in fuzzy topological spaces on introduit les notions de 2 compacite et de metacompacite floue pour des espaces topologiques flous et on demontre le theoreme suivant un espace topologique flou x est proprement compact si et seulement si il est 2 compact et metacompact flou

order homomorphisms on fuzzes abstract in this paper basic properties of the concept of order homomorphisms on fuzzes 4 which is a proper generalization of the concept of fuzz functions 1 are studied conditions for fuzz functions to be functions of zadeh s type are obtained moreover the concepts of continuous closed and open order homomorphisms are introduced and studied

large time behavior for a porous medium equation in a nonhomogeneous medium with critical density abstract we study the large time behavior of solutions to the cauchy problem for the porous medium equation in nonhomogeneous media with critical singular density x 2 t u u m in r n 0 where m 1 and n 3 with nonnegative initial condition u x 0 u 0 x 0 the asymptotic behavior proves to have some interesting and striking properties we show that there are different asymptotic profiles for the solutions depending on whether the continuous initial data u 0 vanishes at x 0 or not moreover when u 0 0 0 we show the convergence towards a peak type profile presenting a jump discontinuity coming from an interesting asymptotic simplification to a conservation law while when u 0 0 0 the limit profile remains continuous these phenomena illustrate the strong effect of the singularity at x 0 we improve the time scale of the convergence in sets avoiding the singularity on the way we also study the large time behavior for a porous medium equation with convection which is interesting for itself

on a topological model for the category of fuzzy topological spaces i we study global properties of fuzzy topological spaces which depend only on open sets fuzzy continuous functions and the relations we obtain many known theorems as purely topological theorems

fuzzy addition in the l fuzzy real line abstract under the hypothesis l is a chain we construct a binary operation on the l fuzzy real line r l which reduces to the usual addition on r if is restricted to the embedded image of r in r l which yields a partially ordered abelian cancellation semigroup with identity and which is jointly fuzzy continuous on r l we show is unique i e it is the only extension of addition to r l which is consistent we study the relationship between and other fuzzy continuous extensions of the usual addition we also show that fuzzy translation is a weak fuzzy homeomorphism and under certain conditions a fuzzy homeomorphism

a categorical accommodation of various notions of fuzzy topology different definitions of fuzzy topology have been stated and developed in the literature but have not been satisfactorily related to each other and to ordinary topology to remedy this a new fuzzy topological category fuzz is defined it is a significant generalization of previous definitions it is the simplest setting yet constructed into which ordinary topology and these previous definitions may be placed by identifying each with a different subcategory of fuzz it therefore allows us to conveniently analyze the relative merits of previous definitions give coherence to known results and indicate appropriate directions for future development and it generates and may be viewed as both including and included in categories of fuzzy topological spaces which exhibit higher order fuzziness