a nonparametric test for spatial isotropy using subsampling a common requirement for spatial modeling is the development of an appropriate correlation structure although the assumption of isotropy is often made for this structure it is not always appropriate a conventional practice when checking for isotropy is to informally assess plots of direction specific sample semi variograms although a useful diagnostic these graphical techniques are difficult to assess and open to interpretation formal alternatives to graphical diagnostics are valuable but have been applied to a limited class of models in this article we propose a formal approach to test for isotropy that is both objective and valid for a wide class of models this approach which is based on the asymptotic joint normality of the sample variogram can be used to compare sample variograms in multiple directions an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample variogram is derived and used to construct a test statistic a subsampling approach and a limiting

roughness in cayley graphs in this paper rough approximations of cayley graphs are studied and rough edge cayley graphs are introduced furthermore a new algebraic definition for pseudo cayley graphs containing cayley graphs is proposed and a rough approximation is expanded to pseudo cayley graphs in addition rough vertex pseudo cayley graphs and rough pseudo cayley graphs are introduced some theorems are provided from which properties such as connectivity and optimal connectivity are derived this approach opens new research fields such as data networks

rough ideals in semigroups abstract we shall introduce the notion of a rough left right two sided bi ideal in a semigroup which is an extended notion of a left right two sided bi ideal in a semigroup and give some properties of such ideals

a short note on some properties of rough groups it is a useful method in research of group theory to construct a new group by using known groups lower and upper approximation operators of rough sets are applied into group theory and so the notion of a rough group has been introduced in this paper we first point out that there are still some incomplete propositions in n kuroki p p wang the lower and upper approximations in a fuzzy group inform sci 90 1996 203 220 although some authors have showed several incorrect statements in the literature we then present improved versions of the incomplete propositions and continue to study the image and inverse image of rough approximations of a subgroup with respect to a homomorphism between two groups

fuzzy g congruences on a groupoid abstract the definition of a fuzzy reflexive relation on a set s is generalized by demanding that x y z z 0 for all x y z s fuzzy equivalence relations on a given set and fuzzy congruences on a given groupoid are studied under this generalized setting

rough set theory applied to fuzzy ideal theory we use covers of the universal set to define approximation operators on the power set of the given set in section 1 we determine basic properties of the upper approximation operator and show how it can be used to give algebraic structural properties of certain subsets we define a particular cover on the set of ideals of a commutative ring with identity in such a way that both the concepts of the fuzzy prime spectrum of a ring and rough set theory can simultaneously be brought to bear on the study of fuzzy ideals of a ring

some properties of fuzzy groups on definit des sous groupes flous normaux des sous groupes flous normaux de niveau et leurs homomorphismes et on donne certaines de leurs proprietes

fuzzy radicals and prime fuzzy ideals of ordered semigroups let s be an ordered semigroup a fuzzy subset of s is by definition an arbitrary mapping f s 0 1 where 0 1 is the usual interval of real numbers motivated by studying prime fuzzy ideals in rings semigroups and ordered semigroups and as a continuation of kehayopulu and tsingelis s works in ordered semigroups in terms of fuzzy subsets in this paper we introduce the notion of ordered fuzzy points of an ordered semigroup s and give a characterization of prime fuzzy ideals of an ordered semigroup s we also introduce the concepts of weakly prime fuzzy ideals completely prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of an ordered semigroup s and establish the relationship between the five classes of ideals furthermore we characterize weakly prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of s by their level ideals finally we introduce and investigate the fuzzy radicals of ordered semigroups by means of ordered fuzzy points and prove that the fuzzy radical of every completely semiprime fuzzy ideal of an ordered semigroup s can be expressed as the intersection of all weakly completely prime fuzzy ideals containing it as an application of the results of this paper the corresponding results of semigroups without order are also obtained

on the structure of rough prime primary ideals and rough fuzzy prime primary ideals in commutative rings this paper is a continuation of ideas presented by davvaz roughness in rings inform sci 164 2004 147 163 roughness based on fuzzy ideals inform sci 176 2006 2417 2437 we introduce the notions of rough prime primary ideals and rough fuzzy prime primary ideals in a ring and give some properties of such ideals also we discuss the relations between the upper and lower rough prime primary ideals and the upper and lower approximations of their homomorphism images

fuzzy relations and fuzzy groups abstract given a group s we consider fuzzy relations on s that is maps from s s into 0 1 of particular interest is to investigate conditions under which the fuzzy relation becomes a fuzzy subgroup on s s we prove that if is a fuzzy subset of s and is the strongest fuzzy relation on s that is a fuzzy relation on then is a fuzzy subgroup if and only if is a fuzzy subgroup a number of other results are obtained about the interrelationships between fuzzy relations on s including the weakest fuzzy relation and fuzzy subgroups on s s

affine processes a test of isotropy based on level sets the class of affine processes is defined as a reasonable alternative to test the null hypothesis that a given process is isotropic estimators for the affinity parameters based only on one level set of the observed process are provided and they are shown to be consistent under partial independence assumptions then asymptotic procedures are proposed to test the isotropy of a stationary process with parameter in bf r 2

on t congruence l relations on groups and rings in this paper we further study t congruence l relations on groups and rings and give the formulas for calculating the t congruence l relations generated by l relations where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l

fuzzy groups some group theoretic analogs abstract we introduce the concepts of 1 order of a fuzzy subgroup of a finite group 2 a fuzzy abelian group and 3 a fuzzy solvable group we obtain some results involving these notions which are analogs of results from group theory also we prove analogs of two basic theorems of group theory namely cayley s theorem and lagrange s theorem

fuzzy normal subgroups and fuzzy cosets abstract we introduce here the notion of 1 i a fuzzy normal subgroup and 2 ii a fuzzy coset we prove that for a group g a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of g further we show that the level subgroups of a fuzzy normal subgroup are all normal we obtain several results which are analogs of some basic theorems of group theory in particular a fuzzy version of lagrange s theorem is established

on fuzzy congruence of a near ring module the aim of this paper is to introduce fuzzy submodule and fuzzy congruence of an r module near ring module to obtain the correspondence between fuzzy congruences and fuzzy submodules of an r module to define quotient r module of an r module over a fuzzy submodule and to obtain correspondence between fuzzy congruences of an r module and fuzzy congruences of quotient r module over a fuzzy submodule of an r module

the join of fuzzy algebraic substructures of a group and their lattices this is a continuation of work in previous papers n ajmal and k v thomas fuzzy sets and systems 58 1993 217 inform sci 76 1994 1 here we provide a common technique of constructing the join of fuzzy substructures consequently it leads to the formation of various types of lattices and sublattices of fuzzy substructures of a group including those of normal and quasinormal fuzzy subgroups a lattice theoretic relationship of these sublattices is established moreover we present simple and direct proofs for the fact that the lattice of fuzzy normal subgroups is modular

rough 3 valued algebras rough set theory is an important tool for dealing with granularity and vagueness in information systems this paper studies a kind of rough set algebra the collection of all the rough sets of an approximation space can be made into a 3 valued lukasiewicz algebra we call the algebra a rough 3 valued lukasiewicz algebra in this paper we focus on the rough 3 valued lukasiewicz algebras which are a special kind of 3 valued lukasiewicz algebras firstly we examine whether the rough 3 valued lukasiewicz algebra is an axled 3 valued lukasiewicz algebra secondly we present the condition under which the rough 3 valued lukasiewicz algebra is also a 3 valued post algebra then we investigate the 3 valued post subalgebra problem of the rough 3 valued lukasiewicz algebra finally this paper studies the relationship between the rough 3 valued lukasiewicz algebra and the boolean algebra constructed by all the exact sets of the corresponding approximation space

construction of rough approximations in fuzzy setting in this paper two l rough approximation operators are defined by an arbitrary mapping from the set of all singletons to the set of all l sets which is a graded extension of jarvinen s method it also provides a convenient method to compute rough sets in fuzzy setting then the algebraic structure of rough sets and the relation to l topology are investigated in the end three special cases are discussed f is extensive symmetric and intensive

nonparametric estimation of the moments of a general statistic computed from spatial data abstract a statistic s is computed on spatially indexed data x i i d where d is a finite subset of the integer lattice z2 we propose a simple nonparametric method for estimating the moments e g variance skewness of s d using only the observed data at hand the method uses replicates of s computed on smaller subsets of d no explicit knowledge of the underlying spatial dependence mechanism is needed and the marginal distribution of x i may also be unknown the shape of d can be quite irregular and s is allowed to be a general statistic the proposed estimator is shown to be consistent and asymptotically normal under mild conditions on s d and mixing conditions on the strength of spatial dependence as a numerical example the estimator is used in assessing the geographic clumping of cancer deaths in the united states

the ϑ lower and t upper fuzzy rough approximation operators on a semigroup in this paper we consider a semigroup as a universal set and investigate the properties of q lower and t upper fuzzy rough approximation operators a new fuzzy algebraic structure called a tl fuzzy rough semigroup is introduced and some related properties are studied finally the homomorphism properties of q lower and t upper fuzzy rough approximation operators are investigated

distributivity in lattices of fuzzy subgroups the main goal of this paper is to study the finite groups whose lattices of fuzzy subgroups are distributive we obtain a characterization of these groups which is similar to a well known result of group theory

a short note on algebraic t rough sets our aim in this paper is to introduce the concept of a set valued homomorphism for groups which is a generalization of ordinary homomorphism then using the definitions of lower inverse and upper inverse we introduce the definition of uniform set valued homomorphism and prove that every set valued homomorphism is uniform finally the concept of probabilistic t rough set is defined

representation of lattices by fuzzy weak congruence relations fuzzy lattice valued weak congruences of abstract algebras are investigated for an algebra the family of all such fuzzy relations is a complete lattice its structure and cut properties are investigated and fully described these fuzzy weak congruences are applied in representation of complete and algebraic lattices a wider class of lattices can be represented in such a fuzzy framework than in classical algebra we prove that there is a straightforward representation of any complete lattice using it as a co domain in a more general case it is proved that several subdirect powers of lattices are also representable by fuzzy weak congruences

roughness in rings in this paper basic notions of the rough set theory will be given in fact the paper concerns a relationship between rough sets and ring theory we shall introduce the notion of rough subring resp ideal with respect to an ideal of a ring which is an extended notion of a subring resp ideal in a ring and we shall give some properties of the lower and the upper approximations in a ring

a kpss test for stationarity for spatial point processes we propose a formal method to test stationarity for spatial point processes the proposed test statistic is based on the integrated squared deviations of observed counts of events from their means estimated under stationarity we show that the resulting test statistic converges in distribution to a functional of a two dimensional brownian motion to conduct the test we compare the calculated statistic with the upper tail critical values of this functional our method requires only a weak dependence condition on the process but does not assume any parametric model for it as a result it can be applied to a wide class of spatial point process models we study the efficacy of the test through both simulations and applications to two real data examples that were previously suspected to be nonstationary based on graphical evidence our test formally confirmed the suspected nonstationarity for both data

fuzzy groups with sup property we investigate the inner structure of fuzzy subgroups with sup property we provide a characterization of this type of fuzzy subgroups in terms of their level subsets it is shown that the property of being a fuzzy subgroup with sup property is invariant under homomorphism and the homomorphic preimage of a fuzzy subgroup with sup property is also a fuzzy subgroup with sup property moreover we investigate the lattice structure of the class lnt of fuzzy normal subgroups of a group g each of which assumes the same value t at the identity of g it is proved that the subclass lnst of fuzzy subgroups with sup property of lnt constitutes a sublattice of lnt the modularity of lnst is derived as a consequence of the modularity of lnt

the lower and upper approximations in a hypergroup this paper presents a relationship between rough sets and hypergroup theory we analyze the lower and upper approximations of a subset with respect to an invertible subhypergroup and we consider some particular situations moreover the notion of a rough subhypergroup is introduced finally fuzzy rough subhypergroups are introduced and characterized

a framework for consistent prediction rules based on markers summary recently interest has developed regarding the statistical properties and uses of marker processes in the context of the analysis of failure time data or survival analysis a marker process is a stochastic process that acts as a time dependent covariate that is internal to the unit under study in the language of kalbfleisch prentice 1980 as such the sample path of the process up to a certain point in time may carry information about the subsequent hazard for failure uses of marker processes in the analysis of survival data are manifold here we consider the specific area of prediction of future failure times at a point in time based on various forms of information about the history of the marker process we provide a stochastic framework for the consideration of prediction functions demonstrate a simple consistency condition that such functions should satisfy and discuss construction of prediction functions in a general sense several examples are used to illustrate the ideas and we show that certain recently suggested imputation schemes fail to meet the consistency condition the consistency condition also elucidates the model assumed by cox 1983 in his work on surrogate responses we also briefly consider a closely related backward prediction problem

roughness based on fuzzy ideals the theory of rough set proposed by pawlak and the theory of fuzzy set proposed by zadeh are complementary generalizations of classical set theory many sets are naturally endowed with two binary operations addition and multiplication one concept which does this is a ring this paper concerns a relationship between rough sets fuzzy sets and ring theory it is a continuation of ideas presented by kuroki and wang n kuroki p p wang the lower and upper approximations in a fuzzy group inform sci 90 1996 203 220 we consider a ring as a universal set and we assume that the knowledge about objects is restricted by a fuzzy ideal in fact we apply the notion of fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring some characterizations of the above approximations are made and some examples are presented

rough sets induced by ideals in lattices this paper is to study the rough sets within the context of lattices we study the special properties of the rough sets which can be constructed by means of the congruences determined by ideals of lattice also the properties of the generalized rough sets with respect to ideals of lattice are investigated finally we give an example of their application in formal concept analysis

pawlak s approximations in γ semihypergroups the c semihypergroup is a generalization of a semigroup a generalization of a semihypergroup and a generalization of a c semigroup in this paper we discuss the roughness of c subsemihypergroups and c hyperideals bi c hyperideals in c semihypergroups in addition we consider rough sets with respect to the idempotent regular relations in a quotient c semihypergroup the upper approximations with respect to green s equivalence relations are derived in the context of c subsemihypergroups and c hyperideals

notes on the lower and upper approximations in a fuzzy group and rough ideals in semigroups in this note we show by examples that propositions 2 4 and 2 5 in n kuroki p p wang the lower and upper approximations in a fuzzy group information sciences 90 1996 203 and theorem 2 5 in n kuroki rough ideals in semigroups information sciences 100 1997 139 are incorrect and offer their modified versions c 2007 elsevier inc all rights reserved

reference points and roughness in this paper we introduce the notion of a reference point and provide local approximations for a subset of the universe the notion of a reference point naturally gives rise to a rough approximations framework wherein several approximations are possible on the same set also we present an extension to the decision theoretic rough set model by using reference points

roughness in modules the theory of rough sets was proposed by pawlak in 1982 the relations between rough sets and algebraic systems have been already considered by many mathematicians important algebraic structures are groups rings and modules rough groups and rough rings have been investigated by biswas and nanda kuroki and wang and davvaz in this paper we consider an r module as a universal set and we introduce the notion of rough submodule with respect to a submodule of an r module which is an extended notion of a submodule in an r module we also give some properties of the lower and the upper approximations in an r module

t type regular l relations on a complete brouwerian lattice abstract in this paper using a general infinitely distributive t norm t on a complete brouwerian lattice l we introduce the concept of t type regular l relations study some basic properties of them and give out some methods of calculating the maximal t type generalized inverse l relations of t type regular l relations

a multistate markov chain model for longitudinal categorical quality of life data subject to non ignorable missingness summary quality of life qol is an important outcome in clinical research particularly in cancer clinical trials typically data are collected longitudinally from patients during treatment and subsequent follow up missing data are a common problem and missingness may arise in a non ignorable fashion in particular the probability that a patient misses an assessment may depend on the patient s qol at the time of the scheduled assessment we propose a markov chain model for the analysis of categorical outcomes derived from qol measures our model assumes that transitions between qol states depend on covariates through generalized logit models or proportional odds models to account for non ignorable missingness we incorporate logistic regression models for the conditional probabilities of observing measurements given their actual values the model can accommodate time dependent covariates estimation is by maximum likelihood summing over all possible values of the missing measurements we

the fuzzy normal subgroup using the concept of fuzzy spaces we define the fuzzy normal subgroup in a fuzzy group its relation with the classical fuzzy normal subgroup is studied

moment estimation for statistics from marked point processes in spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations in other words the data form a realization of a marked point process in this paper we formulate subsampling estimators of the moments of general statistics computed from marked point process data and we establish their l 2 consistency the variance estimator in particular can be used for the construction of confidence intervals for estimated parameters a practical data based method for choosing a subsampling parameter is given and illustrated on a data set finite sample simulation examples are also presented

on rough set and fuzzy sublattice let l be a lattice with the least element 0 and the greatest element 1 and let be a full congruence relation on l in this paper the notion of upper and lower approximations of a fuzzy subset of l is introduced and some important properties will be studied

models for variable stress accelerated life testing experiments based on wiener processes and the inverse gaussian distribution variable stress accelerated life testing trials are experiments in which each of the units in a random sample of units of a product is run under increasingly severe conditions to get information quickly on its life distribution we consider a fatigue failure model in which accumulated decay is governed by a continuous gaussian process w y whose distribution changes at certain stress change points to t l t k continuously increasing stress is also considered failure occurs the first time w y crosses a critical boundary the distribution of time to failure for the models can be represented in terms of time transformed inverse gaussian distribution functions and the parameters in models for experiments with censored data can be estimated using maximum likelihood methods a common approach to the modeling of failure times for experimental units subject to increased stress at certain stress change points is to assume that the failure times follow a distribution that consists of segments of weib

the lower and upper approximations in a quotient hypermodule with respect to fuzzy sets this paper provides a continuation of ideas presented by davvaz and mahdavipour b davvaz m mahdavipour roughness in modules inform sci 176 2006 3658 3674 the notion of hypermodule is a generalization of the notion of module in this paper we consider the quotient hypermodule m a and interpret the lower and upper approximations as subsets of the quotient hypermodule m a then we introduce the concept of quotient rough sub hypermodule also using the concept of fuzzy sets we introduce and discuss the concept of fuzzy rough hypermodules and then we obtain the relation between fuzzy rough sub hypermodules and level rough sets this relation is characterized as a necessary and sufficient condition

the cylindrical k function and poisson line cluster point processes the analysis of point patterns with linear structures is of interest in many applications to detect anisotropy in such patterns in particular in the case of a columnar structure we introduce a functional summary statistic the cylindrical k function which is a directional k function whose structuring element is a cylinder we further introduce a class of anisotropic cox point processes called poisson line cluster point processes the points of such a process are random displacements of poisson point processes defined on the lines of a poisson line process parameter estimation for this model based on moment methods or bayesian inference is discussed in the case where the underlying poisson line process is latent to illustrate the proposed methods we analyse two and three dimensional point pattern datasets the three dimensional dataset is of particular interest as it relates to the minicolumn hypothesis in neuroscience which claims that pyramidal and other brain cells have a columnar arrangement perpendicular to the surface of the brain

θ t fuzzy rough approximation operators and the tl fuzzy rough ideals on a ring in this paper we consider a ring as a universal set and study t fuzzy rough approximation operators with respect to a tl fuzzy ideal of a ring first some new properties of generalized t fuzzy rough approximation operators are obtained then a new fuzzy algebraic structure tl fuzzy rough ideal is defined and its properties investigated and finally the homomorphism of t fuzzy rough approximation operators is studied

a complete study of the lattices of fuzzy congruences and fuzzy normal subgroups in this paper we introduce the concepts of t fuzzy congruences and t fuzzy equivalences using these ideas we investigate completely on one hand the lattice structures of the set of fuzzy equivalence relations on a group and the set of fuzzy congruences and on the other hand the lattice structures of the set of fuzzy subgroups and fuzzy normal subgroups our study reveals some finer and interesting facts about these lattices it is proved among other results that the set ct of all t fuzzy congruences of a group g forms lattice and also the set lnt of all those fuzzy normal subgroups which assume the same value t at e the identity of g forms a lattice as an important result we prove that the lattices ct and lnt are isomorphic it is also shown that the lattices ct and lnt are modular moreover we construct various important sublattices of the lattice ct and exhibit their relationship by lattice diagrams in the process we improve and unify many results of earlier authors on fuzzy congruences

a model for markers and latent health status summary we extend the bivariate wiener process considered by whitmore and co workers and model the joint process of a marker and health status the health status process is assumed to be latent or unobservable the time to reach the primary end point or failure death onset of disease etc is the time when the latent health status process first crosses a failure threshold level inferences for the model are based on two kinds of data censored survival data and marker measurements covariates such as treatment variables risk factors and base line conditions are related to the model parameters through generalized linear regression functions the model offers a much richer potential for the study of treatment efficacy than do conventional models treatment effects can be assessed in terms of their influence on both the failure threshold and the health status process parameters we derive an explicit formula for the prediction of residual failure times given the current marker level also we discuss model validation this model does not require the proportional hazards assumption and hence can be widely used to demonstrate the usefulness of the model we apply the methods in analysing data from protocol 116a of the aids clinical trials group

fuzzy congruences on inverse semigroups abstract we introduce the notion of a quotient semigroup s induced by a fuzzy congruence relation on a semigroup s and give homomorphism theorems with respect to the fuzzy congruence we also introduce the notion of an idempotent separating fuzzy congruence a group fuzzy congruence on inverse semigroups and give some of their properties on inverse semigroups

roughness in n ary hypergroups this paper is aimed at studying the rough sets within the context of the commutative n ary hypergroups for this approach the presentation of a detailed study of the various types of n ary subhypergroups is of the greatest importance this study was initiated in v leoreanu fotea several types of n ary subhypergroups italian journal of pure and applied mathematics in press subsequently we shall use the findings in this study to define the upper and lower approximation of a subset with respect to an invertible n ary subhypergroup of a commutative n ary hypergroup in the final part the concept of n ary rough subhypergroup is introduced

assessing isotropy for spatial point processes summary a common assumption while analyzing spatial point processes is direction invariance i e isotropy in this article we propose a formal nonparametric approach to test for isotropy based on the asymptotic joint normality of the sample second order intensity function we derive an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample second order intensity function and use this to construct a test statistic with a 2 limiting distribution we demonstrate the efficacy of the approach through simulation studies and an application to a desert plant data set where our approach confirms suspected directional effects in the spatial distribution of the desert plant species

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

rough set theory applied to lattice theory in this paper we intend to study a connection between rough sets and lattice theory we introduce the concepts of upper and lower rough ideals filters in a lattice then we offer some of their properties with regard to prime ideals filters the set of all fixed points compact elements and homomorphisms

a thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns when modeling inhomogeneous spatial point patterns it is of interest to fit a parametric model for the first order intensity function foif of the process in terms of some measured covariates estimates for the regression coefficients say can be obtained by maximizing a poisson maximum likelihood criterion little work has been done on the asymptotic distribution of except in some special cases in this article we show that is asymptotically normal for a general class of mixing processes to estimate the variance of we propose a novel thinned block bootstrap procedure that assumes that the point process is second order reweighted stationary to apply this procedure only the foif and not any high order terms of the process needs to be estimated we establish the consistency of the resulting variance estimator and demonstrate its efficacy through simulations and an application to a real data example

dominance based rough set approach and knowledge reductions in incomplete ordered information system many methods based on the rough set to deal with incomplete information systems have been proposed in recent years however they are only suitable for the incomplete systems with regular attributes whose domains are not preference ordered this paper thus attempts to present research focusing on a complex incomplete information system the incomplete ordered information system in such incomplete information systems all attributes are considered as criterions a criterion indicates an attribute with preference ordered domain to conduct classification analysis in the incomplete ordered information system the concept of similarity dominance relation is first proposed two types of knowledge reductions are then formed for preserving two different notions of similarity dominance relations with introduction of the approximate distribution reduct into the incomplete ordered decision system the judgment theorems and discernibility matrixes associated with four novel approximate distribution reducts are obtained a numerical example is employed to substantiate the conceptual arguments

variance estimation for statistics computed from spatial lattice data summary a statistic s is computed on spatially indexed data x i e d where d is a finite subset of the integer lattice 22 we propose a method for estimating the variance and other moments of s by using only the data the set d may be irregularly shaped the statistic s may be arbitrarily complicated and no distributional assumptions marginal or joint are necessary the method uses the statistic computed on overlapping subshapes of d as replicates of s the estimator is simply the sample variance of the standardized replicates we demonstrate c2 consistency of the estimator under mild conditions on s and the strength of spatial dependence a rate of convergence is also given giving guidance into the appropriate choice of subshape size and the estimator is illustrated in two data examples

the lattice of fuzzy normal subgroups is modular abstract we have introduced and discussed in a recent paper 2 various sublattices such as lf lt and lfnt of the lattice l of fuzzy subgroups of a given group in particular we proved that the sublattice lfn of fuzzy normal subgroups with finite range and tip t is a modular sublattice of l here we remove all the restrictions on the choice of fuzzy normal subgroups and prove that the class of all fuzzy normal subgroups ln forms the modular sublattice of l as a tool we prove an important result that the fuzzy subgroups generated by a pair of fuzzy normal subgroups of a group is fuzzy normal

generalized rough sets over fuzzy lattices this paper studies generalized rough sets over fuzzy lattices through both the constructive and axiomatic approaches from the viewpoint of the constructive approach the basic properties of generalized rough sets over fuzzy lattices are obtained the matrix representation of the lower and upper approximations is given according to this matrix view a simple algorithm is obtained for computing the lower and upper approximations as for the axiomatic approach a set of axioms is constructed to characterize the upper approximation of generalized rough sets over fuzzy lattices

generalized fuzzy quotient subgroups abstract in this paper we consider the fuzzy subgroup of a given group defined by generalized triangular norms and conorms introduced by yager 1986 the definitions of a anti fuzzy subgroup and a anti pseudo fuzzy subgroup are reviewed then a generalized fuzzy cayley theorem as well as a partial generalization of fuzzy lagrange theorem are given also a unified approach for studying fuzzy quotient subgroups is discussed some correspondence theorems for several kinds of fuzzy subgroups are proved and examples of generalized triangular norms conorms are given

the product structure of fuzzy rough sets on a group and the rough t fuzzy group in this paper we study the product structures of rough fuzzy sets on a group we also propose the notions of t rough fuzzy subgroups in a group with respect to a t fuzzy normal subgroup and study their properties

the lower and upper approximations in a fuzzy group in this paper we shall introduce the notion of a rough subgroup with respect to a normal subgroup of a group and give some properties of the lower and the upper approximations in a group also we will discuss a rough subgroup with respect to a t level subset of a fuzzy normal subgroup

fuzzy subgroups some characterizations the notion of a fuzzy set was first introduced in 1965 by zadeh 12 since then the theory of fuzzy sets has gone through remarkably rapid strides with well over 4000 papers by now see for example the bibliography 3 several textbooks for example 2 and 6 and an international journal solely devoted to it s the theory has found wideranging applications in such diverse fields as automata control theory decision theory and social behavior pattern studies to name just a few for an interesting expository account see rosenfeld lo and also the book review 7 in 9 rosenfeld introduced the notion of a fuzzy group and showed that many concepts of group theory can be extended in an elementary manner to develop the theory of fuzzy groups in particular he characterized all the fuzzy subgroups of cyclic groups of prime order 9 proposition 5 101 fuzzy groups were further investigated by das in 1 where he characterized all the fuzzy subgroups of finite cyclic groups l theorem 4 21 in this connection he introduced the notion of level subgroups of a fuzzy subgroup which is based on the notion of a level subset introduced earlier by zadeh for a finite group das showed that these level subgroups of a fuzzy subgroup form a chain 1 corollary 3 11 and also constructed a fuzzy subgroup whose chain of level subgroups is maximal in the following special cases when the group is i a direct product of cyclic groups of prime orders ii abelian l theorem 3 41 we analyze the level subgroups of a fuzzy subgroup in more detail and investigate whether the family of level subgroups of a fuzzy subgroup deter

generalized lower and upper approximations in a ring in this paper the concepts of set valued homomorphism and strong set valued homomorphism of a ring are introduced and related properties are investigated the notions of generalized lower and upper approximation operators constructed by means of a set valued mapping which is a generalization of the notion of lower and upper approximation of a ring are provided we also propose the notion of generalized lower and upper approximations with respect to an ideal of a ring which is an extended notation of rough ideal introduced lately by davvaz b davvaz roughness in rings information science 164 2004 147 163 in a ring and discuss some significant properties of them

a semi parametric threshold regression analysis of sexually transmitted infections in adolescent women time to event analysis of sexually transmitted infection data is often complicated by the existence of nonproportional hazards and nonlinear independent variable effects methods without the proportional hazards assumption such as threshold regression models have been successfully used in many applications this paper seeks to extend the existing threshold regression models to accommodate the nonlinear independent variable effects specifically we incorporated penalized and regression splines to the threshold regression models for added modeling flexibility cross validation methods were used for the selection of the number of knots and for the determination of smoothing parameters variance estimates were proposed for inference purposes simulation results showed that the proposed methods were able to achieve nonparametric function and parametric coefficient estimates that are close to their true values simulation also demonstrated satisfactory performance of variance estimates using the proposed methods we analyzed time from sexual debut to the first infection with chlamydia trachomatis infection in a group of young women analysis shows that the lifetime number of sexual partners has a nonlinear effect on the risk of c trachomatis infection and the infection risks were differential by ethnicity and age of sexual debut

fuzzy congruences and fuzzy normal subgroups abstract a complete description of the congruences on a group in terms of its normal subgroups can be seen in papers by a rosenfeld and w j howie in this paper we shall introduce the concept of fuzzy congruences on a groupoid and a group and characterize fuzzy congruences on a group in terms of fuzzy normal subgroups

on sample reuse methods for dependent data we suggest a sample reuse method for dependent data based on a cross between the block bootstrap and richardson extrapolation instead of simulating a same size resample by resampling blocks and placing them end to end it analyses the blocks directly and employs a variant of richardson extrapolation to adjust for block size a simple empirical rule also based on richardson extrapolation is suggested for empirically selecting the block size performance in the contexts of distribution and bias estimation is discussed via theoretical analysis and numerical simulation

fuzzy rees congruences on semigroups fuzzy congruences on semigroups and groups have been introduced and studied by samhan 1993 and samhan and ahsanullah 1994 among others here we introduce fuzzy rees congruences on semigroups and fuzzy rees congruences semigroups using these ideas we establish a relation between fuzzy ideals of a semigroup s and fuzzy ideals of a quotient semigroup of s as an important result we prove that the lattice of all fuzzy congruences on a fuzzy congruences semigroup is a distributive lattice moreover we obtain that a homomorphic image of a fuzzy rees congruences semigroup is a fuzzy rees congruences semigroup as well

using threshold regression to analyze survival data from complex surveys with application to mortality linked nhanes iii phase ii genetic data the cox proportional hazards ph model is a common statistical technique used for analyzing time to event data the assumption of ph however is not always appropriate in real applications in cases where the assumption is not tenable threshold regression tr and other survival methods which do not require the ph assumption are available and widely used these alternative methods generally assume that the study data constitute simple random samples in particular tr has not been studied in the setting of complex surveys that involve 1 differential selection probabilities of study subjects and 2 intracluster correlations induced by multistage cluster sampling in this paper we extend tr procedures to account for complex sampling designs the pseudo maximum likelihood estimation technique is applied to estimate the tr model parameters computationally efficient taylor linearization variance estimators that consider both the intracluster correlation and the differential selection probabilities are developed the proposed methods are evaluated by using simulation experiments with various complex designs and illustrated empirically by using mortality linked third national health and nutrition examination survey phase ii genetic data

operator domains on fuzzy groups abstract the fuzzy subgroups of a group which are invariant under various operator domains are studied in particular the classes of all inner automorphisms automorphisms and endomorphisms are applied on the fuzzy subgroups of a group as a consequence two distinct partitions of a group which are successively coarser than the family of all conjugate classes are discovered

fuzzy subgroup some characterizations ii abstract we consider an analysis of fuzzy subgroups in terms of the corresponding family of level subgroups given a finite chain of subgroups of a group g we prove that there exists a fuzzy subgroup of g whose level subgroups are exactly the subgroups of this chain as a corollary we obtain an interpretation of the number of chains of subgroups of a group g in which a subgroup h is a member when the group g is a supersolvable group some further interpretation of this number is obtained