a unifying study between modal like operators topologies and fuzzy sets the paper presents the essential connections between modal like operators topologies and fuzzy sets we show for example that each fuzzy set determines a preorder and an alexandrov topology and that similar correspondences hold also for the other direction further a category for preorder based fuzzy sets is defined and it is shown that its equivalent subcategory of representatives is isomorphic to the categories of preordered sets and alexandrov spaces moreover joins meets and complements for the objects in this category of representatives are determined this suggests how to define for fuzzy subsets of a certain universe the lattice operations in a canonical way

order based dependent dirichlet processes in this article we propose a new framework for bayesian nonparametric modeling with continuous covariates in particular we allow the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick breaking representation we focus mostly on the class of random distributions that induces a dirichlet process at each covariate value we derive the correlation between distributions at different covariate values and use a point process to implement a practically useful type of ordering two main constructions with analytically known correlation structures are proposed practical and efficient computational methods are introduced we apply our framework through mixtures of these processes to regression modeling the modeling of stochastic volatility in time series data and spatial geostatistical modeling

partial ordering in l underdeterminate sets abstract the purpose of this paper is to improve results on fuzzy partial orderings obtained by zadeh in 9 we overcome the difficulties connected with the axioms of antisymmetry and linearity moreover if the underlying lattice l is a complete residuated lattice we establish a szpilrajn theorem i e any l fuzzy partial ordering has a linear extension in opposition to zadeh s our point of view is that an axiom of antisymmetry without a reference to a concept of equality is meaningless therefore we first introduce the category lus cf 2 which can be considered as a mathematical model of fuzzy equality and subsequently we specify the axioms of l fuzzy partial orderings with respect to the frame given by lus the axioms we use clearly display the usefulness of having a zadeh like complementation and as a consequence the usefulness of a positivistic and nonintuitionistic frame of study an example concerning l rn which we give clearly shows that the lus version of the szpilrajn theorem cannot be reduced to a fuzzification of an already existing theorem but provides us with additional information

implication structures fuzzy subsets and enriched categories we show that there are natural ways to make a fuzzy set into an enriched category and that in doing so some basic results in fuzzy set theory are applications of enriched category theory thus we argue that the theory of enriched categories is a useful tool for fuzzy set theorists

enriched categories and many valued preorders a question from programming arises if bitstring x compares with bitstring y to some degree and if bitstring y satisfies predicate a to some degree then how should the possibility be mathematically modeled that bitstring x satisfies predicate a to at least some degree related to both and mathematically modeling this question is surprisingly intricate when the underlying conjunctions e g of predicates are non commutative potential applications of this question occur in data mining a field in which pattern matching is important and commonly used this paper uses ideas from enriched categories over monoidal categories to address such issues and enable pattern matching techniques to extend to many valued contexts equipped with non commutative conjunctions first we consider the notion of a set enriched by a po monoid l which turns out to be a set equipped with an l valued preorder second we extend the notion of enriched functors to formulate the appropriate definition of variable basis morphisms between preordered sets over different lattice theoretic bases third we construct the notion of topological systems enriched with many valued preorders and use their extent spaces to motivate and formulate enriched or preordered topological spaces the compatibility or enrichment axioms for such systems and spaces model the programming question stated above using non commutative tensor products en route are determined a number of related notions and results many valued antisymmetry characterizes the l t0 separation axiom many valued preorders are categorically topological and many valued partial orders are monotopological enriched topological spaces form a topological category a large inventory of example classes is provided including programming examples and an extensive discussion of examples based on the l spectra of complete po groupoids and each of these related developments is provided a suitable lattice theoretic and categorical foundation

triangular norms position paper ii general constructions and parameterized families this second part out of three of a series of position papers on triangular norms for part i see triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press deals with general construction methods based on additive and multiplicative generators and on ordinal sums also included are some constructions leading to non continuous t norms and a presentation of some distinguished families of t norms

closedness of the category of liminf complete fuzzy orders it is shown that the category of liminf complete fuzzy orders and liminf continuous maps valued in the complete residuated lattice based on a continuous t norm on the unit interval is monoidal closed and that this category is cartesian closed if and only if the t norm is the minimum

the categorical topology approach to fuzzy topology and fuzzy convergence it is the purpose of this paper to have a look at fuzzy topology from the point of view of categorical topology we first look at interesting subcategories of fts and determine whether they are bireflective and or coreflective we also describe the set of all subcategories of fts which are at the same time bireflective and coreflective due to the fact that top is one of these subcategories of fts ffs itself can be neither cartesian closed nor extensional we therefore secondly construct a supercategory of bts which is a topological quasitopos the construction of this quasitopos is based on the theory of convergence in fts

almost periodic higher order statistic estimation in this paper stochastic processes with higher order statistical functions decomposable into an almost periodic function plus a residual term not containing finite strength additive sinewave components are considered these processes arise in mobile communications when almost cyclostationary acs processes pass through time varying channels they include as special case the generalized almost cyclostationary processes which in turn include the acs processes in the paper the problem of estimating the fourier coefficients of the generalized fourier series expansion of the almost periodic component of higher order statistical functions is addressed estimators are proposed for cyclic temporal cross moment and cumulants they are proved to be mean square consistent and asymptotically complex normal under mild assumptions on the memory of the processes expressed in terms of summability of cross cumulants numerical results confirm the theoretical results and the derived rate of convergence to zero of bias and standard deviation of the estimators

robust estimation in generalized partial linear models for clustered data in this article we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear models gplms for longitudinal data or clustered data in general we approximate the nonparametric function in the gplm by a regression spline and use bounded scores and leverage based weights in the estimating equation to achieve robustness against outliers we show that the regression spline approach avoids some of the intricacies associated with the profile kernel method and that robust estimation and inference can be carried out operationally as if a generalized linear model were used

interpolation of fuzzy data analytical approach and overview we propose a general framework for the interpolation problem our framework stems from the classical elaboration of the problem we introduce the notion of an interpolating fuzzy function and show how this function can be characterized we examine and analyze previously published fuzzy interpolation algorithms to choose those algorithms that can be represented analytically we also propose an analytic solution of the interpolation problem that unifies various algorithmic approaches

a comparative study of variable precision fuzzy rough sets based on residuated lattices abstract although qiao and hu intended to propose granular variable precision l fuzzy rough sets based on residuated lattices l actually denotes a doubly residuated lattice with an involutive negation however there exist doubly residuated lattices without involutive negations this paper presents a comparative study of variable precision fuzzy rough sets based on residuated lattices in which we compare variable precision l fuzzy rough sets with the preexisting models a variable precision upper l fuzzy rough approximation operator is proposed with l fuzzy granules based on l fuzzy implication on a residuated lattice l instead of a doubly residuated lattice the variable precision upper l fuzzy rough approximation operator is investigated with respect to different l fuzzy relations regardless of proposing an involutive negation on a residuated lattice

fundamental study complete and directed complete ω categories let w be a commutative unital quantale complete and directed complete w categories are the core objects in quantitative domain theory this paper based on the theory of f completeness for enriched categories presents a systematic investigation of completeness and directed completeness of w categories

bayesian kernel mixtures for counts although bayesian nonparametric mixture models for continuous data are well developed the literature on related approaches for count data is limited a common strategy is to use a mixture of poissons which unfortunately is quite restrictive in not accounting for distributions with variance less than the mean other approaches include mixing multinomials which requires finite support and using a dirichlet process prior with a poisson base measure which does not allow for smooth deviations from the poisson we propose broad class of alternative models nonparametric mixtures of rounded continuous kernels we develop an efficient gibbs sampler for posterior computation and perform a simulation study to assess performance focusing on the rounded gaussian case we generalize the modeling framework to account for multivariate count data joint modeling with continuous and categorical variables and other complications we illustrate our methods through applications to a developmental toxicity study and m

connecting fuzzy preorders fuzzy consequence operators and fuzzy closure and co closure systems abstract the relations between fuzzy preorders fuzzy consequence operators fuzzy closure systems and co closure systems lattice structures are studied given a continuous t norm we will prove that the complete lattice of all fuzzy preorders is isomorphic with a subfamily of the complete lattice of fuzzy consequence operators moreover we will show that it is possible to embed both structures in the class of fuzzy closure systems by a lattice dual monomorphism between semilattices a solution to the following open problem when two families of fuzzy possible valuations produce the same fuzzy implication relation is given concept of interior operator of a fuzzy consequence operator is suggested and a characterization of the previous open problem through interior operator is shown

an interference tolerant algorithm for localization of cyclostationary signal sources a method for detecting the number of cyclostationary signals radiated by remote sources and for estimating their directions of arrival by a linear and uniform array is presented whereas the traditional techniques exploit the spatial coherent properties the new method locates the signal sources using the spectral coherence properties as well this approach eliminates the need to know the characteristics of the noise and the interference regardless of the extent of their spectral overlap moreover the method applied equally well to environments containing more interferers than sensors the conditions of applicability of the method are the existence and the knowledge of a cycle frequency at which all the signal sources exhibit spectral correlation but the noise and interference signals do not and the existence and the knowledge of a value of the lag parameter such that the cyclic cross correlation matrix of the desired signals has full rank

fixed points and generators of fuzzy relations abstract the fixed points of a t indistinguishability operator are characterized as its generators in the sense of the representation theorem of valverde the geometric description of the set of fixed points of a reflexive and symmetric fuzzy relation based on this characterization gives a way to explicitly calculate it

the l ordered semigroups based on l partial orders abstract fuzzy frame valued ordered semigroups are investigated with the orders being l partial orders in this framework l left resp l right ideals l bi ideals and l quasi ideals of an l ordered semigroup are discussed the idea of which is applied to the characterizations of regular and duo l ordered semigroups in addition the relationship between an l ordered semigroup and an l topological semigroup is studied as a consequence an isomorphism between the category of l ordered semigroups and the category of l topological semigroups with the topologies being l t 0 and alexandrov is obtained

granular variable precision l fuzzy rough sets based on residuated lattices abstract firstly as for the beginning of this paper we introduce the granular variable precision l fuzzy rough sets based on residuated lattices with arbitrary l fuzzy relations and then the equivalent expressions for the lower and upper approximation operators are given with l fuzzy implications and l fuzzy coimplications on arbitrary l fuzzy relations which can calculate the lower and upper approximation operators efficiently finally some basic properties of the granular variable precision l fuzzy rough sets on residuated lattices are investigated and the conclusions on the granular variable precision fuzzy rough sets are generalized into the situations of the truth values set becoming residuated lattices

the aggregation of transitive fuzzy relations revisited abstract in this paper we consider the problem of aggregating a collection of transitive fuzzy binary relations in such a way that the aggregation process preserves transitivity specifically we focus our efforts on the characterization of those functions that aggregate a collection of fuzzy binary relations which are transitive with respect to a collection of t norms preserving the transitivity we characterize them in terms of triangular triplets further the relationship between triangular triplets the monotonicity of the aggregation function and an appropriate dominance notion is explicitly stated special attention is paid to a few classes of transitive fuzzy binary relations that are relevant in the literature concretely we describe in terms of triangular triplets those functions that aggregate a collection of fuzzy pre orders fuzzy partial orders relaxed indistinguishability relations indistinguishability relations and equalities a surprising relationship between functions that aggregate transitive fuzzy relations into a t m transitive fuzzy relation and those that aggregate relaxed indistinguishability relations is shown a few consequences of the new results are also provided for those cases in which all the t norms of the given collection are the same some celebrated results are retrieved as a particular case from the exposed theory

on the relationship between limit spaces many valued topological spaces and many valued preorders let l 1 be a residuated complete lattice with the underlying lattice l a meet continuous lattice this paper presents a systematic investigation of the interrelationship between the categories of limit spaces l topological spaces and l preorders the results exhibit a close connection between these different mathematical structures

fuzzy topological spaces with conical neighborhood systems abstract for a commutative integral and meet continuous quantale q a cns space is defined to be a q topological space such that the q neighborhood system of each point is a conical q filter these spaces reduce to fuzzy t locality spaces in the case that the quantale is the unit interval endowed with a left continuous t norm t and reduce to probabilistic q topological spaces in the case that q is an mv algebra for a continuous quantale q a necessary and sufficient condition is obtained for the category of cns spaces to be simultaneously reflective and coreflective in the category of stratified q topological spaces this result provides an interesting example of the interaction between properties of the quantale q and that of q topological spaces

blind adaptive spatiotemporal filtering for wide band cyclostationary signals an algorithm that blindly adapts spatiotemporal filters to extract from sensor array data one or more desired signals having known cyclostationarity properties is presented this method referred to as the spectral self coherence restoral score method can accommodate multiple signals of interest multiple interferers and unknown noise does not require complicated searches and requires knowledge of only a cycle frequency of the desired signal the score method is reinterpreted using the framework of canonical correlation analysis and extended to accommodate wide band received data that do not adhere to the narrow band assumption background information on cyclostationarity is presented and canonical correlation analysis is explained briefly the score method for wide band array data is from the perspective of canonical correlation analysis results of computer simulations are presented to illustrate the performance of the method and to compare it with that of the minimum variance distortionless response beamformer

on the construction of fuzzy betweenness relations from metrics abstract we consider the problem of constructing a fuzzy betweenness relation from a metric more precisely given a continuous archimedean triangular norm we present two construction methods for a fuzzy betweenness relation from a metric by making use of the pseudo inverse of either a continuous additive generator or a continuous multiplicative generator of the triangular norm in case the metric is bounded and given a 1 lipschitz continuous triangular norm we present a third construction method for a fuzzy betweenness relation from a metric by making use of the residual implication of the triangular norm since the ukasiewicz and product triangular norms are both continuous archimedean and 1 lipschitz continuous all three construction methods may be used interestingly the construction method based on the residual implication is proved to coincide with that based on a continuous additive generator for the ukasiewicz triangular norm and with that based on a continuous multiplicative generator for the product triangular norm we end by noting that all three construction methods result in a fuzzy prebetweenness relation when considering a pseudometric instead of a metric

kernel systems on l ordered sets abstract this paper presents fuzzy versions of kernel operators and kernel systems on l ordered sets and establishes a one to one correspondence between them

on the topological properties of fuzzy rough sets this paper is devoted to the discussion of the relationship between fuzzy rough set models and fuzzy topologies on a finite universe the tc axiom for fuzzy topology is proposed it is proved that the set of all lower approximation sets based on a reflexive and transitive fuzzy relation consists of a fuzzy topology which satisfies tc axiom and conversely a fuzzy topology which obey tc axiom is just the set of all lower approximation sets under a reflexive and transitive fuzzy relation that is to say there exists a one to one correspondence between the set of all reflexive and transitive fuzzy relations and the set of all fuzzy topologies which satisfy tc axiom

a stone type duality for st0 stratified alexandrov l topological spaces abstract we show that for every complete lattice a both the set of completely prime elements and the set of completely coprime elements are one to one corresponding to ch a the set of complete lattice homomorphisms from a to the two element lattice 2 a complete lattice is called completely generated a cg lattice for short if it is generated by the set of completely prime elements or equivalently by the set of completely coprime elements then we restudy the duality between the category of t 0 alexandrov topological spaces and the category of cg lattices by means of ch a with these preparations for a frame l as the truth value table we introduce s t 0 separation axiom for stratified alexandrov l topological spaces and finally establish a duality between the category of s t 0 stratified alexandrov l topological spaces and the category of completely generated complete l ordered sets we also investigate some properties of the s t 0 axiom for example it is hereditary by closed subspaces and productive

fuzzy rough sets fuzzy preorders and fuzzy topologies this paper shows that observations made by different authors at different times regarding one to one correspondence between the family of fuzzy preorders on a nonempty set and the family of all fuzzy topologies on this set satisfying certain extra conditions are essentially equivalent

common pitfalls in the application of stationary process theory to time sampled and modulated signals the common practice of applying the theory of stationary stochastic processes to a cyclostationary process by introducing random phase s into the probabilistic model in order to stationarize the process can lead to erroneous results such as incorrect formulas for power spectral density this is illustrated by showing that commonly used formulas for signals that have undergone frequency conversion or time sampling can be incorrect the source of error is shown to be inappropriate phase randomization procedures the correct procedure is described and corrected formulas are given the problem is further illustrated by showing that commonly used resolution and reliability mean and variance formulas for spectrum analyzers must be corrected for cyclostationary signals it is explained that all corrections to formulas reflect the effects of spectral correlation these effects are inappropriately averaged out by inappropriate phase randomization procedures it is further explained that these inappropriate procedures destroy the important property of ergodicity of the probabilistic model

metrics and t equalities abstract the relationship between metrics and t equalities is investigated the latter are a special case of t equivalences a natural generalization of the classical concept of an equivalence relation it is shown that in the construction of metrics from t equalities triangular norms with an additive generator play a key role conversely in the construction of t equalities from metrics this role is played by triangular norms with a continuous additive generator or equivalently by continuous archimedean triangular norms these results are then applied to the biresidual operator e t of a triangular norm t it is shown that e t is a t equality on 0 1 if and only if t is left continuous furthermore it is shown that to any left continuous triangular norm t there correspond two particular t equalities on f x the class of fuzzy sets in a given universe x one of these t equalities is obtained from the biresidual operator e t t by means of a natural extension procedure these t equalities then give rise to interesting metrics on f x

bayesian semiparametric analysis of developmental toxicology data modeling of developmental toxicity studies often requires simple parametric analyses of the dose response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure this article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations we approach our analysis using a bayesian semiparametric model that we tailored specifically to developmental toxicology studies it combines parametric dose response relationships with a flexible nonparametric specification of the distribution of the response obtained via a product of dirichlet process mixtures approach pdpm our formulation achieves three goals 1 the distribution of the response is modeled in a general way 2 the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data and 3 the marginal posterior distribution of the parameters of interest is available in closed form the logistic regression model as well as many of its extensions such as the beta binomial model and finite mixture models are special cases in the context of the two motivating examples and a simulated example we provide model comparisons illustrate overdispersion diagnostics that can assist model specification show how to derive posterior distributions of the effective dose parameters and predictive distributions of response and discuss the sensitivity of the results to the choice of the prior distribution

lattice valued preordered sets as lattice valued topological systems this paper provides variable basis lattice valued analogues of the well known results that the construct prost of preordered sets firstly is concretely isomorphic to a full concretely coreflective subcategory of the category top of topological spaces which employs the concept of the dual of the specialization preorder and secondly is non concretely isomorphic to a full coreflective subcategory of the category topsys of topological systems of s vickers which employs the spatialization procedure for topological systems dualizing these results one arrives at the similar properties of quasi pseudo metric spaces built over locales

on the structure of f indistinguishability operators abstract some properties concerning the structure of f indistinguishability operators are analyzed it is shown that any of such operators is generated by a family of fuzzy subsets this result since it gives the way to construct f indistinguishabilities facilitates new applications of fuzzy relations the links between f indistinguishability operators and a kind of generalized metrics in the unit interval which are also explored are used to define the canonical generators of an f indistinguishability operator that is the fuzzy partition associated with the operator

nonparametric time series analysis for periodically correlated processes correlation functions of continuous time periodically correlated processes can be represented by a fourier series with coefficient functions it is shown that the usual estimator for stationary covariances formed from a single sample path of the process can be simply modified to provide a consistent in quadratic mean estimator for any of the coefficient functions resulting from the aforementioned representation it is shown that if the process is gaussian and b sub k tau is a fourier integral with respect to a density function g sub k lambda a two dimensional periodogram formed from a single sample function can be smoothed along a line of constant difference frequency to provide a consistent estimator for g sub k lambda this natural extension of the well known procedure for stationary processes provides a method for nonparametric spectral analysis of periodically correlated processes

semiparametric bayesian inference for stochastic frontier models in this paper we propose a semiparametric bayesian framework for the analysis of stochastic frontiers and efficiency measurement the distribution of inefficiencies is modelled nonparametrically through a dirichlet process prior we suggest prior distributions and implement a bayesian analysis through an efficient markov chain monte carlo sampler which allows us to deal with practically relevant sample sizes we also consider the case where the efficiency distribution varies with firm characteristics the methodology is applied to a cost frontier estimated from a panel data set on 382 u s hospitals

a method for combining inference across related nonparametric bayesian models summary we consider the problem of combining inference in related nonparametric bayes models analogous to parametric hierarchical models the hierarchical extension formalizes borrowing strength across the related submodels in the nonparametric context modelling is complicated by the fact that the random quantities over which we define the hierarchy are infinite dimensional we discuss a formal definition of such a hierarchical model the approach includes a regression at the level of the nonparametric model for the special case of dirichlet process mixtures we develop a markov chain monte carlo scheme to allow efficient implementation of full posterior inference in the given model

on relationships among fuzzy approximation operators fuzzy topology and fuzzy automata the fuzzy approximation operator associated with an approximation space x r turns out to be a saturated kuratowski fuzzy closure operator on x precisely when the relation r on x is reflexive and transitive it is shown that all the level topologies of the fuzzy topology so obtained on x coincide these observations are then applied to fuzzy automata

nonparametric bayes testing of changes in a response distribution with an ordinal predictor in certain biomedical studies one may anticipate changes in the shape of a response distribution across the levels of an ordinal predictor for instance in toxicology studies skewness and modality might change as dose increases to address this issue we propose a bayesian nonparametric method for testing for distribution changes across an ordinal predictor using a dynamic mixture of dirichlet processes we allow the response distribution to change flexibly at each level of the predictor in addition by assigning mixture priors to the hyperparameters we can obtain posterior probabilities of no effect of the predictor and identify the lowest dose level for which there is an appreciable change in distribution the method also provides a natural framework for performing tests across multiple outcomes we apply our method to data from a genotoxicity experiment

new results on single axioms for l fuzzy rough approximation operators abstract this paper further studies axiomatic characterizations of l fuzzy rough sets where l denotes a residuated lattice single axioms for upper l fuzzy rough approximation operators are investigated in two different approaches which describe upper l fuzzy approximation operators with ordinary l fuzzy operations and l fuzzy product operation respectively we characterize upper l fuzzy rough approximation operators by only one axiom with ordinary l fuzzy operations when the l fuzzy relation is euclidean as well as the composition of euclidean with serial resp reflexive we also discuss the single axioms for upper l fuzzy rough approximation operators with l fuzzy product operation on arbitrary l fuzzy relations that are not limited as either general l fuzzy relations or symmetric l fuzzy relations the single axioms for lower l fuzzy rough approximation operators are discussed with ordinary l fuzzy operations regardless of the regularity of residuated lattice l

preordered sets valued in a gl monoid let m l be a gl monoid an m valued preordered set is an l subset endowed with a reflexive and m transitive l relation it is essentially a category enriched in a quantaloid generated by m this paper presents a study of m valued preordered sets with emphasis on symmetrization and the cauchy completion the main result states that symmetrization and the cauchy completion of m valued preordered sets commute up to a natural isomorphism

finitary solvability conditions for systems of fuzzy relation equations in this paper we consider the problem of solving systems of fuzzy relation equations two types of these systems with different compositions are considered and processed simultaneously a new sufficient condition and new solvability criteria are proposed for systems of both types all these conditions are finitary and thus can be easily verified the sufficient condition and criteria of solvability characterize a relationship between a skeleton nxn matrix n is a number of equations and a vector of the right hand side

estimation of second order cross moments of generalized almost cyclostationary processes in this paper the problem of estimating second order cross moments of generalized almost cyclostationary gacs processes is addressed gacs processes have statistical functions that are almost periodic functions of time whose generalized fourier series expansions have both frequencies and coefficients that depend on the lag shifts of the processes the class of such nonstationary processes includes the almost cyclostationary acs processes which are obtained as a special case when the frequencies do not depend on the lag shifts acs processes filtered by doppler channels and communications signals with time varying parameters are further examples it is shown that the second order cross moment of two jointly gacs processes is completely characterized by the cyclic cross correlation function moreover it is proved that the cyclic cross correlogram is an asymptotically normal mean square consistent estimator of the cyclic cross correlation function furthermore it is shown that well known consistency results for acs processes can be obtained by specializing the results of this paper

hierarchical dirichlet processes we consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups we assume that the number of mixture components is unknown a priori and is to be inferred from the data in this setting it is natural to consider sets of dirichlet processes one for each group where the well known clustering property of the dirichlet process provides a nonparametric prior for the number of mixture components within each group given our desire to tie the mixture models in the various groups we consider a hierarchical model specifically one in which the base measure for the child dirichlet processes is itself distributed according to a dirichlet process such a base measure being discrete the child dirichlet processes necessarily share atoms thus as desired the mixture models in the different groups necessarily share mixture components we discuss representations of hierarchical dirichlet processes

on un suitable fuzzy relations to model approximate equality in this paper we state that fuzzy equivalence relations in general are not suitable to model approximate equality since then the notion of transitivity is counter intuitive to substantiate this we investigate some of the undesirable results caused by transitivity among other things in the case of approximate reasoning we then introduce a new framework to model approximate equality i e the concept of a pseudometric based resemblance relation we go into the properties of this new kind of fuzzy relation and illustrate it by means of some examples

some results on the degree of symmetry of fuzzy relations abstract in this paper we investigate the degree of the symmetry of fuzzy relations on a set x based on the fuzzy e equality derived from uninorms with unit element e the degree of the symmetry of fuzzy relations are defined by two different approaches the type i degree of symmetry and the type ii degree of symmetry the main work of this paper include first we discuss some basic properties of those two degrees especially for the relationship between them in particular for continuous t norms we give a necessary and sufficient condition such that the type i degree of symmetry and the type ii degree of symmetry are equal and then we obtain that the type ii degree of symmetry is more appropriate to character the degree of the symmetry of fuzzy relations than the type i degree of symmetry with respect to whether they preserve the fuzzy e equalities or not in the meantime for a special case with continuous t norms we provide a necessary and sufficient condition such that the type i degree of symmetry preserves the fuzzy equalities finally for conjunctive left continuous idempotent uninorms with neutral element e 0 1 we find out a symmetric fuzzy relation s which is close enough to the given fuzzy relation r with respect to fuzzy e equality such that the degree of fuzzy e equality of s and r is the type ii degree of symmetry of r in particular we obtain analogous results for continuous t norms and one class of left continuous t norms

fuzzy galois connections on fuzzy sets abstract in fairly elementary terms this paper presents how the theory of preordered fuzzy sets more precisely quantale valued preorders on quantale valued fuzzy sets is established under the guidance of enriched category theory motivated by several key results from the theory of quantaloid enriched categories this paper develops all needed ingredients purely in order theoretic languages for the readership of fuzzy set theorists with particular attention paid to fuzzy galois connections between preordered fuzzy sets

asymptotic moments of estimated cyclic correlation matrices the first and second moments of the cyclic cross correlogram matrix of two vector valued cyclostationary processes are derived in this paper these results generalize those of hurd 1989 to accommodate incommensurate cycle frequencies and complex vector valued discrete time nongaussian processes as an example application of the results the moments of the left singular vectors of the cyclic cross correlogram matrix are derived which are needed in the performance analysis of subspace fitting methods of direction of arrival estimation for cyclostationary signals including even those methods that do not exploit cyclostationarity but are often applied in practice to cyclostationary signals

fuzzy complete lattices in this paper based on l fuzzy posets previously introduced by the third author l fuzzy complete lattices are defined which are generalizations of usual complete lattices and coincide with wagner s complete and cocomplete w categories enriched over the frame l and are consequently a special kind of complete w lattices defined by lai and zhang however tarski fixed point theorem for the l fuzzy complete lattices is proved in a different way from that by lai and zhang furthermore some fuzzy powerset operators are suggested they are not only generalizations of ordinary powerset operators but also generalizations of l valued zadeh powerset operators and their properties are discussed

topological properties of the class of generators of an indistinguishability operator the present paper investigates the relations between topologies in the classical sense fuzzy topologies in lowen s sense and indistinguishability operators as well as constructing topologies and fuzzy topologies by means of indistinguishability operators furthermore as a particular consequence of the results in this paper a characterization theorem for pseudo metrizable topological spaces in the classical sense is also surprisingly obtained

on many valued stratified l fuzzy convergence spaces based on complete residuated lattices the relations between stratified l fuzzy convergence spaces and enriched l fuzzy topological spaces are studied it is shown that as a reflective subcategory the category of enriched l fuzzy topological spaces can embedded in the category of stratified l fuzzy convergence spaces also the specialization l preorder of stratified l fuzzy convergence spaces is investigated

fuzzy t transitive relations eigenvectors and generators abstract after some preliminaries the set of generators of a generalized equality relation t indistinguishability operator is studied this set is identified with the set of the eigenvectors of the relation the relation between the fuzzy and metric topologies derived from these equalities is stablished the concept of basis is introduced and the construction of a procedure in order to calculate explicitly a basis of a t indistinguishability operator for t archimedean is proposed

partially blind adaptive mmse interference rejection in asynchronous ds cdma networks over frequency selective fading channels in this work the problem of joint suppression of multiple access and narrow band interference nbi for an asynchronous direct sequence code division multiple access cdma system operating on a frequency selective fading channel is addressed the receiver structure we consider can be deemed as a two stage one the first stage consists of a bank of minimum mean square error mmse filters each keyed to a given replica of the useful signal and aimed at suppressing the overall interference the second stage assuming knowledge of the fading channel coefficients realizations combines the mmse filters outputs according to a maximal ratio combining rule due to the presence of the nbi the resulting structure is in general time varying and becomes periodically time varying if the nbi bit rate has a rational ratio to that of the cdma system moreover enlarging the observation window beyond the signaling interval and oversampling the signal space may yield a noticeable performance improvement for the relevant case that the said ratio is rational a new cyclic blind recursive least squares rls based algorithm is introduced capable of tracking the periodically time varying receiver structure and allowing adaptive interference cancellation with a moderate complexity increase we also come up with a closed form expression for the conditional bit error rate ber which is useful both to evaluate semi analytical methods to assess the unconditional ber and to derive bounds on the system near far resistance the results indicate that the receiver achieves very satisfactory performance in comparison to previously known structures computer simulations also demonstrate that the cyclic blind rls algorithm exhibits quite fast convergence dynamics

an enriched category approach to many valued topology in this paper we discuss a basic question in fuzzy set theory what is a many valued topology on a set x an answer is presented by interpreting the axioms two logical formulas for classical topological spaces in the fuzzy setting making use of the intrinsic fuzzy partial order on the fuzzy power set of x as preparation a systematic investigation of fuzzy partial orders is presented from the viewpoint of enriched category theory

representations and constructions of similarity based fuzzy orderings this contribution advocates the dissemination of similarity based fuzzy orderings a generalized concept of fuzzy orderings which appears to be unavoidable as soon as the classical correspondences between preorderings equivalence relations and orderings are taken into account in contrast to earlier papers on the topic this paper is focused on representation and construction results which once more demonstrate the feasibility of the proposed concept

fuzzy preorder and fuzzy topology this paper presents by means of alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces a systematic investigation of the interrelationship between fuzzy preordered sets topological spaces and fuzzy topological spaces

a survey of fuzzifications of frames the papert papert isbell adjunction and sobriety this paper gives a survey of fuzzifications of frames the papert papert isbell adjunction between the categories of topological spaces and locales as well as the related concept of sobriety it then establishes categorical isomorphisms between yao l frames zhang liu l frames and l algebras lastly it studies the relationships between l sobriety modified l sobriety and i l sobriety the obtained results suggest that modified l sobriety is the most fruitful notion between the above concepts of lattice valued sobriety

fuzzy relation equations and inequalities with two unknowns and their applications abstract in this paper we study several types of systems of fuzzy relation equations and inequalities composed of a given family of fuzzy relations between two sets and two unknown fuzzy relations on these sets solutions to these systems are pairs of fuzzy relations on the underlying sets and can be ordered coordinatewise we show that solutions to each of these systems form a complete lattice and provide procedures for computing the greatest solution which is less than or equal to a given pair of fuzzy relations we also demonstrate the application of solutions to these systems in data reduction

mixed model functional anova for studying human tactile perception human tactile perception is studied through digitized images of hand drawn curves generated by subjects treated with various facial preparations the drawings represent their subjective assessment of a small brush moving across the face in this study exploratory data analysis is carried out through a functional data analog of principal components analysis and curve decomposition based on fourier representations in addition high dimensional analysis of variance is adapted for mixed model functional data and applied to test whether preparation effects are significant

quantitative domains via fuzzy sets part ii fuzzy scott topology on fuzzy directed complete posets this paper pursues an investigation on quantitative domains via fuzzy sets initiated by the first author this time we define an l topology called the fuzzy scott topology on fuzzy dcpos and investigate its properties scott convergence of stratified l filters is also defined and studied we show that a fuzzy dcpo x e is continuous if and only if for any stratified l filter on x scott convergence coincides with the convergence with respect to the fuzzy scott topology at last we show that the category of fuzzy dcpos with fuzzy scott continuous maps is cartesian closed

signal interception a unifying theoretical framework for feature detection the unifying framework of the spectral correlation theory of cyclostationary signals is used to present a broad treatment of weak random signal detection for interception purposes the relationships among a variety of previously proposed ad hoc detectors optimum detectors and newly proposed detectors are established the spectral correlation plane approach to the interception problem is put forth as especially promising for detection classification and estimation in particularly difficult environments involving unknown and changing noise levels and interference activity a fundamental drawback of the popular radiometric methods in such environments is explained

laplacian matrices and alexandrov topologies of digraphs abstract we explore the spectral properties of digraph laplacians and how they relate to topological properties of digraphs such as openness closure and strong connectedness under the alexandrov topology

nonparametric regression with missing outcomes using weighted kernel estimating equations we consider nonparametric regression of a scalar outcome on a covariate when the outcome is missing at random mar given the covariate and other observed auxiliary variables we propose a class of augmented inverse probability weighted aipw kernel estimating equations for nonparametric regression under mar we show that aipw kernel estimators are consistent when the probability that the outcome is observed that is the selection probability is either known by design or estimated under a correctly specified model in addition we show that a specific aipw kernel estimator in our class that employs the fitted values from a model for the conditional mean of the outcome given covariates and auxiliaries is double robust that is it remains consistent if this model is correctly specified even if the selection probabilities are modeled or specified incorrectly furthermore when both models happen to be right this double robust estimator attains the smallest possible asymptotic variance of all aipw kernel

regression analysis using dependent polya trees many commonly used models for linear regression analysis force overly simplistic shape and scale constraints on the residual structure of data we propose a semiparametric bayesian model for regression analysis that produces data driven inference by using a new type of dependent polya tree prior to model arbitrary residual distributions that are allowed to evolve across increasing levels of an ordinal covariate e g time in repeated measurement studies by modeling residual distributions at consecutive covariate levels or time points using separate but dependent polya tree priors distributional information is pooled while allowing for broad pliability to accommodate many types of changing residual distributions we can use the proposed dependent residual structure in a wide range of regression settings including fixed effects and mixed effects linear and nonlinear models for cross sectional prospective and repeated measurement data a simulation study illustrates the flexibility of our novel semiparametric regression model to accurately capture evolving residual distributions in an application to immune development data on immunoglobulin g antibodies in children our new model outperforms several contemporary semiparametric regression models based on a predictive model selection criterion copyright 2013 john wiley sons ltd

completely lattice l ordered sets with and without l equality a relationship between l order based on an l equality and l order based on crisp equality is explored in detail this enables to clarify some properties of completely lattice l ordered sets and generalize some related assertions namely belohlavek s main theorem of fuzzy concept lattices is generalized as well as his theorem dealing with dedekind macneille completion analogously completion of an l ordered set via completely lattice l ordered set of all down l sets is described

bayesian semiparametric isotonic regression for count data this article proposes a semiparametric bayesian approach for inference on an unknown isotonic regression function f x characterizing the relationship between a continuous predictor x and a count response variable y adjusting for covariates z a dirichlet process mixture of poisson distributions is used to avoid parametric assumptions on the conditional distribution of y given x and z then to also avoid parametric assumptions on f x a novel prior formulation is proposed that enforces the nondecreasing constraint and assigns positive prior probability to the null hypothesis of no association through the use of carefully tailored hyperprior distributions we allow for borrowing of information across different regions of x in estimating f x and in assessing hypotheses about local increases in the function due to conjugacy properties posterior computation is straightforward using a markov chain monte carlo algorithm the methods are illustrated using data from an epidemiologic study of sleep pr

i fuzzy alexandrov topologies and specialization orders the aim of this paper is to investigate the relationships between certain generalized topological structures and fuzzy order structures on a universe set x in details a fuzzy preordered relation induces an i fuzzy alexandrov topology and an i fuzzy topology induces a fuzzy preordered relation which turns out to be a specialization order in i fuzzy setting in addition the representation theorem of fuzzy preorders by i fuzzy topologies is obtained these results coincide with the conclusions obtained in literature in the version of two valued logic

one to one correspondence between fuzzifying topologies and fuzzy preorders this paper is devoted to the discussion of the relationship between fuzzifying topologies and fuzzy relations a saturated fuzzifying topology can be generated by a reflexive fuzzy relation and conversely a fuzzy preorder can be generated by a fuzzifying topology in fact there exists a one to one correspondence between the set of all saturated fuzzifying topologies and that of all fuzzy preorders

the relationship between l fuzzy rough set and l topology various fuzzy generalizations of rough approximations have been proposed in the literature this paper is devoted to the discussion of the relationship between l fuzzy rough sets and l topologies on an arbitrary universe finally one to one correspondence between the set of all reflexive transitive l relations and the set of all alexandrov l topologies is obtained

a non commutative and non idempotent theory of quantale sets in fuzzy set theory non idempotency arises when the conjunction is interpreted by arbitrary t norms there are many instances in mathematics where set theory ought to be non commutative and or non idempotent the purpose of this paper is to combine both ideas and to present a theory of non commutative and non idempotent quantale sets among other things standard concepts like fuzzy preorders and fuzzy equivalence relations will be exhibited as special cases more specifically the category q set is investigated where q is an arbitrary involutive quantale objects quantale sets are pairs consisting of a set and a q valued equality with a suitable symmetry axiom three important properties of q set are shown it is complete cocomplete and has the epi extremal mono factorization property its subcategory s q set of separated quantale sets is reflective in q set and shares the same fundamental properties with q set in particular s q set is also a complete and cocomplete epi extremal mono category the objects of the category q set are interesting categories in their own right two categorical frameworks for objects of q set are exhibited first it is shown that q valued equalities arise from q valued preorders with self adjoint extents by symmetrization which leaves q valued equalities invariant here sets with quantale preorders are shown to be b categories with base b being a specific quantaloid the second approach is based on involutive quantaloids a combination of two well known things quantaloids and ordered categories with involution in this context quantale sets are precisely symmetric b categories w r t appropriately chosen quantaloid b with involution further the cauchy completion preserves the symmetry axiom for a large class of involutive quantales which include quantic frames our non commutative generalization of frames and all left continuous t norms there exist at least two monads on q set the singleton monad and quasi singleton monad which are of special interest for fuzzy set theory the kleisli category associated with the singleton monad is the non commutative and non idempotent analogue of higgs topos while the eilenberg moore category of the quasi singleton monad permits the internalization of lukasiewicz negation as truth arrow finally an application of quantale sets to c algebras is given and the change of base is treated

a short note on l fuzzy approximation spaces and l fuzzy pretopological spaces in this note we investigate the relationship between l fuzzy pretopological spaces and l fuzzy approximation spaces based on the reflexive l fuzzy relations from a categorical viewpoint

fuzzy betweenness relations and their connection with fuzzy order relations abstract fuzzy relations and in particular fuzzy order relations have been largely studied since zadeh first introduced the concept back in 1971 bearing in mind that betweenness relations and their relationship with order relations have historically attracted the attention of mathematicians it is very surprising that the study of fuzzy betweenness relations has had a very limited scientific reach so far and barely no attention has been given to their relationship with fuzzy order relations in this manuscript we study fuzzy betweenness relations in depth and discuss their connection with both schools of thought in the study of fuzzy order relations the already mentioned one introduced by zadeh and the one initiated by hohle and blanchard and popularized by bodenhofer

towards probabilistic partial metric spaces diagonals between distance distributions abstract the quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories motivated by the categorical interpretation of partial metric spaces we are led to investigate the quantaloid of diagonals between distance distributions which is expected to establish the categorical foundation of probabilistic partial metric spaces observing that the quantale of distance distributions w r t an arbitrary continuous t norm is non divisible we precisely characterize diagonals between distance distributions and prove that one step functions are the only distance distributions on which the set of diagonals coincides with the generated down set

performance analysis of the cyclic music method of direction estimation for cyclostationary signals the cyclic music algorithm exploits the cyclostationarity exhibited by most man made communication signals to perform signal selective estimation of directions of arrival at an array of sensors in the paper the bias and mean squared error of these direction estimates are derived under the assumption that the signals are complex possibly non gaussian and cyclostationary the analytical results are shown to be excellent predictors of empirical results obtained from computer simulation of the cyclic music algorithm and are also compared with the cramer rao bound which in certain cases can be orders of magnitude less than the cramer rao bound for the directions of arrival of stationary signals

semiparametric regression for count data we introduce a class of bayesian semiparametric models for regression problems in which the response variable is a count our goal is to provide a flexible easy to implement and robust extension of generalised linear models for datasets of moderate or large size our approach is based on modelling the distribution of the response variable using a dirichlet process whose mean distribution function is itself random and is given a parametric form such as a generalised linear model the effects of the explanatory variables on the response are modelled via both the parameters of the mean distribution function of the dirichlet process and the total mass parameter we discuss modelling options and relationships with other approaches we derive in closed form the marginal posterior distribution of the regression coefficients and discuss its use in inference and computing we illustrate the benefits of our approach with a prognostic model for early breast cancer patients