on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy metric spaces

the completion of a fuzzy normed linear space abstract the concept of a fuzzy normed linear space was introduced in an earlier paper by the author finite dimensional fuzzy normed linear space fuzzy sets and systems 48 1992 239 248 it was shown therein that any finite dimensional fuzzy normed linear space is necessarily complete there do exist incomplete fuzzy normed linear spaces incompleteness is shown to have handicaps see section 3 there is a need for completion in the sense of enlarging the incomplete space so that the given space is embedded in the enlarged space it is shown in this paper see theorem 3 that this is really possible

a fixed point approach to almost quartic mappings in quasi fuzzy normed spaces we will define a notion for a quasi fuzzy p normed space then we use the fixed point alternative theorem to establish hyers ulam rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy p normed space later we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost quartic function control function and the unique quartic mapping which approximates the almost quartic map finally some applications of our results in the stability of quartic mappings from a linear space into a quasi p norm space will be exhibited

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

on the uniform boundedness theorem in fuzzy quasi normed spaces we prove that a family of continuous linear operators from a fuzzy quasi normed space of the half second category to a fuzzy quasi normed space is uniformly fuzzy bounded if and only if it is pointwise fuzzy bounded this result generalizes and unifies several well known results in fact the classical uniform boundedness principle or banach steinhauss theorem is deduced as a particular case furthermore we establish the relationship between uniform fuzzy boundedness and equicontinuity which allows us to give a uniform boundedness theorem in the class of paratopological vector spaces the classical result for topological vector spaces is deduced as a corollary

distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution summary a fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry and to generate a whole set of non symmetric densities the approach is sufficiently general to encompass some recent proposals in the literature variously related to the skew normal distribution the special case of skew elliptical densities is examined in detail establishing connections with existing similar work the final part of the paper specializes further to a form of multivariate skew t density likelihood inference for this distribution is examined and it is illustrated with numerical examples

convex optimization approaches for blind sensor calibration using sparsity we investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains we focus on blind calibration using measures performed on multiple unknown but sparse signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem we divide this problem in 3 subproblems with different conditions on the gains specifially i gains with different amplitude and the same phase ii gains with the same amplitude and different phase and iii gains with different amplitude and phase in order to solve the first case we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals for the second case we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals an alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals finally for the third case we propose a formulation that combines the earlier two approaches to solve the problem the performance of the proposed algorithms is investigated extensively through numerical simulations which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many unknown but sparse calibrating signals are provided

fuzzy bounded linear operators in felbin s type fuzzy normed linear spaces in this paper definitions of strongly fuzzy bounded linear operator and weakly fuzzy bounded linear operators are given and the idea of their fuzzy norms are introduced the concept of fuzzy dual spaces are introduced and the hahn banach theorem is established in fuzzy setting

widely linear estimation with complex data mean square estimation of complex and normal data is not linear as in the real case but widely linear the purpose of the paper is to calculate the optimum widely linear mean square estimate and to present its main properties the advantage with respect to the linear procedure is especially analyzed

multisource self calibration for sensor arrays calibration of a sensor array is more involved if the antennas have direction dependent gains and multiple calibrator sources are simultaneously present we study this case for a sensor array with arbitrary geometry but identical elements i e elements with the same direction dependent gain pattern a weighted alternating least squares wals algorithm is derived that iteratively solves for the direction independent complex gains of the array elements their noise powers and their gains in the direction of the calibrator sources an extension of the problem is the case where the apparent calibrator source locations are unknown e g due to refractive propagation paths for this case the wals method is supplemented with weighted subspace fitting wsf direction finding techniques using monte carlo simulations we demonstrate that both methods are asymptotically statistically efficient and converge within two iterations even in cases of low snr

a unified framework and sparse bayesian perspective for direction of arrival estimation in the presence of array imperfections self calibration methods play an important role in reducing the negative effects of array imperfections during direction of arrival doa estimation however the dependence of most such methods on the eigenstructure techniques greatly degrades their adaptation to demanding scenarios such as low signal to noise ratio snr and limited snapshots this paper aims at formulating a unified framework and sparse bayesian perspective for array calibration and doa estimation a comprehensive model of the array output is presented first when a single type of array imperfection is considered with mutual coupling gain phase uncertainty and sensor location error treated as typical examples the spatial sparsity of the incident signals is then exploited and a bayesian method is proposed to realize array calibration and source doa estimation the array perturbation magnitudes are assumed to be small according to most application scenarios and the geometries of mutually coupled arrays are assumed to be uniform linear and those of arrays with sensor location errors are assumed to be linear cramer rao lower bounds crlbs for the array calibration and doa estimation precisions are also obtained the sparse bayesian method is finally extended to deal with the doa estimation problem when more than one type of array perturbation coexists

array shape calibration using sources in unknown locations a maximum likelihood approach sensor location uncertainty can severely degrade the performance of direction finding systems an iterative maximum likelihood method for simultaneously estimating directions of arrival doa and sensor locations is developed to alleviate this problem the case of nondisjoint sources i e sources observed in the same frequency cell and at the same time is emphasized the algorithm converges to the global maximum of the likelihood function if the initial conditions are sufficiently good numerical examples are presented illustrating the performance of the proposed technique a distinctive feature of the algorithm is its ability to locate the sensors accurately without deploying calibration sources at known locations

theoretical analyses of gain and phase error calibration with optimal implementation for linear equispaced array in array signal processing high resolution direction of arrival doa estimation algorithms are known to be sensitive to system errors in practice the system should be properly calibrated before doa estimation in this paper a calibration method of gain and phase errors of linear equispaced arrays leas is considered a class of simplified calibration algorithms based on different diagonal lines of the covariance matrix is proposed the statistical performance analyses of the calibration algorithms due to finite data perturbations are presented expressions for average bias abias and square root of average variance srav of the calibration algorithms are derived using first order approximation these statistical and computer simulation results reveal and explain why the more diagonal lines that are used for gain and phase error estimations the more inferior performance that may be obtained based on this conclusion the simple and optimal gain and phase error calibration algorithms for such model are obtained

perturbation of generalized derivations in fuzzy menger normed algebras in this paper we introduce a notion for fuzzy menger normed algebra then we will investigate continuity of algebraic operations in this space we will show that the class of all fuzzy menger normed algebras strictly contains the class of normed algebras finally we will prove hyers ulam rassias superstability of generalized derivation functional equationf ax by vw af x bf y vf w g v w x y v email protected x 0 a email protected c in complete fuzzy menger normed algebras a few applications of our results will be exhibited

on the topological structure of km fuzzy metric spaces and normed spaces in this paper some relations among the axioms of km fuzzy metric spaces and km fuzzy normed spaces are discussed and some characterizations concerning the additional axiom are given also a quasi metric family and a quasi norm family corresponding respectively to the km fuzzy metric spaces and the km fuzzy normed spaces are introduced and studied using their properties the different topological structures of km fuzzy metric spaces and km fuzzy normed spaces with variable t norm are described and some new properties on these spaces are obtained as their special cases the topological structures and properties concerning gv fuzzy metric spaces and gv fuzzy normed spaces are presented

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

fuzzy bounded linear operators in this paper a notion of boundedness of a linear operator from a fuzzy normed linear space to another fuzzy normed linear space is introduced and two types strong and weak of fuzzy bounded linear operators are defined relation between fuzzy continuity and fuzzy boundedness is studied definitions of fuzzy bounded linear functionals are given and the notions of fuzzy dual spaces are developed the hahn banach theorem the open mapping theorem the closed graph theorem and the uniform boundedness principle theorem are established

fuzzy approximately cubic mappings we establish some stability results concerning the cubic functional equationf 2x y f 2x y 2f x y 2f x y 12f x in fuzzy normed spaces we discuss the fuzzy continuity of the cubic mappings and show that the existence of a solution for any approximately cubic mapping guarantees the completeness of the fuzzy normed space

a comparative study of fuzzy norms on a linear space in this paper a comparative study among several types of fuzzy norms on a linear space defined by various authors has been made and it is shown that broadly they may be classified into two types one of which is katsaras s type and the other is felbin s type

two stage selection and testing designs for comparative clinical trials summary a two stage design which selects the best of several experimental treatments and compares it to a standard control is proposed the design allows early termination with acceptance of the global null hypothesis optimal sample size and cut off parameters are obtained by minimizing expected total sample size for fixed significance level and power with many other factors moreover the usual error rate computations associated with comparative testing do not account for the preliminary selection process consequently the overall procedure may be neither effective nor efficient for identifying an experimental treatment which is an improvement over c in this paper we propose a new approach to the problem of identifying the best of k experimental treatments and determining whether it is superior to a control we deal with the binomial setting where patient response may be characterized as either success or failure with ok the success probability for ek k 0 corresponds to c for ease of notation assume 01 ok we propose a two stage procedure which allows early termination with acceptance of h0 o 01 ok with design parameters chosen to minimize expected total sample size the design and accompanying generalized definitions of size a and power 1 3 are given in 2 the algorithm used for optimization is described in 3 numerical results are presented in 4 followed by a discussion of the relative merits of the proposed design

statistical applications of the multivariate skew normal distribution azzalini and dalla valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter the first part of the present paper examines further probabilistic properties of the distribution with special emphasis on aspects of statistical relevance inferential and other statistical issues are discussed in the following part with applications to some multivariate statistics problems illustrated by numerical examples finally a further extension is described which introduces a skewing factor of an elliptical density

non parametric detection of the number of signals hypothesis testing and random matrix theory detection of the number of signals embedded in noise is a fundamental problem in signal and array processing this paper focuses on the non parametric setting where no knowledge of the array manifold is assumed first we present a detailed statistical analysis of this problem including an analysis of the signal strength required for detection with high probability and the form of the optimal detection test under certain conditions where such a test exists second combining this analysis with recent results from random matrix theory we present a new algorithm for detection of the number of sources via a sequence of hypothesis tests we theoretically analyze the consistency and detection performance of the proposed algorithm showing its superiority compared to the standard minimum description length mdl based estimator a series of simulations confirm our theoretical analysis

cramer rao bound for circular and noncircular complex independent component analysis despite an increased interest in complex independent component analysis ica during the last two decades a closed form expression for the cramer rao bound crb for the demixing matrix is not known yet in this paper we fill this gap by deriving a closed form expression for the crb of the demixing matrix for instantaneous noncircular complex ica it contains the crb for circular complex ica and noncircular complex gaussian ica as two special cases we also study the crb numerically for the family of noncircular complex generalized gaussian distributions and compare it to simulation results of two ica estimators furthermore we show how to extend the crb to the case where the source signals are not temporally independent and identically distributed

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

an eigenstructure method for estimating doa and sensor gain phase errors in this paper we consider the problem of direction of arrival doa estimation in the presence of sensor gain phase errors under some mild assumptions we propose a new doa estimation method based on the eigendecomposition of a covariance matrix which is constructed by the dot product of the array output vector and its conjugate by combining the new doa estimation with the conventional gain phase error estimation a method is proposed to simultaneously estimate the doa and gain phase errors without joint iteration theoretical analysis shows that the proposed method performs independently of phase errors and thus behaves well regardless of phase errors however the resolution capability of the proposed method is lower than that of the method in a j weiss and b friedlander eigenstructure methods for direction finding with sensor gain and phase uncertainties circuits systems signal process vol 9 no 3 pp 271 300 1990 named as the wf method in order to improve the resolution capability and maintain phase error independence a combined strategy is developed using the proposed and wf methods the advantage of the proposed methods is that they are independent of phase errors leading to the cancellation of phase error calibration during the operation life of an array moreover the proposed methods avoid the problem of suboptimal convergence which occurs in the wf method the drawbacks of the proposed methods are their high computational complexity and their requirement for the condition that at least two signals are spatially far from each other and they are not applicable to a linear array simulation results verify the effectiveness of the proposed methods

fuzzy versions of hyers ulam rassias theorem we introduce three reasonable versions of fuzzy approximately additive functions in fuzzy normed spaces more precisely we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense

schauder bases and approximation property in fuzzy normed spaces our aim in this article is to introduce and study the notion of weak and strong schauder bases in fuzzy normed spaces further we introduce strong and weak fuzzy approximation properties and set a relationship between these two new notions which may provide an acceleration to the structural analysis of fuzzy normed spaces

sensor array calibration using a maximum likelihood approach high resolution array processing algorithms for source localization are known to be sensitive to errors in the model for the sensor array spatial response in particular unknown gain phase and mutual coupling as well as errors in the sensor positions can seriously degrade the performances of array processing algorithms this paper describes a calibration algorithm that estimates the calibration matrix consisting of the unknown gain phase and mutual coupling coefficients as well as the sensor positions using a set of calibration sources in known locations the estimation of the various parameters is based on a maximum likelihood approach cramer rao lower bound crb expressions for the sensor positions and the calibration matrix parameters are also derived numerical results are shown to illustrate the potential usefulness of the proposed calibration algorithm toward better accuracy and resolution in parametric array processing algorithms

on generalized fuzzy normed spaces and coincidence point theorems in this paper generalized fuzzy norms are defined on a set of objects endowed with a structure of linear space the relationships between these fuzzy norms and the fuzzy metrics and between these fuzzy norms and the topological structures on the base linear space are analyzed finally coincidence and fixed point theorems for mappings with values in fuzzy metric spaces and in such fuzzy normed spaces are proved

separation of fuzzy normed linear spaces abstract this paper deals with hausdorff separation axiom for fuzzy topological spaces the necessary and sufficient condition obtained in the fuzzy vector topology induced by a fuzzy norm is separated properties of separated and non separated fuzzy norms along with examples are studied separation of a fuzzy norm in terms of the ordinary norm it induces and its consequences are characterised separation of quotient fuzzy semi norm is studied

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

level topologies of fuzzifying topological linear spaces and their applications in this paper some properties of level topologies of fuzzifying topological linear spaces are discussed then the characterizations of fuzzy boundedness and fuzzy precompactness are obtained they may be considered as reply to the problem suggested by qiu fuzzifying topological linear spaces fuzzy sets and systems 147 2004 249 272 as applications in menger probabilistic normed spaces with respect to t norm minimum unified fuzzifying topological characterizations of probabilistic bounded probabilistic semi bounded probabilistic unbounded sets and probabilistic precompact probabilistic semi precompact probabilistic unprecompact sets are proved respectively

characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy quasi norms we obtain characterizations of those paratopological vector spaces that are quasi metrizable locally bounded quasi metrizable locally convex and quasi normable respectively in terms of appropriate kinds of fuzzy quasi norms characterizations of distinguished kinds of metrizable topological vector spaces some of them known already are deduced as particular cases of our approach

high order analysis of the efficiency gap for maximum likelihood estimation in nonlinear gaussian models in gaussian measurement models the measurements are given by a known function of the unknown parameter vector contaminated by additive zero mean gaussian noise when the function is linear the resulting maximum likelihood estimate mle is well known to be efficient unbiased with a mean square estimation error mse matrix attaining the cramer rao lower bound crlb however when the function is nonlinear the mle is only asymptotically efficient the classical derivation of its asymptotic efficiency uses a first order perturbation analysis relying on a small errors assumption which under subasymptotic conditions turns inaccurate rendering the mle generally biased and inefficient although a more accurate higher order performance analysis for such cases is of considerable interest the associated derivations are rather involved requiring cumbersome notations and indexing building on the recent assimilation of tensor computations into signal processing literature we exploit the tensor formulation of higher order derivatives to derive a tractable formulation of a higher up to third order perturbation analysis predicting the bias and mse matrix of the mle of parameter vectors in general nonlinear models under subasymptotic conditions we provide explicit expressions depending on the first three derivatives of the nonlinear measurement function and demonstrate the resulting ability to predict the efficiency gap relative excess mse beyond the crlb in simulation experiments we also provide matlab code for easy computation of our resulting expressions

finite dimensional fuzzy normed linear space abstract the concept of a fuzzy normed linear space is introduced it is proved that in a finite dimensional fuzzy normed linear space fuzzy norms are the same upto fuzzy equivalence finite dimensional fuzzy subspaces of a fuzzy normed linear space are proved to be necessarily complete fuzzy normed linear spaces

asymptotically optimal blind calibration of uniform linear sensor arrays for narrowband gaussian signals an asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband gaussian signals is proposed rather than taking the direct maximum likelihood ml approach for joint estimation of all the unknown model parameters which leads to a multi dimensional optimization problem with no closed form solution we revisit paulraj and kailath s p k s classical approach in exploiting the special toeplitz structure of the observations covariance however we offer a substantial improvement over p k s ordinary least squares ls estimates by using asymptotic approximations in order to obtain simple non iterative quasi linear optimally weighted ls owls estimates of the sensors gains and phases offsets with asymptotically optimal weighting based only on the empirical covariance matrix of the measurements moreover we prove that our resulting estimates are also asymptotically optimal w r t the raw data and can therefore be deemed equivalent to the ml estimates mle which are otherwise obtained by joint ml estimation of all the unknown model parameters after deriving computationally convenient expressions of the respective cramer rao lower bounds we also show that our estimates offer improved performance when applied to non gaussian signals and or noise as quasi mle in a similar setting the optimal performance of our estimates is demonstrated in simulation experiments with a considerable improvement reaching an order of magnitude and more in the resulting mean squared errors w r t p k s ordinary ls estimates we also demonstrate the improved accuracy in a multiple sources directions of arrivals estimation task

on the normability of generalized serstnev pn spaces probabilistic normed spaces have been redefined by c alsina b schweizer and a sklar but even today whether the generalized serstnev pn space is normable or not is still an open question in this paper through applying kolmogorov s theorem we will give several sufficient conditions under which many generalized serstnev pn spaces are normable as the application of our results we will give two examples which are normable generalized serstnev pn space but not serstnev space

on fuzzy approximately cubic type mapping in fuzzy banach spaces abstract the first study of the fuzzy approximately cubic mappings in nonlinear analysis is due to mirmostafaee and moslehian 2008 and a fuzzy version of a generalized hyers ulam rassias type stability for the cubic functional equation in the fuzzy normed linear space setting is presented in this note we give an alternative proof of this result using the fixed point method in probabilistic metric spaces moreover we investigate fuzzy generalized hyers ulam rassias stability of an n dimensional cubic type functional equation in fuzzy banach spaces

fuzzy quasi pseudometrics on algebraic structures abstract in this work we state a number of theorems about fuzzy quasi pseudometrizable algebraic structures our most useful results are 1 a fuzzy semitopological group whose topology is induced by a left invariant fuzzy quasi pseudometric then it is a fuzzy paratopological topological group 2 if the topology on a semigroup s is induced by an invariant fuzzy quasi pseudometric then s is a fuzzy topological semigroup and 3 the same conclusion is valid for a left invariant fuzzy quasi pseudometric on a monoid g such that the left translations are open and the right translations are continuous at the identity e of g by means of the standard fuzzy quasi pseudometric m d associated to a quasi pseudometric d our results apply in the case of semitopological groups semigroups and monoids in order to obtain new results that allow us to generalize and to strengthen previous outcomes

stability of additive mappings in non archimedean fuzzy normed spaces in this paper we introduce a notion of a non archimedean fuzzy norm and study the stability of the cauchy equation in the context of non archimedean fuzzy spaces in the spirit of hyers ulam rassias gavruta as a corollary the stability of the jensen equation is established we indeed present an interdisciplinary relation between the theory of fuzzy spaces the theory of non archimedean spaces and the theory of functional equations

resonance theorems for family of quasi homogeneous operators in fuzzy normed linear spaces in this paper we establish some resonance theorems for families of point wise bounded semi bounded and non unbounded quasi homogeneous and email protected subadditive operators in fuzzy normed linear spaces as their consequences we obtain the corresponding resonance theorems in classical normed spaces and menger probabilistic normed spaces

interim treatment selection using the normal approximation approach in clinical trials we consider a study starting with two treatment groups and a control group with a planned interim analysis the inferior treatment group will be dropped after the interim analysis and only the winning treatment and the control will continue to the end of the study this two stage winner design is based on the concepts of multiple comparison adaptive design and winner selection in a study with such a design there is less multiplicity but more adaptability if the interim selection is performed at an early stage if the interim selection is performed close to the end of the study the situation becomes the conventional multiple comparison where dunnett s method may be applied the unconditional distribution of the final test statistic from the winner treatment is no longer normal the exact distribution of which is provided in this paper but numerical integration is needed for its calculation to avoid complex computations we propose a normal approximation approach to calculate the type i error the power the point estimate and the confidence intervals due to the well understood and attractive properties of the normal distribution the winner design can be easily planned and adequately executed which is demonstrated by an example we also provide detailed discussion on how the proposed design should be practically implemented by optimizing the timing of the interim look and the probability of winner selection

fuzzy normed space of operators and its completeness in this paper the new definition of the fuzzy norm of a linear operator from one fuzzy normed linear space into another is introduced and the boundedness of such an operator is described furthermore the space of all bounded linear operators endowed with this fuzzy norm is studied consequently its topological structure as well as completeness is given and that it can itself be made into a fuzzy normed linear space is also shown

complete invariant fuzzy metrics on groups abstract we study some questions related to complete fuzzy metric topological groups in the sense of kramosil and michael invariant fuzzy metrics are characterized and we prove that if g m is a fuzzy metric group such that m is invariant then a fuzzy metric completion g m of g m is a fuzzy metric group and m is invariant moreover if m is an invariant complete metric on g then every compatible left invariant or right invariant fuzzy metric on g is complete we also study the so called three spaces problem given a fuzzy metric group g m and a closed normal subgroup n if one has information about two complete fuzzy metric groups g m n m and g n m what can be said about the third one our results apply to fuzzy banach spaces