on the completion of fuzzy metric spaces this paper discusses the completion of a fuzzy metric space in the sense of kaleva and seikkala that is modeled by a pair of two place functions l and r previous work on this question is based on l min r max under the condition that l and r are a generic class of two place functions we characterize the completable fuzzy metric space and show that the corresponding completion is uniquely determined up to isometry furthermore we point out that with more conditions on r including on r max the completion of each fuzzy metric space exists and is unique up to isometry this improves the corresponding result of kaleva the completion of fuzzy metric spaces j math anal appl 109 1985 194 198

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

frequency identification of nonparametric wiener systems containing backlash nonlinearities this paper addresses the problem of identifying wiener systems constituted of nonparametric linear dynamics and backlash nonlinearities the linear subsystem is arbitrary but stable the backlash nonlinearity borders are almost arbitrary shape in particular these are allowed to be nonsmooth noninvertible and crossing a frequency identification method is developed to estimate the system frequency response function at a given set of frequencies and the backlash nonlinearity borders within a given working domain the identification method involves sine excitations and consistent estimators designed using analytic geometry tools e g fictive limit cycles informative backlash limit cycles spread and orientation compatibility

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

coupled coincidence point results for compatible mappings in partially ordered fuzzy metric spaces coupled fixed point problems have attracted much attention in recent times in this paper we establish coupled coincidence point and coupled fixed point results in the context of fuzzy metric spaces the two mappings considered here are assumed to be compatible hadzic type t norm is used by an application of the coincidence point theorem in fuzzy metric spaces a corresponding result is obtained in metric spaces the main theorem of this paper is illustrated with an example our work extends some existing results

tripled fuzzy metric spaces and fixed point theorem abstract one of the most important topics of research in fuzzy sets is to get an appropriate notion of fuzzy metric space fms in the paper we propose a new fms tripled fuzzy metric space tfms which is a new generalization of george and veeramani s fms then we present some related examples topological properties convergence of sequences cauchy sequence cs and completeness of the tfms moreover we introduce two kinds of notions of generalized fuzzy contractive f c mappings and derive a fixed point theorem fpt on the mappings in the space

global solution branches for equations involving nonhomogeneous operators of p laplace type abstract it is shown that if is not an eigenvalue of an associated p laplacian then the equation div x u u p 2 u f x u u with nonhomogeneous which is assumed to behave asymptotically as the function generating the associated p laplacian has a global branch of solutions u also the case of modified p laplace operators and generalizations thereof are discussed

strong consistence of recursive identification for wiener systems the paper concerns identification of the wiener system consisting of a linear subsystem followed by a static nonlinearity f with no invertibility and structure assumption recursive estimates are given for coefficients of the linear subsystem and for the value f v at any fixed v the main contribution of the paper consists in establishing convergence with probability one of the proposed algorithms to the true values this probably is the first strong consistency result for this kind of wiener systems a numerical example is given which justifies the theoretical analysis

identification of hammerstein systems with quantized observations this work is concerned with identification of hammerstein systems whose outputs are measured by quantized sensors the system consists of a memoryless nonlinearity that is polynomial and possibly noninvertible followed by a linear subsystem the parameters of linear and nonlinear parts are unknown but have known orders input design identification algorithms and their essential properties are presented under the assumptions that the distribution function of the noise is known and the quantization thresholds are known the concept of strongly scaled full rank signals is introduced to capture the essential conditions under which the hammerstein system can be identified with set valued observations under strongly scaled full rank conditions a strongly convergent algorithm is constructed asymptotic consistency and efficiency of the algorithm are investigated

common fixed point theorems in fuzzy metric spaces in this paper we prove common fixed point theorems for six mappings in fuzzy metric space our main results extend generalize and fuzzify some known results in fuzzy metric spaces probabilistic metric spaces and uniform spaces

recursive prediction error identification using the nonlinear wiener model the nonlinear wiener model consisting of a linear dynamic block in cascade with a static nonlinearity is considered a recursive prediction error identification algorithm based on the wiener model is derived the linear dynamic block is modelled as a siso transfer function operator and the static nonlinearity is approximated with a piecewise linear function a theoretical analysis of the method is carried out and conditions for local convergence to the true parameter vector are given in particular the analysis shows that the input signal should be such that there is signal energy in the whole range of the piecewise linear approximation a numerical example illustrates the performance of the algorithm further practical guidelines on how to apply the algorithm are also included in the paper

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

completeness in probabilistic quasi uniform spaces abstract in this paper we give a kind of cauchy completeness in probabilistic quasi uniform space by using pair filters and prove that this kind of cauchy completeness is equivalent to the completeness of induced probabilistic uniform space introduced by hohle we also give a characterization of cauchy completeness by lawvere completeness then we study the completion of probabilistic quasi uniform space and show that each t 0 separated probabilistic quasi uniform space has a t 0 cauchy completion finally in probabilistic quasi metric space we study the relationship between the completeness of induced quasi uniform space and the completeness of probabilistic quasi metric space

recursive identification for nonlinear arx systems based on stochastic approximation algorithm the nonparametric identification for nonlinear autoregressive systems with exogenous inputs narx described by yk 1 f yk yk 1 n0 uk uk 1 n0 ek 1 is considered first a condition on f is introduced to guarantee ergodicity and stationarity of yk then the kernel function based stochastic approximation algorithm with expanding truncations saawet is proposed to recursively estimate the value of f at any given y 1 y n0 u 1 u n0 r2n0 it is shown that the estimate converges to the true value with probability one in establishing the strong consistency of the estimate the properties of the markov chain associated with the narx system play an important role numerical examples are given which show that the simulation results are consistent with the theoretical analysis the intention of the paper is not only to present a concrete solution to the problem under consideration but also to profile a new analysis method for nonlinear systems the proposed method consisting in combining the markov chain properties with stochastic approximation algorithms may be of future potential although a restrictive condition has to be imposed on f that is the growth rate of f x should not be faster than linear with coefficient less than 1 as x tends to infinity

a global bifurcation for nonlinear equations with nonhomogeneous part abstract we study the following boundary value problem with a nonhomogeneous principal part div u u 0 u p 2 u q x u u in with the dirichlet boundary condition under certain assumptions on and q when 0 is not an eigenvalue of the p laplacian the aim of this paper is to show a bifurcation result on a noncompact component of solutions for the above nonlinear equation

parameter identification of wiener systems with discontinuous nonlinearities abstract the paper deals with modeling and parameter identification of wiener type nonlinear dynamic systems having discontinuous asymmetric piecewise linear characteristics with preloads and dead zones multiple application of a decomposition technique provides a special form of static nonlinearity description its incorporation into the wiener model leads to an input output equation where all the model parameters are separated and can be estimated iteratively using input output data and internal variable estimates more illustrative examples are included to demonstrate the feasibility of the proposed approach

existence of radial solutions for an asymptotically linear p laplacian problem abstract we prove that an asymptotically linear dirichlet problem which involves the p laplacian operator has multiple radial solutions when the nonlinearity has a positive zero and the range of the p derivative of the nonlinearity includes at least the first j radial eigenvalues of the p laplacian operator the main tools that we use are a uniqueness result for the p laplacian operator and bifurcation theory

identifying mimo hammerstein systems in the context of subspace model identification methods in this paper we outline the extension of the moesp family of subspace model identification schemes to the hammerstein type of nonlinear system two types of identification problem are considered the first type assumes the polynomial structure of the static nonlinearity to be given and the task is to identify both the linear system dynamics and the unknown proportional constants in the para metrization of the static nonlinearity the second type addresses the identification of both the linear dynamic part and the static nonlinearity where only limited a priori information regarding the structure of the nonlinearity is available the improved robustness properties of the algorithms developed for this second type of hammerstein identification problem over existing correlation based schemes is illustrated by a numerical example

std convergence in fuzzy metric spaces in this note we answer two recent questions posed by morillas and sapena 10 related to standard convergence in fuzzy metric spaces in the sense of george and veeramani the obtained results lead us to establish what conditions must satisfy a concept about sequential convergence to be considered compatible with a concept of cauchyness

a recursive local linear estimator for identification of nonlinear arx systems asymptotical convergence and applications in this paper we propose a recursive local linear estimator rlle for nonparametric identification of nonlinear autoregressive systems with exogenous inputs narx first the rlle is introduced next the strong consistency as well as the asymptotical mean square error properties of the rlle are established and then an application of the rlle to an additive nonlinear system is discussed the rlle provides recursive estimates not only for the function values but also their gradients at fixed points a simulation example is provided to confirm the theoretical analysis

meir keeler theorems in fuzzy metric spaces abstract in this paper we propose the concept of fuzzy meir keeler contractive mappings in fuzzy metric spaces which covers fuzzy contractive mappings and fuzzy h contractive mappings as special cases with the aid of the proposed concept we obtain some meir keeler type fixed point theorems the derived theorems improve and extend the corresponding ones developed by d mihet d wardowski and v gregori et al and an example in the end of the paper illustrates the validity of our results

pathwise convergence of recursive identification algorithms for hammerstein systems this paper gives estimates for 1 coefficients contained in the linear part of the hammerstein system 2 the value of the nonlinear function f u in the hammerstein system at any u 3 ef u sub k and eu sub k f u sub k with u sub k denoting the system input no assumption is made on structure of f spl middot the estimates given by the stochastic approximation algorithms with expanding truncations are recursive and convergent to the true values with probability one two numerical examples are given

adaptive control of weiner type nonlinear systems abstract this study is concerned with the problem of adaptive control of a wiener type nonlinear process it is assumed that the linear dynamic part of the process can be represented by a pulse transfer function of known order with stable inverse followed by a known time delay the memoryless nonlinearity is one to one on a compact set and belongs to one of two classes 1 piecewise linear with known breakpoints or 2 smooth function in which case an approximation is made it is represented by linear splines the output signal from the linear part is not available for measurement the global stability of the proposed model reference adaptive control scheme is established subject to the assumption that the nonlinearity can be represented exactly by the linear spline function with a given set of breakpoints otherwise there will be a residual tracking error which depends on the nonlinearity approximation error but the boundedness of all signals can be assured the proposed scheme is used for adaptive control of the ph process in a continuous flow reactor

global bifurcation for equations involving nonhomogeneous operators in an unbounded domain abstract we study the structure of the set of solutions of a nonlinear equation involving nonhomogeneous operators div x u u 0 g x u p 2 u f x u in r n satisfying certain conditions on g and f when 0 is not an eigenvalue of the p laplacian in some sense this is based on a bifurcation result on noncompact connected sets of solutions for nonlinear operator equations

a note on compactness in a fuzzy metric space we study the compactness in a fuzzy metric space we also give a generalization of niemytzki tychonoff theorem for a fuzzy metric space

circle criteria in recursive identification positive real conditions and differential sector conditions have recently been shown to imply global convergence w p 1 for recursive identification schemes based on a class of single input single output linear wiener models the models consist of linear dynamics followed by a static output nonlinearity the model structure is hence closely related to that of the lure problem in the stability theory of feedback systems this paper proves that the conditions for convergence can be transformed to graphical circle criteria depending on the sector conditions and on the nyquist plot of a transfer function related to the prior knowledge of the poles of the identified system

some properites of fuzzy metric spaces abstract we prove that the topology induced by any complete fuzzy metric space in the sense of george and veeramani is completely metrizable we also show that every separable fuzzy metric space admits a precompact fuzzy metric and that a fuzzy metric space is compact if and only if it is precompact and complete finally we generalize among other classical results the niemytzki tychonoff theorem to fuzzy metric spaces

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

approximation properties in fuzzy normed spaces the paper is concerned with approximation properties which are defined in fuzzy normed spaces first we introduce the approximation property and the bounded approximation property next we provide two main examples first example is a fuzzy normed space that does not have the approximation property and second example is a fuzzy normed space with the approximation property that does not have the bounded approximation property finally we provide characterizations of approximation properties in fuzzy normed spaces

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

hutton 0 1 quasi uniformities induced by fuzzy quasi metric spaces it is well known that given a probabilistic metric space menger space with continuous t norm t there is a hausdorff topology associated this association factorizes through strong uniformities or e l uniformities similarly any fuzzy metric space x m can be endowed with a hausdorff topology t m in the case of fuzzy quasi metric spaces a t 1 topology and again this association factorizes through quasi uniform spaces in this paper we associate to each fuzzy quasi metric space a hutton 0 1 quasi uniformity u m this allows us to give a factorization of the previous association via hutton 0 1 quasi uniformities it is also proved that the topology t m is exactly the image under lowen s functor i of the 0 1 topology induced by u m as a consequence we get a class of hutton 0 1 quasi uniformities which are probabilistic metrizable

multidimensional coincidence point results for compatible mappings in partially ordered fuzzy metric spaces in recent times coupled tripled and quadruple fixed point theorems have been intensively studied by many authors in the context of partially ordered complete metric spaces using different contractivity conditions roldan et al showed a unified version of these results for nonlinear mappings in any number of variables which were not necessarily permuted or ordered introducing the notion of multidimensional coincidence point very recently choudhury et al proved coupled coincidence point results in the context of fuzzy metric spaces in the sense of george and veeramani in this paper using the idea of coincidence point for nonlinear mappings in any number of variables we study a fuzzy contractivity condition to ensure the existence of coincidence points in the framework of fuzzy metric spaces provided with hadzic type t norms then we present an illustrative example in which our methodology leads to the existence of coincidence points but previous theorems cannot be applied

the hausdorff fuzzy quasi metric removing the condition of symmetry in the notion of a fuzzy pseudo metric in kramosil and michalek s sense one has the notion of a fuzzy quasi pseudo metric then for each fuzzy quasi pseudo metric on a set x we construct a fuzzy quasi pseudo metric on the collection of all nonempty subsets of x called the hausdorff fuzzy quasi pseudo metric we investigate several properties of this structure and present several illustrative examples as well as an application to the domain of words the notion of hausdorff fuzzy quasi pseudo metric when quasi pseudo metric fuzziness is considered in the sense of george and veeramani is also discussed

on contractions in probabilistic and fuzzy metric spaces in this paper by means of weakening conditions of the gauge function a new fixed point theorem for probabilistic contraction in menger probabilistic metric spaces with a t norm of h type is established this theorem improves and generalizes the recent results of iric 2010 4 jachymski 2010 12 and xiao et al 2013 25 by using the theorem we also obtain some important corollaries and the fixed point theorems for contraction in fuzzy metric spaces

iterated function systems and attractors in the km fuzzy metric spaces fractal attractors are considered as invariant sets for contraction mappings in hyperspaces of the km fuzzy metric spaces using the properties of hausdorff fuzzy metrics several existence results of attractors are obtained for a finite family and a countable family of nonlinear contractions in particular unbounded invariant sets are also examined for the iterated function systems in km fuzzy metric spaces our results are generalizations in some aspects and analogous to their counterparts in usual metric spaces

l valued bornologies on powersets in m abel and a ostak 2011 1 the concept of an l fuzzy bornology was introduced actually an l fuzzy bornology on a set x is a certain ideal in the family lx of l fuzzy subsets of a set x here we propose an alternative approach to fuzzification of the concept of bornology we define an l valued bornology on a set x as an l fuzzy subset b of the powerset 2x satisfying l valued analogues of the axioms of a bornology basic properties of l valued bornological spaces are studied our special interest concerns l valued bornologies induced by fuzzy metrics and relative compactness type l valued bornologies in changgoguen l topological spaces

identification of certain time varying nonlinear wiener and hammerstein systems the problem of identification and tracking of time varying nonlinear systems is addressed in particular the wiener system that consists of a dynamic time varying linear part followed by a fixed nonlinearity and the hammerstein system in which the order of these two blocks is reversed are studied the extended kalman filter ekf algorithm is applied it is also shown that this algorithm can be reformulated in terms of a nonlinear minimization problem with a quadratic inequality constraint in order to ensure exponential stability resulting in the algorithm cekf as indicated by means of numerical examples this latter algorithm is less sensitive to the chosen initialization than the ekf the proposed algorithms depend on certain second order statistics that may be unknown in a typical scenario a method for estimation of these quantities is proposed it is demonstrated that the suggested algorithms can be successfully applied to the problem of acoustic echo cancelation

consistent identification of wiener systems a machine learning viewpoint wiener system identification has been recently performed by adopting a bayesian semiparametric approach in this framework the linear system entering the first block is given a finite dimensional parametrization while nonparametric gaussian regression is used to estimate the static nonlinearity in the second block in this paper we study the asymptotic behavior of this estimator when the number of noisy output samples tends to infinity without assuming the correctness of the bayesian prior models for this purpose we interpret wiener identification under a machine learning perspective this allows us to extend recent results on function estimation in reproducing kernel hilbert spaces to derive a condition guaranteeing the statistical consistency of the identification procedure we also discuss how the violation of such a condition can lead to useless estimates of the wiener structure

output error convergence of adaptive filters with compensation for output nonlinearities output error convergence of a wiener model based nonlinear stochastic gradient algorithm is analyzed the normalized scheme estimates the parameters of a linear finite impulse response model in cascade with a known output nonlinearity the algorithm can be interpreted as a normalized least mean square algorithm with compensation for an output nonlinearity linearizing inversion of the nonlinearity is not utilized global output error convergence is then proved provided that the nonlinearity is monotone not strictly monotone and provided that a previously observed mechanism resulting in deadlock does not occur the algorithm and the analysis include important practical cases like sensor saturation and dead zones that must be excluded when global parametric convergence is studied

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

an analytic geometry approach to wiener system frequency identification this paper addresses the problem of wiener system identification the underlying linear subsystem is stable but not necessarily parametric the nonlinear element in turn is allowed to be nonparametric noninvertible and nonsmooth as wiener models are uniquely defined up to an uncertain multiplicative factor it makes sense to start the frequency identification process estimating the system phase which is common to all models to this end a consistent estimator is designed using analytic geometry tools accordingly the system frequency behavior is characterized by a family of lissajous curves interestingly all these curves are candidates to modelling the system nonlinearity but the most convenient one is the less spread of them finally the frequency gain is in turn consistently estimated optimizing an appropriate cost function involving the obtained phase and nonlinearity estimates

identification input design for consistent parameter estimation of linear systems with binary valued output observations input design is of essential importance in system identification for providing sufficient probing capabilities to guarantee convergence of parameter estimates to their true values this paper presents conditions on input signals that characterize their probing richness for strongly consistent parameter estimation of linear systems with binary valued output observations necessary and sufficient conditions on periodic signals are derived for sufficient richness these conditions are further studied under different system configurations including open loop and feedback systems and different scenarios of noises including actuator noise input measurement noise and output measurement noise in addition to system parameter estimation essential properties of identifiability and input conditions are also derived when sensor thresholds or noise distribution functions are unknown the findings of this paper provide a foundation to study identification of systems that either use binary valued or quantized sensors or involve communication channels which mandate quantization of signals

fixed point theorems in fuzzy metric spaces using property e a abstract we prove two common fixed point theorems for a pair of weakly compatible maps in fuzzy metric spaces both in the sense of kramosil and michalek and in the sense of george and veeramani by using e a property

identification of wiener hammerstein and narx systems as markov chains with improved estimates for their nonlinearities abstract the wiener hammerstein and nonlinear arx systems are identified not only for their linear subsystems if they exist but also for the nonlinearities with their first derivatives it is assumed that the input signals and noises are mutually independent and both are sequences of independent and identically distributed iid random variables the estimates based on the stochastic approximation algorithms with expanding truncations saawet are proved to be strongly consistent with the help of the markov properties possessed by these systems the estimates of the first derivatives improve the accuracy of interpolating the nonlinearity curves as validated by simulation examples

brief paper recursive identification for multivariate errors in variables systems the recursive algorithm is given for estimating matrix coefficients of the multivariate errors in variables eiv systems it is shown that under mild conditions the estimate given by the algorithm converges to a limit belonging to the solution set of the yule walker equation satisfied by the true coefficients of the system the sufficient conditions guaranteeing the uniqueness of the solution to the yule walker equation are given in this case the estimate provided by the recursive algorithm is strongly consistent

towards identification of wiener systems with the least amount of a priori information on the nonlinearity in this paper we investigate what constitutes the least amount of a priori information on the nonlinearity so that the fir linear part is identifiable in the non gaussian input case three types of a priori information are considered including quadrant information point information and locally monotonous information in all three cases identifiability has been established and corresponding identification algorithms are developed with their convergence proofs

nonlinear system analysis and identification from random data 1991 nonlinear system analysis and identification from random data technometrics vol 33 no 4 pp 482 483

towards identification of wiener systems with the least amount of a priori information iir cases in this paper we investigate what constitutes the least amount of a priori information on the nonlinearity so that the linear part is identifiable in the non gaussian input case under the white noise input three types of a priori information are considered quadrant information point information and monotonic information in all three cases identifiability has been established and the corresponding nonparametric identification algorithms are developed along with their convergence proofs

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

fuzzy lipschitz maps and fixed point theorems in fuzzy metric spaces in this paper we introduce the notion of dilation and fuzzy lipschitz of a map from a fuzzy metric space into a fuzzy metric space and we prove continuity properties for such maps we also define the notion of the fuzzy lipschitz distance between two fuzzy metric spaces and show that two compact fuzzy metric spaces whose lipschitz distance is zero is fuzzy isometric to each other on the other hand we introduce the concept of minimal slope of a map between fuzzy metric spaces which is defined by the ratio of two fuzzy metrics and derive some properties on it and relations with the dilation in particular we show that if the dilation of a map from a fuzzy metric space which is complete in george and veeramani sense into itself is less than the minimal slope then the map must have a fixed point in case that a fuzzy metric space is considered in the sense of kramosil and michalek and that the completeness in the sense of grabiec the same result holds

fixed points in weak non archimedean fuzzy metric spaces mihet fuzzy j contractive mappings in non archimedean fuzzy metric spaces fuzzy sets and systems 159 2008 739 744 proved a theorem which assures the existence of a fixed point for fuzzy j contractive mappings in the framework of complete non archimedean fuzzy metric spaces motivated by this we introduce a notion of weak non archimedean fuzzy metric space and prove that the weak non archimedean fuzzy metric induces a hausdorff topology we utilize this new notion to obtain some common fixed point results for a pair of generalized contractive type mappings

recursive identification of mimo wiener systems stochastic approximation sa algorithms are proposed to identify a multi input and multi output mimo wiener system in which the system input is taken to be a sequence of independent and identically distributed i i d gaussian random vectors uk n 0 i the algorithm for identifying the nonlinear part is designed with multi variable kernel functions under suitable conditions we show that the estimates of the coefficients of the linear subsystem and of the values of the nonlinear function converge to the respective true values with probability one

the bicompletion of fuzzy quasi metric spaces extending the well known result that every fuzzy metric space in the sense of kramosil and michalek has a completion which is unique up to isometry we show that every km fuzzy quasi metric space has a bicompletion which is unique up to isometry and deduce that for each km fuzzy quasi metric space the completion of its induced fuzzy metric space coincides with the fuzzy metric space induced by its bicompletion

on the existence and the uniqueness of fixed points of sehgal contractions we discuss the problem of existence and uniqueness of fixed points for fuzzy contraction maps in fuzzy menger spaces and quasi pseudo menger spaces

standard fuzzy uniform structures based on continuous t norms this paper deals with fuzzy uniform structures previously introduced by the authors fuzzy uniform structures and continuous t norms fuzzy sets syst 161 2009 1011 1021 our approach involves a covariant functor j from the category of fuzzy uniform spaces and fuzzy uniformly continuous mappings in our sense to the category of uniform spaces and uniformly continuous mappings we show that j is well behaved with respect to some significant fuzzy uniform concepts and its behavior provides a method to introduce notions of fine fuzzy uniform structure and stone cech fuzzy compactification in this context our method also applies to obtain fuzzy versions of some classical results on topological algebra and hyperspaces the case of quasi uniform structures is also analyzed

on fuzzy metric groups we introduce and study a notion of fuzzy metric group which permits us to obtain satisfactory extensions of classical theorems on metric groups to the fuzzy setting we also investigate properties of the quotient subgroups of a fuzzy metric group

on fixed point theorems in fuzzy metric spaces we give fixed point theorems for complete fuzzy metric spaces in the sense of george and veeramani and also for kramosil and michalek s fuzzy metric spaces which are complete in grabiec s sense

fixed points in fuzzy metric spaces abstract in this note the well known fixed point theorems of banach and edelstein are extended to fuzzy metric spaces in the settle of kramosil and michalek

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

identification of wiener systems with binary valued output observations this work is concerned with identification of wiener systems whose outputs are measured by binary valued sensors the system consists of a linear fir finite impulse response subsystem of known order followed by a nonlinear function with a known parametrization structure the parameters of both linear and nonlinear parts are unknown input design identification algorithms and their essential properties are presented under the assumptions that the distribution function of the noise is known and the nonlinearity is continuous and invertible it is shown that under scaled periodic inputs identification of wiener systems can be decomposed into a finite number of core identification problems the concept of joint identifiability of the core problem is introduced to capture the essential conditions under which the wiener system can be identified with binary valued observations under scaled full rank conditions and joint identifiability a strongly convergent algorithm is constructed the algorithm is shown to be asymptotically efficient for the core identification problem hence achieving asymptotic optimality in its convergence rate for computational simplicity recursive algorithms are also developed

topological stability for fuzzy expansive maps abstract we introduce the definitions of expansivity and topological stability for homeomorphisms on fuzzy metric spaces we show some basic properties of fuzzy expansive homeomorphisms moreover we prove walters s theorem in the context of fuzzy metric spaces i e a fuzzy expansive system with the fuzzy shadowing property is fuzzy topologically stable

on completable fuzzy metric spaces in this paper we construct a non completable fuzzy metric space in the sense of george and veeramani which allows to answer an open question related to continuity on the real parameter t in addition the constructed space is not strong non archimedean