steady states of max łukasiewicz fuzzy systems abstract the paper gives a systematic characterization of the eigenspaces in a max t algebra where t is the ukasiewicz t norm a max ukasiewicz fuzzy algebra can be used for the description of the states of discrete event systems the states can represent a balance between the resources expended during the run of a system for example fuel or money the classification of max ukasiewicz eigenspaces is described and illustrated by two and three dimensional examples in this case it is possible to accompany the example with graphs however the description of the eigenspaces for higher dimensions is also outlined

further facts about input to state stabilization previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls provided that a more general type of feedback is allowed applications to certain stabilization problems and coprime factorizations as well as comparisons to other results on input to state stability are briefly discussed

parallel algorithms for fuzzy ontology reasoning the need to deal with imprecise and vague information in ontologies is rising in importance as required by several real world application domains as a consequence there is a growing interest in fuzzy ontologies which combine ontologies and fuzzy logic theory in fuzzy ontologies some reasoning tasks usually become harder to solve such as the concept subsumption problem and the computation of the best degree bound bdb of an axiom in fact the current existing algorithms to solve these problems usually require performing some simpler tests several times in this paper we present a parallelization of these algorithms implemented in the delorean reasoner and discuss the encouraging results of an empirical evaluation

the role of crisp elements in fuzzy ontologies the case of fuzzy owl 2 el in the last years fuzzy ontologies and fuzzy description logics dls have been applied successfully to several real world domains some recent results on fuzzy dls show an increase in the theoretical complexity even for not expressive languages however it still may be possible to obtain reasoning algorithms performing well in practice this paper studies some cases where reasoning with a fuzzy ontology can be reduced to reasoning with a tractable classical language an owl 2 profile then building on the assumption that not all concepts and roles in fuzzy ontologies are indeed fuzzy we show that reasoning algorithms can be optimized by taking into account the existence of possible crisp concepts and roles we also prove the usefulness on crisp representation reasoning algorithms over an empirical evaluation over fuzzy owl 2 el ontologies and discuss some preliminary techniques to learn which elements should be considered to be crisp or noncrisp

which logic is the real fuzzy logic this paper is a contribution to the discussion of the problem whether there is a fuzzy logic that can be considered as the real fuzzy logic we give reasons for taking imtl bl email protected and ev l fuzzy logic with evaluated syntax as those fuzzy logics that should be indeed taken as the real fuzzy logics

reasoning with the finitely many valued łukasiewicz fuzzy description logic sroiq fuzzy description logics are a formalism for the representation of structured knowledge affected by imprecision or vagueness they have become popular as a language for fuzzy ontology representation to date most of the work in this direction has focused on the so called zadeh family of fuzzy operators or fuzzy logic which has several limitations in this paper we generalize existing proposals and show how to reason with a fuzzy extension of the logic sroiq the logic behind the language owl 2 under finitely many valued lukasiewicz fuzzy logic we show for the first time that it is decidable over a finite set of truth values by presenting a reasoning preserving procedure to obtain a non fuzzy representation for the logic this reduction makes it possible to reuse current representation languages as well as currently available reasoners for ontologies

event based control of nonlinear systems with partial state and output feedback this paper studies the event triggered control problem for nonlinear systems with partial state and output feedback we first consider the control systems that are transformable into an interconnection of two input to state stable iss subsystems with the sampling error as the external input it is shown that infinitely fast sampling can be avoided and asymptotic stabilization can be achieved by appropriately choosing the decreasing rate of the threshold signal of the event trigger then we focus on the event triggered output feedback control problem for nonlinear uncertain systems in the output feedback form the key idea is to introduce a novel nonlinear observer based control design and to transform the control system into the form of interconnected iss systems iss small gain methods are used as a fundamental tool in the discussions

asymptotics for kernel estimate of sliced inverse regression to explore nonlinear structures hidden in high dimensional data and to estimate the effective dimension reduction directions in multivariate nonparametric regression li and duan proposed the sliced inverse regression sir method which is simple to use in this paper the asymptotic properties of the kernel estimate of sliced inverse regression are investigated it turns out that regardless of the kernel function the asymptotic distribution remains the same for a wide range of smoothing parameters

fuzzy spatial relation ontology for image interpretation the semantic interpretation of images can benefit from representations of useful concepts and the links between them as ontologies in this paper we propose an ontology of spatial relations in order to guide image interpretation and the recognition of the structures it contains using structural information on the spatial arrangement of these structures as an original theoretical contribution this ontology is then enriched by fuzzy representations of concepts which define their semantics and allow establishing the link between these concepts which are often expressed in linguistic terms and the information that can be extracted from images this contributes to reducing the semantic gap and it constitutes a new methodological approach to guide semantic image interpretation this methodological approach is illustrated on a medical example dealing with knowledge based recognition of brain structures in 3d magnetic resonance images using the proposed fuzzy spatial relation ontology

fuzzy description logics with general t norms and datatypes fuzzy description logics dls are a family of logics which allow the representation of and the reasoning within structured knowledge affected by vagueness although a relatively important amount of work has been carried out in the last years current fuzzy dls still present several limitations in this work we face two problems the common restriction to zadeh and lukasiewicz fuzzy logics and the inability to deal with datatypes different from fuzzy sets in particular we propose a semantics based on the use of a general left continuous t norm and an involutive negation specially focused on product logic and furthermore we show how to handle functional concrete roles relating individuals of the domain and strings real or integer numbers

stability improvement of nonlinear systems by feedback this paper is concerned with the property of stabilizing a nonlinear system to a specified equilibrium point arbitrarily fast by appropriate smooth feedback two closely related forms of this property are explored one refers to the asymptotic transfer to the critical point with exponential decay and it is shown that the systems possessing the above property are precisely those whose corresponding linearization is controllable the second stabilizability form defined here amounts to driving the system back to an arbitrarily small neighborhood of the given point arbitrarily fast by smooth feedback a global stabilization result is also included finding application in hamiltonian systems special emphasis is given to the bilinear case

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

nonlinear observers robust to measurement disturbances in an iss sense this paper formulates and studies the concept of quasi disturbance to error stability qdes which characterizes robustness of a nonlinear observer to an output measurement disturbance in essence an observer is qdes if its error dynamics are input to state stable iss with respect to the disturbance as long as the plant s input and state remain bounded we develop lyapunov based sufficient conditions for checking the qdes property for both full order and reduced order observers we use these conditions to show that several well known observer designs yield qdes observers while some others do not our results also enable the design of novel qdes observers as we demonstrate with examples when combined with a state feedback law robust to state estimation errors in the iss sense a qdes observer can be used to achieve output feedback control design with robustness to measurement disturbances as an application of this idea we treat a problem of stabilization by quantized output feedback

a small gain approach to robust event triggered control of nonlinear systems this paper presents a new approach to event triggered control for nonlinear uncertain systems by using the notion of input to state stability iss and the nonlinear small gain theorem the contribution of this paper is threefold first it is proved that infinitely fast sampling can be avoided if the system is input to state stabilizable with the sampling error as the external input and the corresponding iss gain is locally lipschitz no assumption on the existence of known iss lyapunov functions is made in the discussions moreover the forward completeness problem with event triggered control is studied systematically by using iss small gain arguments second the proposed approach gives rise to a new self triggered sampling strategy for a class of nonlinear systems subject to external disturbances if an upper bound of the external disturbance is known then the closed loop system can be designed to be robust to the external disturbance and moreover the system state globally asymptotically converges to the origin if the external disturbance decays to zero third a new design method is developed for event triggered control of nonlinear uncertain systems in the strict feedback form it is particularly shown that the iss gain with the sampling error as the input can be designed to satisfy the proposed condition for event triggered control and self triggered control

adaptive backstepping controller design using stochastic small gain theorem a more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper with the concept of input to state practical stability isps and nonlinear small gain theorem being extended to stochastic case by combining stochastic small gain theorem with backstepping design technique an adaptive output feedback controller is proposed it is shown that the closed loop system is practically stable in probability a simulation example demonstrates the control scheme

reasoning within expressive fuzzy rough description logics it is generally accepted that the management of imprecision and vagueness will yield more intelligent and realistic knowledge based applications description logics dls are suitable well known logics for managing structured knowledge that have gained considerable attention the last decade the current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in dls are analyzed in this paper an integration between the theories of fuzzy dls and rough dls has been attempted by providing fuzzy rough dls based on fuzzy rough set theory the syntax semantics and properties of fuzzy rough dls are given it is proved that the satisfiability subsumption entailment and abox consistency reasoning in fuzzy rough dls may be reduced to the abox consistency reasoning in the corresponding fuzzy dls

asymptotics for sliced average variance estimation in this paper we systematically study the consistency of sliced average variance estimation save the findings reveal that when the response is continuous the asymptotic behavior of save is rather different from that of sliced inverse regression sir sir can achieve sqrt n consistency even when each slice contains only two data points however save cannot be sqrt n consistent and it even turns out to be not consistent when each slice contains a fixed number of data points that do not depend on n where n is the sample size these results theoretically confirm the notion that save is more sensitive to the number of slices than sir taking this into account a bias correction is recommended in order to allow save to be sqrt n consistent in contrast when the response is discrete and takes finite values sqrt n consistency can be achieved therefore an approximation through discretization which is commonly used in practice is studied a simulation study is carried out for the purposes of illustration

on the un decidability of fuzzy description logics under łukasiewicz t norm recently there have been some unexpected results concerning fuzzy description logics fdls with general concept inclusions gcis they show that unlike the classical case the dl alc with gcis does not have the finite model property under lukasiewicz logic or product logic the proposed reasoning algorithms are neither correct nor complete and specifically knowledge base satisfiability is an undecidable problem for product logic in this work we show that knowledge base satisfiability is also an undecidable problem for lukasiewicz logic we additionally provide a decision algorithm for acyclic alc knowledge bases under lukasiewicz logic via a mixed integer linear programming milp based procedure note however that the decidability of this problem is already known while similar milp based algorithms have been proposed in the literature for acyclic alc knowledge bases under lukasiewicz logic none of them exhibit formal proofs of their correctness and completeness which is the additional contribution here

robust control of uncertain nonlinear systems via measurement feedback the authors consider the problem of robust control via measurement feedback for a class of uncertain nonlinear systems usual assumptions like triangularity conditions and global lipschitzness used in previous work on this topic are not imposed the key tool employed in the constructive control design procedure is the recent small nonlinear gain theorem which has already proved very powerful in solving diverse control problems

dissipativity based small gain theorems for stochastic network systems in this paper some small gain theorems are proposed for stochastic network systems which describe large scale systems with interconnections uncertainties and random disturbances by the aid of conditional dissipativity and showing times of stochastic interval small gain conditions proposed for the deterministic case are extended to the stochastic case when some design parameters are tunable in practice we invaginate a simpler method to verify small gain condition by selecting one subsystem as a monitor compared with the existing results the existence and uniqueness of solution and ultimate uniform boundedness of input are removed from requirements of input to state stability and small gain theorems

reasoning with rough description logics the current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in description logics are analyzed in this paper approximate concepts are introduced to description logics based on rough set theory and a kind of new rough description logic rdl ac rough description logic based on approximate concepts is proposed based on approximate concepts the syntax semantics and properties of the rdl ac are given it is proved that the approximate concept satisfiability definitely satisfiability and possibly satisfiability reasoning problem and approximate concepts rough subsumption reasoning problem w r t rough tbox in rdl ac may be reduced to the concept satisfiability reasoning problem in almost standard alc the description logic that provides the boolean concept constructors plus the existential and universal restriction constructors the works of this paper provide logic foundations for approximate ontologies and theoretical foundations for reasoning algorithms of more expressive rough description logics including approximate concepts number restrictions nominals inverse roles and role hierarchies

global internal stabilizability does not imply global external stabilizability for small sensor disturbances it was shown by sontag ibid vol 34 no 4 p 435 43 1989 that for control affine nonlinear systems global asymptotic stabilizability via continuous state feedback implies global input to state stabilizability with respect to actuator disturbances we show that the analogous result for sensor disturbances does not hold we construct a second order system which admits a continuous memoryless globally asymptotically stabilizing state feedback controller but for which no such controller can prevent finite escape times from every initial condition in the presence of small sensor disturbances

u processes rates of convergence on introduit un nouveau processus stochastique une collection de statistiques u indicees par une famille de noyaux symetriques on obtient des conditions pour la convergence presque sure uniforme d une suite de tels processus

asymptotic inference for eigenvectors abstract asymptotic procedures are given for testing certain hypotheses concerning eigenvectors and for constructing confidence regions for eigenvectors these asymptotic procedures are derived under fairly general conditions on the estimates of the matrix whose eigenvectors are of interest applications of the general results to principal components analysis and canonical variate analysis are given author

generalized fuzzy rough description logics description logics dls are a family of logics for representing structured knowledge which have proved to be very useful as ontology languages classical dls are not suitable to represent vague pieces of information the attempts to achieve a solution have led to the birth of fuzzy dls and rough dls in this work we provide a simple solution to join these two formalisms and define a fuzzy rough dl this logic is more general than other related approaches including tight and loose fuzzy rough approximations and being independent of the fuzzy logic operators considered we show the usefulness of our approach by presenting some uses case and we also describe how to extend two reasoning algorithms for fuzzy dls which are implemented in the fuzzy dl reasoners fuzzydl and delorean

reasoning in fuzzy description logics using automata automata based methods have been successfully employed to prove tight complexity bounds for reasoning in many classical logics and in particular in description logics dls very recently the ideas behind these automata based approaches were adapted for reasoning also in fuzzy extensions of dls with semantics based either on finitely many truth degrees or the godel t norm over the interval 0 1 clearly due to the different semantics in these logics the construction of the automata for fuzzy dls is more involved than for the classical case in this paper we provide an overview of the existing automata based methods for reasoning in fuzzy dls with a special emphasis on explaining the ideas and the requirements behind them the methods vary from deciding emptiness of automata on infinite trees to inclusions between automata on finite words overall we provide a comprehensive perspective on the automata based methods currently in use and the many complexity results obtained through them

making fuzzy description logic more general a version of fuzzy description logic based on the basic continuous t norm based fuzzy predicate logic bl is presented problems of satisfiability validity and subsumption of concepts are discussed and reduced to problems of fuzzy propositional logic known to be decidable for any continuous t norm for lukasiewicz t norm some stronger results are obtained

slicing regression a link free regression method slicing regression a link free regression m e t h o d author s naihua duan and k e r c h a u l i s o u r c e the annals of statistics v o l 19 n o 2 t u n 1991 p p 5 0 5 5 3 0 p u b l i s h e d b y institute of mathematical statistics s t a b l e u r l http www jstor org stable 2242072 accessed 16 05 2011 your use of the jstor archive indicates your acceptance of jstor s terms and conditions of use available at http www jstor org page info about policies terms jsp jstor s terms and conditions of use provides in part that unless you have obtained prior permission you may not download an entire issue of a journal or multiple copies of articles and you may use content in the jstor archive only for your personal non commercial use please contact the publisher regarding any further use of this work publisher contact information may be obtained at http www jstor org action showpublisher publishercode ims each copy of any part of a jstor transmission must contain the same copyright notice that appears on the screen or printed page of such transmission jstor is a not for profit service that helps scholars researchers and students discover use and build upon a wide range of content in a trusted digital archive we use information technology and tools to increase productivity and facilitate new forms of scholarship for more information about jstor please contact support jstor org http www jstor org

characterizations of regular ordered semigroups in terms of α β fuzzy generalized bi ideals in this paper the concept of an a b fuzzy generalized bi ideal in an ordered semigroup is introduced which is a generalization of the concept of a fuzzy generalized bi ideal in an ordered semigroup using this concept some characterization theorems are provided the upper lower parts of an q fuzzy generalized bi ideal are introduced and some characterizations of regular ordered semigroups are given also we consider the concept of implication based fuzzy generalized bi ideals in an ordered semigroup in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

attributive concept descriptions with complements abstract we investigate the consequences of adding unions and complements to attributive concept descriptions employed in terminological knowledge representation languages it is shown that deciding coherence and subsumption of such descriptions are pspace complete problems that can be decided with linear space