particle lattices and fuzzy particle lattices abstract this paper introduces several new concepts a particle in a lattice which is a generalization of an atom in a distributive lattice by weakening the minimality property of atom a particle lattice which is a generalization of distributive complete atomic lattices by replacing atoms by particles a fuzzy particle lattice a particle lattice with an order reversing involution a particulate boolean algebra a fuzzy particle lattice whose involution is a complementation operator and other related concepts points fuzzy points boundary points and boundary quasi points the paper establishes representation theorems for fomse of these concepts establishes connections between others and some well established lattice theoretic concepts and provides some elementary properties for some of the new concepts

constant depth reducibility the purpose of this paper is to study reducibilities that can be computed by combinational logic networks of polynomial size and constant depth containing and s or s and not s with no bound placed on the fan in of and gates and or gates two such reducibilities are defined and reductions and equivalences among several common problems such as parity sorting integer multiplication graph connectivity bipartite matching and network flow are given certain problems are shown to be complete with respect to these reducibilities in the complexity classes deterministic logarithmic space nondeterministic logarithmic space and deterministic polynomial time new upper bounds on the size depth unbounded fan in circuit complexity of symmetric boolean functions are established

observer based adaptive fuzzy tracking control for a class of uncertain nonlinear mimo systems this paper addresses the adaptive fuzzy tracking control problem for a class of uncertain nonlinear mimo systems with the external disturbances the adaptive fuzzy controllers are designed under the constraint that only system output is available for measurement then it is needed to design a state observer to estimate the unmeasured states in the observer design procedure two prominent advantages are that it does not require the sign of the control gain coefficient to be known and only two parameters need to be adjusted on line for each subsystem by using lyapunov analysis method it is proven that all the signals in the closed loop system are guaranteed to be bounded and the system outputs track the reference signals to a bounded compact set the feasibility of the proposed approach is validated by using two simulation examples

decentralized adaptive fuzzy output feedback control of stochastic nonlinear large scale systems with dynamic uncertainties in this paper centralized and decentralized adaptive fuzzy output feedback control schemes are investigated for a class of stochastic nonlinear interconnected large scale systems with dynamic uncertainties and unmeasured states fuzzy systems are used to approximate the unknown nonlinear functions decentralized k filters are designed to estimate the unmeasured states an available dynamic signal is introduced to dominate the unmodeled dynamics by combining dynamic surface control dsc technique with backstepping design the condition in which the approximation errors are assumed to be bounded is avoided using the defined compact set in the stability analysis the unknown smooth interconnections and black box functions are effectively dealt with using it o formula and chebyshev s inequality it is shown that all the signals in the closed loop system are bounded in probability and the error signals are semi globally uniformly ultimately bounded in mean square or the sense of four moment simulation results demonstrate the effectiveness of the proposed approach

adaptive fuzzy control for uncertain interconnected time delay systems in this paper the problem of control for a class of uncertain interconnected time delay systems is studied the interconnections of the system possess time varying delay characteristics and the bounds of uncertainties are not precisely known a decentralized adaptive feedback controller is designed which is independent of the delays lyapunov krasovskii approach is employed to show that the corresponding closed loop system is asymptotically stable a simulation example is given to demonstrate the potential of the proposed techniques

operations on l fuzzy topological spaces abstract the aim of the paper is mainly to introduce and study operations on l fuzzy topological spaces the algebraic properties of some of these operations are discussed most of the concepts of compactness continuity lindelof spaces and separation axioms are considered

sequential convergence in fuzzy neighborhood spaces abstract we introduce the notions of sequential convergence and the first axiom of countability in fuzzy neighborhood spaces we show that these notions fulfil good extension criterion attributed to lowen convergent sequences and cauchy sequences are studied in the light of fuzzy probabilistic pseudometric space

fuzzy nets and their application fuzzy net theory is enriched by the introduction of the fuzzy net of fuzzy sets the limsup liminf and limit of a fuzzy net of fuzzy sets are defined and their various properties are discussed alternative characterizations based on the notion of a fuzzy net are provided for several fuzzy topological concepts including open and closed fuzzy sets fuzzy continuity maps with closed fuzzy graph open fuzzy mapping etc thus the net theoretic approach is shown to be a promising tool in fuzzy topology

fµ strongly semiopen sets fµ strong semicontinuity and fµ strongly semiretracts throughout the literature if x d is an f ts and y x the induced f topological subspace y d y is defined so that d y n g y n d macho stadler and de prada vicente fuzzy sets and systems 58 1993 365 introduced a new concept of f topological subspaces which coincides with the usual definition in the case that m g y also they introduced the concepts of f m open sets and f m continuity in this paper using the previous concepts we introduce weaker forms of f m open sets and f m continuity the notion of an f retract was introduced by rodabough j math anal appl 79 1981 273 here we introduce the notion of a f m retract and weaker forms of it the basic properties of these notions are given many results are obtained

point set lattice theoretic topology this essay attempts to survey in a coherent way certain aspects of point set lattice theoretic or poslat topology by which we mean fuzzy topology grounded in notions of sets functions powersets and powerset operators the latter two being lattice theoretic in nature and examined from a lattice theoretic point of view using methods of category theory connections with other related issues and developments are frequently given

some results on fuzzy supratopological spaces abstract in this note we study some results on the concepts of supracompactness and supracompactness in a fuzzy supratopological space we introduce the notions of hausdorffnessand lindelofness in a fuzzy supratopological space and characterize their properties interms of supracompactness we also introduce and study the concept of fuzzy supra regular space

adaptive neural network tracking control of mimo nonlinear systems with unknown dead zones and control directions in this paper adaptive neural network nn tracking control is investigated for a class of uncertain multiple input multiple output mimo nonlinear systems in triangular control structure with unknown nonsymmetric dead zones and control directions the design is based on the principle of sliding mode control and the use of nussbaum type functions in solving the problem of the completely unknown control directions it is shown that the dead zone output can be represented as a simple linear system with a static time varying gain and bounded disturbance by introducing characteristic function by utilizing the integral type lyapunov function and introducing an adaptive compensation term for the upper bound of the optimal approximation error and the dead zone disturbance the closed loop control system is proved to be semiglobally uniformly ultimately bounded with tracking errors converging to zero under the condition that the slopes of unknown dead zones are equal simulation results demonstrate the effectiveness of the approach

on fuzzy neighbourhood spaces abstract we study the behaviour of the fuzzy closure operator of a fuzzy neighbourhood space fns for short with regard to the two operations of sum and conjunction on fuzzy subsets we supply sufficient conditions on a cech fuzzy closure operator to be the fuzzy closure operator of a fns finally we study quotient fuzzy neighbourhood systems with the help of the notion of dual fuzzy neighbourhood spaces of 11

optimal bounds for decision problems on the crcw pram optimal o log n log log n lower bounds on the time for crcw prams with polynomially bounded numbers of processors or memory cells to compute parity and a number of related problems are proven a strict time hierarchy of explicit boolean functions of n bits on such machines that holds up to o log n log log n time is also exhibited that is for every time bound t within this range a function is exhibited that can be easily computed using polynomial resources in time t but requires more than polynomial resources to be computed in time t 1 finally it is shown that almost all boolean functions of n bits require log n log log n o 1 time when the number of processors is at most polynomial in n the bounds do not place restrictions on the uniformity of the algorithms nor on the instruction sets of the machines

a new fuzzy compactness defined by fuzzy nets compactness is one of the most important notions in topology and is thoroughly investigated in general topology but it seems that the research about this notion in the area of fuzzy topology is not so effective as in general topology in fact it would seem that there was not even a good definition of compactness in this area until recently indeed soon after the famous article written by zadeh 8 was published chang 1 introduced the notion of fuzzy topological spaces and at the same time a certain fuzzy compactness was given from then on a series of different notions of fuzzy compactness have been discussed 2 3 71 and in 5 they were compared in detail but it seems unsatisfactory that all these fuzzy compactness ideas are defined for the whole fuzzy topological space but not for an arbitrary fuzzy subset therefore they are far from the crisp compactness for example it is impossible to discuss the hereditary property with respect to closed subsets of fuzzy compactness in 1977 pu and liu introduced the notion of fuzzy nets and a new concept of so called q neighborhood was given which could reflect the features of neighborhood structure in fuzzy topological spaces and by this new neighborhood structure the moore smith convergence theory was established spendidly 6 it furnishes us a basic tool to investigate the fuzzy compactness in a more general way to investigate the compactness of arbitrary fuzzy subsets in this paper a new fuzzy compactness defined by fuzzy nets we shall call it n compactness is given but we introduce the notion of r neighborhood see section 2 instead of qneighborhood to establish the moore smith convergence theory for it is perhaps more convennient to use n compactness possesses the following properties 1 n compactness is defined for arbitrary fuzzy subsets 2 for n compactness the hereditary property with respect to closed subsets holds 3 n compactness is a good extension 5 4 the continuous images of ncompact sets are n compact 5 for n compactness the tychonoff product theorem holds 6 if an n compact fuzzy topological space is t2 6 then it will satisfy a stronger separation axiom which will be called t4 in this paper 1 0022 247x 83 3 00

functions with closed graphs and strongly closed graphs in fuzzy neighbourhood spaces abstract functions with closed graphs strongly closed graphs weakly closed graphs and weakly strongly closed graphs are defined and studied many properties of these concepts are investigated

adaptive neural control of mimo nonlinear state time varying delay systems with unknown dead zones and gain signs in this paper adaptive neural control is proposed for a class of uncertain multi input multi output mimo nonlinear state time varying delay systems in a triangular control structure with unknown nonlinear dead zones and gain signs the design is based on the principle of sliding mode control and the use of nussbaum type functions in solving the problem of the completely unknown control directions the unknown time varying delays are compensated for using appropriate lyapunov krasovskii functionals in the design the approach removes the assumption of linear functions outside the deadband as an added contribution by utilizing the integral lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead zone disturbance the closed loop control system is proved to be semi globally uniformly ultimately bounded simulation results demonstrate the effectiveness of the approach

some strong separation in fuzzy topological spaces abstract recently macho stadler et al fuzzy sets and systems 43 1991 95 116 introduced the notion of fuzzy separation using the family of its level topologies lt t t i1 the present work deals with introducing and studying the operations on ri fuzzy topological spaces i 0 1 moreover the notion of fuzzy separation which is well defined as a fuzzy topological concept is described a comparison between the above notions with the analogous fuzzy ones are discussed an acceptable clue which indicates that these notions are equivalent is offered

an approach to systematic design of the fuzzy control system abstract this paper presents a new design method of fuzzy control system fcs the concept from the sliding mode control is adopted to construct fuzzy control scheme if the original control rules are inappropriate the adaptive mechanism will modify these rules according to the proposed algorithms in particular the structure of sliding surface provides a reasonable estimation to the universes of discourse on which the fuzzy control rules are based finally an inverted pendulum system is used to demonstrate the availability of the proposed approaches

on fuzzy t1 topological spaces on etudie diverses relations entre les differentes definitions des espaces topologiques t 1 flous

sequential compactness in fuzzy neighborhood spaces abstract the present work deals with introducing and studying the notions of n compactness and n sequential compactness in fuzzy neighbourhood spaces we show that the notion of n sequential compactness fulfils a good extension criterion attributed to lowen j math anal appl 64 1978 446 454 and agrees it well some properties of these concepts are discussed

paracompactness in l fuzzy topological spaces abstract in this paper we introduce a good definition of paracompactness in l fuzzy topological spaces where l is a fuzzy lattice we define paracompactness on general l fuzzy subsets and study its properties

on inductive dimensions for fuzzy topological spaces an approach to the dimension theory for fuzzy topological spaces is being developed the appropriate context for this theory is not the category cft of chang fuzzy topological spaces or some of its modifications but the category hut introduced in the paper this category is a slight extension of the category h of hutton fuzzy topological spaces hutton 1980 the frames of this category allow us to make exposition simple and uniform and on the other hand to make it applicable in quite a general setting

dynamic topologies and their applications to crisp topologies fuzzifications of crisp topologies and fuzzy topologies on the crisp real line abstract we introduce and develop topologies whose members are dynamic sets a la zeleny this development spawns the notions of phase and co phase spaces fuzzy dual dynamic dual and co fuzzy dual with the following results being obtained result a the notion of fuzzy dual provides a unifying framework for the diverse fuzzification schemes of hutton gantner steinlage warren klein and lowen result b the dynamic duals of the fuzzy real lines are both homeostatic and coheterostatic result c the fuzzy real lines re interpreted as fuzzy duals of r with the usual euclidean topology t induce on r via the notion of co fuzzy dual a class of canonical stratified fuzzy topologies co r l e g if l is a demorgan algebra and lc 1 then the compactness of a r is equivalent to the ordinary compactness of a w r t t and if l is a hutton algebra r l co r l is metrizable in the sense of hutton and erceg with erceg metric d l such that d l p r 1 p s 1 r s where pr is the crisp point or impulse with support r i e d l extends the euclidean metric on r

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

applications of localic separation axioms compactness axioms representations and compactifications to poslat topological spaces fuzzy topology first appeared about twenty seven years ago with chang s initial paper 1968 yet the fundamental issues of compactness and low order separation axioms remain unresolved this paper resolves these issues with respect to topological compactification categorical compactification and stone representation theorems using the theory of locales and previous work of the author in fuzzy sobriety our results give the first compactification reflectors for all traditional fuzzy topology construct classes of generalized stone representations of boolean algebras and distributive lattices and show categorically that the fuzzy analogue of classical compact hausdorff spaces is the categories of chang compact localic regular sober fuzzy topological spaces

decentralized adaptive fuzzy control for large scale nonlinear systems abstract a decentralized adaptive fuzzy control scheme for a class of large scale nonlinear systems is proposed in this paper the design is based on the principle of sliding mode control and the approximation capability of fuzzy systems the control architecture employs decentralized fuzzy systems to adaptively compensate for plant uncertainties by using the lyapunov function method the control algorithm is proved to be globally stable with tracking errors converging to a neighborhood of zero

errata complete fuzzy topological hyperfields and fuzzy multiplication in the fuzzy real lines abstract we construct a fuzzy multiplication for the case l a chain in the l fuzzy real line r l which is jointly fuzzy continuous and which is the unique piecewise consistent extension of ordinary multiplication to r l distributing over the fuzzy addition constructed by the author in 47 we also specify the fuzzy integers and give an extensive analysis of fuzzy contractions and expansions these results the constructions of this paper and the results of 47 are used to prove r l and the stratified r c l are nontopologically isomorphic complete fuzzy topological hyperfields if l is a chain with l 3 we can now completely answer for l a chain the following question of 27 in the affirmative can a set of fuzzy numbers its fuzzy topology and its fuzzy addition and multiplication be defined such that these operations are jointly fuzzy continuous extensions of the usual addition and multiplication of r and can we specify the fuzzy integers these results in combination with recent papers of several authors would seem to answer in the affirmative the following philosophical question cf 34 does fuzzy topology have deep specific canonical examples

sufficient conditions on general fuzzy systems as function approximators abstract in a constructive way we have found sufficient conditions under which general fuzzy systems can uniformly approximate any real continuous function on a compact domain to any degree of accuracy more importantly we have revealed the underlying mechanism of such function approximation the fuzzy systems can uniformly approximate any polynomials which according to the weierstrass approximation theorem can uniformly approximate any continuous function on a compact domain these findings lead to the following practical results 1 explicit fuzzy rules of fuzzy systems can now be easily obtained according to functions to be approximated and 2 formulas are derived which can calculate the number of input fuzzy sets output fuzzy sets and fuzzy rules needed in order to satisfy any given approximation accuracy the number increases as required approximation error decreases and as approximation error approaches zero the number approaches these formulas also reveal that the number is minimal when the maximum number of intersection between adjacent input fuzzy sets is one practical implications of these results will be discussed especially in the context of fuzzy control and fuzzy modeling two examples are provided to demonstrate how to design fuzzy systems to approximate given functions with required approximation accuracy

trade offs between depth and width in parallel computation a new technique for proving lower bounds for parallel computation is introduced this technique enables us to obtain for the first time nontrivial tight lower bounds for shared memory models of parallel computation that allow several processors to have simultaneous access to the same memory location specifically we use a concurrent read concurrent write model of parallel computation it has p processors each has access to a common memory of size m also called communication width or width in short the input to the problem is located in an additional read only portion of the common memory for a wide variety of problems including parity majority and summation we show that the time complexity t depth and the communication width m are related by the trade off curve mt 2 omega n where n is the size of the input regardless of the number of processors moreover for every point on this curve with m o n log 2 n we give a matching upper bound with the optimal number of processors we e

on separation axioms in fuzzy topological spaces fuzzy neighborhood spaces and fuzzy uniform spaces submitted by l zadeh a certain number of separation axioms for fuzzy topological spaces are provided all of which are good extensions of the topological t t or t2 all valid implications between the different axioms are studied and counterexamples are given for the nonvalid ones in this paper we introduce and study a number of separation properties of fuzzy topological fuzzy neighborhood and fuzzy uniform spaces all of which are extensions of t t and t in topological spaces we started from the viewpoint that separation axioms at least t originated in the need to guarantee in some sense uniqueness of limits and we tried to generalize the topological t axiom in that direction it appears that a whole range of axioms from a fairly weak condition wt up to a rather strong one tj all give rise to acceptable extensions of the topological property moreover it seems likely that it will not be possible to single out one axiom in fuzzy topology as the best extension of topological t2 we showed in a preceding paper 181 on completions of fuzzy uniform spaces that tj as well as wt collapsing with wt in uniform spaces have a specific role to play in the same sense wt has already shown its usefulness in the study of hyperspaces 131 and t2 in its relation with compactness 191 as to our other axioms from t to wt they all seem to be natural generalizations of the corresponding properties in topological spaces and of the different t notions in fuzzy topological spaces they are moreover hereditary and t and ty excepted also productive as to the relations with other work in this field we first point out that our wt axiom is in fact the 1 hausforff separation property of hiihle 2 31 hutton and reilly in 4 and rodabaugh in 161 also studied separation current address is rijksuniversitair centrum 2020 antwerpen belgium

a performance approach to fuzzy control design for nonlinear systems abstract this paper presents a systematic methodology to the design of a decentralized fuzzy logic controller for large scale nonlinear systems a new method which is based on a performance index of sliding mode control is used to derive fuzzy rules and an adaptive algorithm is used to reduce the chattering phenomenon the simulation results of a two inverted pendulum system and a two link manipulator demonstrate that the attractive features of the proposed approach include a smaller residual error and robustness against nonlinear interactions

stable adaptive fuzzy sliding mode control of interconnected systems the problem of stable adaptive fuzzy control for a class of interconnected systems with unknown control gains is studied in this paper by using fuzzy modeling method a design scheme of an adaptive fuzzy controller is proposed the design is capable of incorporating linguistic and numerical information into controllers by theoretical analysis the closed loop adaptive fuzzy control system is proved to be globally stable in the sense that all signals involved are bounded with tracking errors converging to a neighborhood of zero

adaptive control of a class of nonlinear systems with fuzzy logic an adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture employs fuzzy systems which are expressed as a series expansion of basis functions to adaptively compensate for the plant nonlinearities global asymptotic stability of the algorithm is established in the lyapunov sense with tracking errors converging to a neighborhood of zero simulation results for an unstable nonlinear plant are included to demonstrate that incorporating the linguistic fuzzy information from human experts results in superior tracking performance

sensitive functions and approximate problems properties of functions that are good measures of the crcw pram complexity of computing them are investigated while theblock sensitivityis known to be a good measure of the crew pram complexity no such measure is known for crcw prams it is shown that the complexity of computing a function is related to itseverywhere sensitivity introduced by vishkin and wigderson specifically the time required to compute a functionf dn rof everywhere sensitivityes f withpprocessors and unbounded memory is logloges f log d 4p es f this improves results of azar and of vishkin and wigderson this lower bound is used to derive new lower bounds for someapproximate problems these problems can often be solved faster than their exact counterparts and for many applications it is sufficient to solve the approximate problem it is shown thatapproximate selection approximate counting approximate compaction andpadded sortingall require time loglogn with a linear number of processors if the level of accuracy desired is moderately high for these levels of accuracy no lower bounds were known for these problems on the pram model the lower bounds for some of the problems are tight

h tracking based adaptive fuzzy neural control for mimo uncertain robotic systems with time delays in this paper a novel adaptive fuzzy neural control afnc scheme for multi input multi output uncertain robotic systems is proposed for h tracking performance and to suppress the effects caused by multiple time delayed state uncertainties unmodeled dynamics and disturbances each delayed uncertainty is assumed to be bounded by an unknown gain a reference model with the desired amplitude and phase properties is given to construct an error model a fuzzy neural fn system is used to approximate an unknown controlled system from the strategic manipulation of the model following tracking errors the proposed afnc scheme uses two on line estimations which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the fn system simultaneously stability and robustness of the afnc scheme is analyzed in lyapunov sense it is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed loop system with h tracking performance for the overall system without a priori knowledge on the upper bounds of the delayed state uncertainties the performance of the proposed scheme is evaluated through the simulation results simulations are given to show the validity and confirm the performance of the proposed scheme

a comparison of some hausdorff notions in fuzzy topological spaces abstract several different notions of the hausdorff separation property for fuzzy topological spaces have appeared in the literature this paper is a study of the relationships between 12 of these concepts

on fuzzy topological spaces abstract in this paper a few separation properties and some aspects of subspace fuzzy topology have been studied where both the crisp and the fuzzy elements have been taken into consideration since the conventional definition of compactness is not quite meaningful in hausdorff fuzzy spaces as introduced by us a new more natural definition of proper compactness is given and a few properties resulting from this are established

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

on fuzzy d continuity and a near compactness in fuzzy topological spaces abstract the concept of fuzzy continuity was introduced by saha 18 mashhour et al have introduced the concept of near compactness in fuzzy setting in this paper we give a characterization of fuzzy continuity and fuzzy nearly compactness also we investigate the image of fuzzy nearly compact spaces under some types of functions finally a refinement is made to some results in 15 17

fuzzy topological properties and hereditariness some known compactness notions and separation axioms already given in chang fuzzy topological spaces are extended to a more general context of categories where i topological spaces on arbitrary i sets are defined the invariance under morphisms in these categories and the usual hereditary conditions of the considered topological properties in such a context are investigated

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

a note on some ft 2 concepts abstract in this note we study in particular the fuzzy hausdorffness concepts introduced by adnadjevic 1 ganguly and saha 4 and sarkar 17

separation axioms and the fuzzy real lines we show that for each lattice l which is completely distributive and equipped with an order reversing involution the canonical topology of the fuzzy real line l is uniformizable in the sense of hutton furthermore this uniformity induces a pseudometric which induces the canonical topology consequently l satisfies the higher order separation axioms of hutton and sarkar more generally we answer most of the open questions concerning l and its subspaces with respect to each of the separation axiom schemes of hutton and sarkar answer some of these same questions for the stratified fuzzy real line c l and its subspaces and analyze c l and its subspaces with respect to the separation axioms of rodabaugh

open maps closed maps and local compactness in fuzzy topological spaces on donne des caracterisations des applications floues ouvertes et fermees et on montre que la normalite definie par hutton est invariante sous des applications f fermees f continues

functions and as closedness in fuzzy topological spaces abstract in this paper we discuss s closedness in fuzzy topological spaces and we give some characterizations of s closedness also we investigate the image and the inverse image of s closed spaces under some types of functions and we improve and generalize some results on s closed spaces in fuzzy setting

limits on the power of concurrent write parallel machines abstract the computation of specific functions using the most general form of concurrent read concurrent write parallel ram is considered it is shown that such a machine can compute any function of boolean inputs in time log n log log n o 1 given a polynomial number of processors and memory cells and that this bound is tight for integer addition despite this evidence of the power of the model we show that a very simple function namely parity requires time log n to compute given a polynomial bound on the number of processors independent of the number of memory cells

robust control by fuzzy sliding mode abstract most fuzzy controllers fcs for nonlinear second order systems are designed with a two dimensional phase plane in mind we show that the performance and the robustness of this kind of fc stems from their property of driving the system into the sliding mode sm in which the controlled system is invariant to parameter fluctuations and disturbances additionally the continuous distribution of the control values in the phase plane causes a behavior similar to that of a sliding mode controller smc with a boundary layer bl near the switching line this gives assured tracking quality even in the presence of high model uncertainties tracing the fc back to the principle of an smc one obtains evidence about the stability of the closed loop system the choice of the scaling factors for the crisp inputs and outputs can be guided by the comparison of the fc with the smc and with the modified smc respectively at the end of the paper an fc for a higher order system is proposed simulation results show the practicability of the method

n sequential compactness abstract in this paper we first recall the pathological property of sequentially compact fts defined in 1 and define n sequential compactness in this way the so called general sequential compactness is a special kind of n sequential compactness then we discuss the properties of n sequential compactness finally it is pointed out that n sequantial compactness is a good extension 5 of sequential compactness

on the goodness of some types of fuzzy paracompactness abstract we introduce in fuzzy topological spaces definitions of paracompactness almost paracompactness and nearly paracompactness all of which turn out to be good extensions of their classical topological counterparts fuzzy semi paracompact para s closed weakly compact and rs paracompact spaces are treated to a similar approach

separation axioms in fuzzy topological ordered spaces abstract since the fuzzy topological space x may be considered as a fuzzy topological ordered space when it is realised that the non empty set x is partially ordered by agreeing that x y in x if and only if x y then the study of the fuzzy topological ordered spaces not only includes the study of the abstract fuzzy topological spaces but also reveals many generalizations of well known results concerning the abstract fuzzy topological spaces this paper provides a certain number of separation axioms for fuzzy topological ordered spaces which we label ft i order separation axioms for i 1 2 3 4 the relationships between some of the ft i order separation axioms are studied

fuzzy neighborhood spaces abstract in this paper we introduce a subcategory of the category of fuzzy topological spaces and we prove basic properties of this subcategory the main idea behind these spaces is the notion of fuzzy neighborhoods which enables us to introduce a local theory of fuzzy topologies

on sequentially closed graph mappings in fuzzy neighborhood spaces abstract two notions of closed graph and strongly closed graph in fuzzy neighbourhood spaces have been introduced one in fuzzy sets and system 48 1992 377 382 and the other by the author we prove that those notions are equivalent we introduce the notion of sequential convergence in fuzzy neighbourhood space

on decomposition of proper compactness in fuzzy topological spaces on introduit les notions de 2 compacite et de metacompacite floue pour des espaces topologiques flous et on demontre le theoreme suivant un espace topologique flou x est proprement compact si et seulement si il est 2 compact et metacompact flou

robust adaptive controller design for nonlinear time delay systems via t s fuzzy approach the robust control problem is investigated for a class of uncertain nonlinear time delay systems via the takagi sugeno t s fuzzification we obtain the t s fuzzy systems with each local model in the form of time delay systems with uncertain nonlinear functions the mismatched nonlinear functions satisfy the lipschitz condition while the matched parts are bounded by nonlinear functions with unknown coefficients based on the input matrix the system is decomposed into two cascade subsystems the virtual controller is designed for the first subsystem and then a memoryless adaptive controller is presented by employing a new lyapunov krasovskii functional we show that the resulting closed loop system is exponentially stable and the solutions are uniformly ultimately bounded finally simulation examples are given to show the effectiveness of our main results

on a topological model for the category of fuzzy topological spaces i we study global properties of fuzzy topological spaces which depend only on open sets fuzzy continuous functions and the relations we obtain many known theorems as purely topological theorems

frame fuzzy points and membership for a frame l the collection of l fuzzy subsets of a set x forms a locale the localic definition of points gives rise to l fuzzy points x where x x and is a prime element of l membership is defined in terms of a satisfactory local theory of l fuzzy topology emerges from this supplemented for some purposes by continuity of l

mappings and covering properties of topological groupoids the notion of fuzzy topological groupoid is defined stalk functions and g sets are used to express and study basic properties of topological groupoids separability and compactness in topological groupoids are investigated