paracompactness in l topological spaces in this paper a certain fuzzy paracompactness is presented by means of the concept of locally finite family of l fuzzy sets the concept of locally finite family can be used to characterize fuzzy countable compactness this fuzzy paracompactness is a natural generalization of lowen fuzzy compactness a fuzzy countably compact l set is fuzzy paracompact if and only if it is fuzzy compact a topological space x j is paracompact if and only if its induced space x j is fuzzy paracompact when ms l the fuzzy enhanced real line r l is fuzzy paracompact the product of a fuzzy compact set and a fuzzy paracompact set is fuzzy paracompact a fuzzy strongly t2 paracompact space is strongly s regular and strongly ws normal moreover a strongly s regular lindelof space is fuzzy paracompact

induced i l fuzzy topological spaces abstract in this paper we introduce the notion of induced i l fuzzy topological spaces by using the i l valued lower semicontinuous mappings and investigate some of their basic properties in particular we give a necessary and sufficient condition for an i l fuzzy topological space to be induced and prove that this kind of induced space preserves the cartesian product and the n compactness as well

a tendency to a formation of two dimensional self consistent structures in coulomb systems a class of periodic solutions of the two dimensional poisson boltzmann system was found these jacobi elliptic functions reveal a tendency to self organisation e g periodic spatial distribution for self consistent coulomb ensembles

fuzzy addition in the l fuzzy real line abstract under the hypothesis l is a chain we construct a binary operation on the l fuzzy real line r l which reduces to the usual addition on r if is restricted to the embedded image of r in r l which yields a partially ordered abelian cancellation semigroup with identity and which is jointly fuzzy continuous on r l we show is unique i e it is the only extension of addition to r l which is consistent we study the relationship between and other fuzzy continuous extensions of the usual addition we also show that fuzzy translation is a weak fuzzy homeomorphism and under certain conditions a fuzzy homeomorphism

discrete dynamical systems in l topological spaces in this paper we investigate iteration of zadeh image operators and their discrete dynamical systems in l topological spaces some basic concepts such as limit set invariant set periodic point nonwandering point and recurrent point are discussed in weakly induced topological spaces we also study topological mixing topological transitivity and minimality for such dynamical systems while comparing with those corresponding ones in crisp spaces

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

an iterative algorithm for pole placement by output feedback an iterative algorithm is proposed for solving the pole assignment by output feedback problem for an nth order l input m output linear system the algorithm uses a full rank feedback gain matrix and requires only linear equations of low dimension to be solved at each iteration application of the proposed algorithm allows all n closed loop poles to be almost exactly assigned provided that the iterations converge so that deviations of the resulting closed loop poles from the respective desired values become less than some user specified tolerance and m spl times t spl ges n examples are provided to illustrate the applicability of the proposed method

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

a new definition of fuzzy compactness in this paper a new definition of fuzzy compactness is presented in l topological spaces when l is a complete demorgan algebra this definition does not rely on the structure of the basis lattice l and no distributivity in l is required the intersection of a fuzzy compact l set and a closed l set is fuzzy compact the continuous image of a fuzzy compact l set is fuzzy compact if the set of all prime elements of l is order generating then the alexander subbase theorem is true when l is a completely distributive demorgan algebra it is equivalent to lowen s fuzzy compactness and in this case its many characterizations are presented by means of open l sets and closed l sets

on some types of fuzzy connectedness in fuzzy topological spaces abstract in this paper we present some counter examples related to the product of fuzzy connected spaces in addition fuzzy super c5 connectedness is defined and several relations between fuzzy c5 connectedness are obtained finally it is shown that fuzzy c5 connectedness is preserved under some types of continuity

a recurrent neural network for solving sylvester equation with time varying coefficients presents a recurrent neural network for solving the sylvester equation with time varying coefficient matrices the recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time varying solution of a given sylvester equation theoretical results of convergence and sensitivity analysis are presented to show the desirable properties of the recurrent neural network simulation results of time varying matrix inversion and online nonlinear output regulation via pole assignment for the ball and beam system and the inverted pendulum on a cart system are also included to demonstrate the effectiveness and performance of the proposed neural network

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

fuzzy proximities and totally bounded fuzzy uniformities after the classical papers of zadeh 181 and chang 3 many concepts of general topology have been extended to fuzzy set theory in this paper we are interested to develop the study of fuzzy uniformities fuzzy proximities and of the connexions between such structures fuzzy uniformities have been introduced by lowen in 9 and with slight modifications in lo and by hutton in 5 the two approaches are quite different however the one proposed by hutton seems to suit much better to fuzzy set theory also because it allows to generalize a lot of results in the most proper way therefore in this paper we shall deal with hutton fuzzy uniformities the concept of fuzzy proximity used up to now see e g 7 8 15 1 is quite unsatisfactory indeed its fuzzyness is rather poor since these fuzzy proximities are in a canonical l 1 correspondence with the usual proximities see remark 2 6 moreover the open sets of the induced topologies are crisp and though every lowen fuzzy uniformity induces a fuzzy proximity this correspondence cannot work well since the two structures do not give the same fuzzy topology for these reasons we propose a new definition of fuzzy proximity it differs from the old one only in axiom p5 in short we could say that we privilege complementation with respect to intersection an agreement between the two operations being problematic in fuzzy set theory we point out that as a consequence a fuzzy set may be far from itself however this fact ought not to amaze anyone since it may happen just for pale sets which in a certain sense resemble the empty set nevertheless this modification enables us to associate a topology in a completely different way moreover every fuzzy uniformity induces a fuzzy proximity and vice versa we succeed to construct a fuzzy uniformity starting with a given fuzzy proximity and the induced topologies do not change at any step this implies that the topologies which admit a fuzzy proximity are exactly the completely regular ones moreover we prove that there exists a l l correspondence between fuzzy proximity spaces and a

an algorithm for pole assignment in high order multivariable systems an efficient computational method is presented for solving the problem of pole assignment by state feedback in linear multivariable systems with large dimensions a given multiinput system is first transformed to an upper block hessenberg form by means of orthogonal state coordinate transformations the state feedback problem is then reformulated in terms of the sylvester equation the transformed system matrices along with certain assumed block forms for unknown matrices enable the sylvester equation to be decomposed and solved effectively a distinct point of the proposed algorithm is that the solution procedure can be tailored to parallel implementation and is therefore fast computational aspects of the algorithm are discussed and numerical examples are provided

a new approach for instantaneous pole placement with recurrent neural networks and its application in control of nonlinear time varying systems in this paper we first show that online computation of feedback gain used for pole placement of nonlinear systems in recent years is not reliable and then we present a new approach for instantaneous pole placement and apply it with dynamical recurrent neural networks for online computation of feedback gain because of high speed convergence of neural network to feedback gain we can apply this method for pole placement of nonlinear time varying systems one strategy for realization of this method is instantaneous linearization as we do here by simulation the advantage of the proposed method is a global uniform asymptotical exponential stability guaes of closed loop system around the equilibrium point

a new approach to fuzzy topological spaces and various fuzzy topological notions defined by nets n fuzzy spaces introduced by the authors are further investigated various fuzzy topological motions such as fuzzy local compactness functions with closed fuzzy graph fuzzy subcontinuity inverse fuzzy subcontinuity etc are studied in the light of n i these notions are found to be more coherent in n i than in the chang s category

time coarse graining near critical points the authors investigate the statistical properties of local variables coarse grained in time in systems undergoing continuous phase transitions a general theory is developed which suggests universal scaling behaviour in the limit of large coarse graining times the predictions are substantiated with monte carlo studies of two dimensional scalar models a simple fractal model of the time profile of the ordering variable is developed which captures and illuminates its timescale invariant character the theory is used to study the critical behaviour of local resonance lineshapes in the two dimensional case studied explicitly the critical slowing down is shown to drive a crossover to a split slow motion lineshape

t convergence of nets of l fuzzy sets and its applications abstract in this paper the theory of convergence on nets of l fuzzy sets which is a generalization of the convergence theory of fuzzy nets introduced by sarma and ajmal is established some important and interesting results in l fuzzy topology are obtained by means of the theory

on fuzzy almost continuous functions abstract in this paper we redefine the notions of open fuzzy set closed fuzzy set adherent point of a fuzzy set and closure of a fuzzy set all the results pertaining to these notions see velicko 17 are extended to fuzzy setting and several related characterization of fuzzy almost continuous functions are obtained which are the counterparts of the corresponding results in general topological spaces 12 some more properties of fuzzy almost continuous functions are established subsequently a characaterization of normal fuzzy topological spaces is also obtained the notion of fuzzy almost quasi compact mapping is introduced and its characterizations and relationship with fuzzy almost continuous functions are discussed

connectedness and local connectedness in fuzzy topological spaces and heyting algebra valued sets abstract in this paper we introduce four notions of local connectedness in fuzzy topological spaces the question of these notions to be good extensions is discussed and their preservation under fuzzy quotients fuzzy sums and fuzzy products is investigated moreover we introduce the notion of quasi local connectedness which is a peculiarity of the fuzzy setting

new applications of l nets in l fuzzy multifunctions in this paper we will give new applications of l net in l fuzzy multifunctions using l net we will further study l fuzzy continuous almost continuous and r continuous multifunctions some interesting characterizations are obtained

fuzzy almost continuity and its pointwise characterization by dual points and fuzzy nets abstract we introduce the notions of fuzzy almost continuity and fuzzy weak continuity at a fuzzy point following the pointwise approach we investigate their fuzzy topological properties we also obtain a pointwise characterization of fuzzy almost continuous functions by dual points and fuzzy nets the main idea behind this work is to establish a local theory in the study of continuity and its weaker forms in general fuzzy topological spaces

pole assignment via sylvester s equation it is shown that the pole assignment problem can be reduced to solving the linear matrix equations ax xa bg fx g successively for x and then f for almost any choice of g the result is a new pole assignment procedure and proof of the pole assignment theorem that should play an important role in both theoretical and practical applications

net convergence in fuzzy neighborhood spaces our aim is to introduce a concept of net convergence in the well behaved subcategory of lowen fuzzy neighborhood spaces of the category of fuzzy topological spaces in doing so we notice that our present notion of net convergence in addition to katsaras and papageorgeou net convergence is generalized sequential convergence we also apply this notion of net convergence in fuzzy neighborhood groups and fuzzy neighborhood linear spaces

fuzzy closed and fuzzy perfect mappings abstract it is shown that a fuzzy continuous map f is fuzzy perfect iff f i z is fuzzy closed for every fuzzy topological space z

minimal hausdorff l fuzzy topological spaces abstract in this paper the author introduced the concept of minimal hausdorff l fuzzy topological spaces investigated basic properties of it by means of fuzzy ideals and fuzzy nets and compared it with the concepts of compactness and h closedness

fuzzy sets and functions on fuzzy spaces abstract we generally follow the terminology of azad j math anal appl 82 1981 14 32 and ming j math anal appl 76 1980 571 599 in addition to the fundamental concepts for fuzzy sets we emphasize the usefulness of the concepts of fuzzy point fuzzy elementhood for fuzzy sets a and b a new characterization is given for relations a b and a b this knowledge permits us to combine the two definitions of fuzzy point fuzzy elementhood in the third section some results are given concerning various special types of fuzzy sets in fuzzy topological spaces and the fuzzy semi regular fuzzy regular spaces defined by azad in the last section the definitions of h almost continuous w almost open functions urysohn space which are defined by hussain wilansky and noiri respectively are extended to fuzzy sets furthermore some results are obtained in the functions of the fuzzy topological spaces defined by azad and those are defined here

fuzzy topologies and topological space objects in a topos abstract the purpose of this paper is to point out the link between lowen s fuzzy topologies and topological space objects in the topos l set as the main result we obtain the following theorem lowen s fuzzy topologies are the external version of the internal topologies in l set

on separation axioms and ti fuzzy continuity abstract we introduce and generalise concepts of t continuous functions in a fuzzy setting and study them in connection with the fuzzy continuity and fuzzy separation axioms some fuzzy topological properties are also investigated under such functions

a transfer matrix approach to random resistor networks introduces a transfer matrix formulation to compute the conductance of random resistor networks the authors apply this method to strips of width up to 40 and use finite size scaling arguments to obtain an estimate for the conductivity critical exponent in two dimensions t 1 28 or 0 03

localisation of charges according to the nonlinear self consistent electrostatic poisson boltzmann theory using the periodic solutions of the nonlinear poisson boltzmann equation it is shown that in a many particle coulomb system a periodic localisation of charges may occur the value of the charge density at which localisation commences is found this density and the spacing of the localised charges are shown to be characteristic properties of the system under investigation their values characterise the self organisation of the system the results depend on the nonlinearity of the poisson boltzmann equation and are not found if the linearised form is used

locale theory and fuzzy topology abstract for a lattice l which is a spatial frame it is shown that every l fuzzy topology t on a set x is isomorphic as a frame to a topology on the set x pt l where pt l is the set of points of l when t is topological the topology on x pt l is the product topology thus providing a simple test of goodness

metric properties of fractal lattices the authors study the connectivity dimension d of fractal lattices viewed as networks graphs of sites and constant length bond two examples are investigated in detail the 2d sierpinski gasket and 2d infinite percolation clusters on square and triangular lattices in the first case d is shown to coincide with the fractal dimension whereas d 1 72 or 0 02 appears as a universal exponent for percolation clusters in two dimensions considered as an intrinsic parameter the connectivity dimension d is compared with other intrinsic and extrinsic characteristic parameters of fractal lattices in particular the authors argue that d or d or d holds on fractal lattices in general d fractal dimension d spectral dimension

paracompactness in fuzzy topological spaces abstract in this paper we introduce two kinds of fuzzy paracompactnesses which are defined on general fuzzy subsets each of them is a good extension of crisp paracompactness they are all hereditary with respect to closed subsets and take n compactness and some other compactnesses in fuzzy topological spaces as special cases of them furthermore in a class of spaces so called weakly induced spaces which connects crisp spaces with fuzzy spaces both a fuzzy regular lindeloff property and a fuzzy pseudo metric property imply these two kinds of paracompactnesses

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

separation axioms for fuzzy spaces abstract using the concepts of fuzzy points as introduced by wong 15 and of belonging to as introduced by r srivastava s n lal and a k srivastava 13 we introduce several notions of fuzzy separation axioms and examine their productivity relations between these axioms have been observed we also introduce four types of separated fuzzy sets and clarify some relations between them

transfer matrix calculation of the relative noise exponent in a two dimensional percolating network a new method is given for calculating the relative noise exponent describing the size dependence of macroscopic fluctuations due to microscopic resistance noise of a random resistor network at the percolation threshold pc the macroscopic fluctuation is calculated exactly using the transfer matrix idea in a given network the asymptotic exponent b is found by finite size scaling

connectedness in fuzzy topological spaces abstract we introduce four notions of connectedness for an arbitrary fuzzy set and discuss all the implications that exist between them using these notions various equivalence relations are defined on the set of fuzzy points components and quasi components are formed as the union of certain equivalence classes a fuzzy space is shown to be a dispoint union of its components in all the four cases and non overlapping union of its quasi components

fuzzy subcontinuity inverse fuzzy subcontinuity and a new category of fuzzy topological spaces the notions of subcontinuity and inverse subcontinuity are extended to the fuzzy setting adopting fuzzy net theoretic approach various properties of fuzzy subcontinuous and inversely fuzzy subcontinuous mappings are studied a category of fuzzy topological spaces is constructed canonical example is constructed by using fuzzy translation of fuzzy numbers introduced by rodabaugh to show that fuzzy subcontinuity does not imply kfuzzy continuity in the process n compactness is characterized and fuzzy unit interval is shown to be n compact also a direct proof is provided showing that fuzzy addition of fuzzy numbers is fuzzy continuous

various fuzzy topological notions and fuzzy almost continuity abstract we extend the notion of almost continuity in the sense of husain 1966 to the fuzzy setting we obtain a pointwise characterization of the notion by dual point and fuzzy net also we formulate conditions under which the two notions of fuzzy almost continuity the one defined in this paper and the one defined by ajmal and azad 1990 turn out to be equivalent the main idea behind this work is to show that using the localized approach developed in earlier papers the study of fuzzy almost continuity can be carried out as successfully as that of its counterpart in general topology in the process we exhibit the compatibility of various existing fuzzy topological notions such as fuzzy regularity c i connectedness i 3 4 c i local connectedness i 3 4 fuzzy t 1 axiom fuzzy t 2 axiom etc

o convergence of fuzzy nets and its applications abstract in this paper an o convergence theory of fuzzy nets is built in l topological spaces by means of neighborhoods of fuzzy points it has many nice properties it can be used to characterize the closed set open set t 2 separation axiom and fuzzy compactness

a note on k k azad s fuzzy hausdorffness concept abstract in this paper we investigate the fuzzy hausdorffness concept of azad 1 and note that it neither generalizes the usual hausdorffness nor is a good extension of usual hausdorffness a new concept of fuzzy hausdorffness called hausdorffness related to azad s concept is then proposed and we observe that it in addition to being free from the drawbacks in azad s concept also possesses several pleasing properties

a new approach to fuzzy topological spaces and fuzzy perfect mappings abstract a net theoretic approach is provided for defining a fuzzy topological space fuzzy topological spaces so defined form a category the main features and advantages of this category which is denoted by n here are discussed the notion of a perfect mapping is introduced and studied in the fuzzy setting it is found that in n a fts is n compact iff any mapping x x where x is any singleton is fuzzy perfect a fuzzy continuous mapping x y from an n compact fts x to a hausdorff fts y is fuzzy perfect in n however these results do not hold in c the chang s category in general it is found that the divergences in the study of fuzzy perfect mappings disappear if the study is carried out in n instead of c

some important applications of nets of l fuzzy sets in this paper some compactness adherence point and accumulation point in l fuzzy topological space are characterized by means of the nets of l fuzzy subsets

fuzzy grills and a characterization of fuzzy proximity in his classical paper lo zadeh introduced the fundamental concept of fuzzy sets this idea was then applied to various other fields of mathematics including topology resulting in the study of fuzzy topology by chang i fuzzy uniformity by lowen 7 and fuzzy proximity by katsaras 5 thron is presented a new approach to poximity structures using the theory of grills an important concept introduced by choquet 3 the importance of grills in the proximity theory is noticed sufficiently in various other papers e g cf 2 4 also recently katsaras 6 introduced and studied filters ultrafilters and clusters in the new setup of fuzzy proximity on a set in the present paper we introduce fuzzy stacks and fuzzy grills and obtain a characterization of fuzzy proximity using fuzzy grills in section 2 fuzzy stacks and fuzzy grills and in section 3 on the lines of basic proximity or c proximity as described in 8 9 the concept of fuzzy basic proximity on a set are introduced also the fuzzy basic proximal neighborhood of a fuzzy set with respect to a fuzzy basic proximity is defined and some of the properties of sets of all fuzzy basic proximal neighborhoods of fuzzy sets are obtained finally in section 4 a necessary and sufficient condition for a fuzzy basic proximity to be a fuzzy proximity is obtained

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

overlapping families and covering dimension in fuzzy topological spaces abstract a non classical approach is used to introduce notions of overlapping families of fuzzy sets and the order of a family of fuzzy sets leading to a coherent theory of covering dimension in fuzzy topological spaces class of semicrisp fuzzy topological spaces is introduced which provides a suitable framework for the study of dimension function in the fuzzy setting

on fuzzy convergence classes abstract the concept of fuzzy point and its quasi coincidence neighborhood have been introduced in 1 using these notions we give the theory of fuzzy convergence classes especially a characterization of fuzzy topology via the fuzzy convergence classes and relative analysis are given

electrical properties of percolation clusters exact results on a deterministic fractal a recursively built deterministic fractal lattice generalising a model proposed by kirkpatrick 1979 is used to examine general electrical properties of percolation clusters in arbitrary dimensions most physical quantities are exactly analytically tractable since the model admits an exact renormalisation group transformation associated with a rational mapping t x of one complex variable the model has one free parameter f the fraction of conducting material which is put equal to the self dual point f 2 3 in two dimensions and chosen to reproduce the numerical values of the exponent ratio t nu in higher dimensions results concern in particular the frequency dependence of the impedance and the loss angle where the authors prove the existence of scaling laws at low and high frequency they also determine exactly the transient response to an arbitrary input signal and relate the distribution of relaxation times of the infinite lattice to well known mathematical objects associated to the rational transform t namely its julia set and its invariant measure the critical amplification of flicker or 1 f resistor noise is also considered it is shown to obey scaling laws with its own critical exponents in agreement with other recent works the relationships to other theoretical models and to experiments on metal insulator mixtures are discussed

zero dimensional and strongly zero dimensional fuzzy topological spaces abstract concepts of zero dimensionality strong zero dimensionality and total disconnectedness are extended to fuzzy topological spaces their basic properties and interrelationships among them are studied a sum theorem for strongly zero dimensional fuzzy topological spaces is also obtained

category n and functions with closed fuzzy graph abstract a net theoretic approach for defining a fuzzy topological space is provided the fuzzy topological spaces so obtained form a category which we denote by n in this paper it is found that the limitations exhibited by the chang category particularly with respect to projections closure of a fuzzy set compactness etc no longer exist in n the notion of closed fuzzy graph is investigated the divergences shown by this notion are immediately put to rest if the study is carried out in n instead of c the chang category

on the correspondence between the self consistent 2d poisson boltzmann structures and the sine gordon waves by means of the transformation connecting the sine gordon equation and the two dimensional poisson boltzmann equation a correspondence between the self consistent two dimensional poisson boltzmann structures and the solutions of the sine gordon equation representing standing waves has been established in this way two new solutions of the sine gordon equation were obtained and studied and their application for description of waves into ferromagnetics was examined

directed family of fuzzy sets and fuzzy perfect maps the present paper deals with the perfect functions in fuzzy setting fuzzy filter bases of fuzzy sets are also studied vis a vis such functions finally certain fuzzy topological properties are taken up for their study with regard to fuzzy perfect functions

on some gross misunderstandings about the theory of topological molecular lattices abstract some gross misunderstandings have arisen since the theory of topological molecular lattices briefly tmls was presented wang 1989 1992 certain scholars think that there is a correspondence between tmls and classical spaces and they could obtain the results in the theory of tmls hence fuzzy topology by simply translating the corresponding results in classical topology the aim of this paper is to clear out such misunderstandings

on some necessary and sufficient conditions for a recurrent neural network model with time delays to generate oscillations in this paper the existence of oscillations for a class of recurrent neural networks with time delays between neural interconnections is investigated by using the fixed point theory and liapunov functional we prove that a recurrent neural network might have a unique equilibrium point which is unstable this particular type of instability combined with the boundedness of the solutions of the system will force the network to generate a permanent oscillation some necessary and sufficient conditions for these oscillations are obtained simple and practical criteria for fixing the range of parameters in this network are also derived typical simulation examples are presented

a categorical accommodation of various notions of fuzzy topology different definitions of fuzzy topology have been stated and developed in the literature but have not been satisfactorily related to each other and to ordinary topology to remedy this a new fuzzy topological category fuzz is defined it is a significant generalization of previous definitions it is the simplest setting yet constructed into which ordinary topology and these previous definitions may be placed by identifying each with a different subcategory of fuzz it therefore allows us to conveniently analyze the relative merits of previous definitions give coherence to known results and indicate appropriate directions for future development and it generates and may be viewed as both including and included in categories of fuzzy topological spaces which exhibit higher order fuzziness