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

q convergence of nets and weak separation axioms in fuzzy lattices abstract in this paper we introduce the concept of q remote neighborhood and establish the q convergence theory of nets in fuzzy lattices next we introduce the st i i 1 0 1 2 separation axioms in fuzzy lattices and discuss some of their characterizations finally we introduce and study s irresolute order homomorphism and s homeomorphism discuss the application of q convergence of nets and show that the st i i 1 0 1 2 separability is preserved under s homeomorphism

on two weakers forms of continuous order homomorphisms the aim of this paper is to find further connections between two different current researches on fuzzy topology the one based on the concepts of neighborhood filter and zadeh function and the other based on the concepts of remote neighborhood ideal and order homomorphism on fuzzy lattices to approach this the paper studies two weaker forms of continuous order homomorphisms the semi continuous order homomorphism and the weakly semi continuous order homomorphism between l fuzzy topological spaces these order homomorphisms can be characterized in each of the notions remote neighborhood neighborhood ideal filter and molecular net in addition some relations connecting weakly semi continuous order homomorphisms semi hausdorff l fts and urysohn l fts have also been established

damage integration in the strain space the focus is on isotropic elastodamaging softening materials where the damage parameter is expressed as a function of the total strain by integrating the mechanical work in the strain space along a stepwise holonomic loading history an incremental strain energy is obtained a coaxiality condition for the incremental strain energy to be potential is identified and its implications on the associativity of the damage evolution are discussed under some hypotheses the increment of the mechanical work is shown to be minimum along strain radial paths these results are used to construct a multifield variational framework supporting finite element nonlocal formulations

construct fuzzy lattices from a given symmetric complete lattice abstract fuzzy lattices are the basic objects which l fuzzy topology bases on we study relations of fuzzy lattices and symmetric complete lattices from category points of view a relevant fuzzy lattice l and a relevant symmetric complete heyting algebra l are constructed from a given symmetric complete lattice l we prove that the constructions and are two functors and they have reflective properties over relevant categories

structures of fuzzy order homomorphisms abstract first the concept of fuzzy order homomorphism is introduced which is a variety of the generalized order homomorphism given in 7 then we show that the fuzzy order homomorphism possesses a nicely local structure furthermore we establish a necessary and sufficient condition under which the fuzz function is a zadeh type function the present condition is simpler than that given in 6 finally for each fuzzy order homomorphism f we yield some characterizations about f 1 1 f which sharpen the corresponding theorem in 6

exponential stability for a class of state dependent delay equations via the crandall liggett approach abstract in this paper we are concerned with the exponential asymptotic stability of the solution of a class of differential equations with state dependent delays our approach is based on the crandall liggett approximation and the properties of semigroups

the uniform boundedness principle in l topological vector spaces in this paper we introduce and study the equicontinuity of a family of l fuzzy linear order homomorphisms we prove a generalization of the uniform boundedness principle in the classical topological vector spaces to l topological vector spaces

induced i l fuzzy topological vector spaces abstract in this paper we introduce and study the induced i l fuzzy topological vector spaces the following main result is proved if l x is an l fuzzy topological vector space then i l x i l is an i l fuzzy topological vector space where i l is the fuzzy unit interval and i l is the induced i l fuzzy topology of the l fuzzy topology furthermore we also prove that the induced i l fuzzy topological vector spaces i l x i l preserve the product and quotient space as well

gradient enhanced damage for quasi brittle materials summary conventional continuum damage descriptions of material degeneration suffer from loss of well posedness beyond a certain level of accumulated damage as a consequence numerical solutions are obtained which are unacceptable from a physical point of view the introduction of higher order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models a consistent numerical solution procedure of the governing partial differential equations is presented which is shown to be capable of properly simulating localization phenomena

connectedness on fuzzy topological spaces in this paper properties of connectedness on completely distributive topological lattices definition 2 1 and fuzzy topological spaces 1 are studied some equivalent propositions on the concepts of functions in completely distributive lattices and connected elements in completely distributive lattices and fuzzy topological spaces are proved specially connectedness is characterized both by the r neighborhoods of molecules and c separations for any family li i i i of fuzzy topological spaces the product 1 is connected iff every li i is connected a continuous function maps connected elements onto connected ones the connectedness on the fuzzy real line r l is discussed in the last section as an important example the intervals defined here definition 4 1 must be connected in the fuzzy real line r l and so the intervals defined by rodabaugh in 13 are too any connected element is connected in the fuzzy real line r l if and only if r l r

iterative lcp solvers for non local loading unloading conditions this paper deals with the finite element analysis of a certain class of non local dissipative constitutive models where the canonical pointwise backward euler scheme cannot be employed for satisfying the loading unloading conditions in the presence of a non local dissipation the admissibility conditions in a point depend on the inelastic strain increment of the surrounding points and can be cast as a linear complementarity problem lcp involving all gauss points of the process zone in order to actually solve the lcp the use of iterative algorithms that can be easily embodied into existing fe codes is discussed the performance of the proposed algorithms is tested in 1d and 2d examples for both elastoplastic and damaging materials copyright 2003 john wiley sons ltd

fuzzy boundary and characteristic properties of order homomorphisms abstract in this paper first the concept of the boundary of an element in a fuzzy topological space is defined and studied then the concepts of boundary preserving interior preserving and closure preserving order homomorphisms etc are introduced and discussed finally the relations among these are obtained

h λ completely hausdorff axiom on l topological spaces this paper defines the new concept of completely hausdorff axiom of an l topological space by means of l continuous mappings from an l topological space to the refined hutton s unit l interval by wang some characterizations of the completely hausdorff axiom defined in this paper are given and many nice properties of this kind of completely hausdorff axiom are proved for example it is hereditary and product invariant the refined hutton s unit l interval satisfy this kind of completely hausdorff axiom and when an l topological space satisfy this kind of completely hausdorff axiom every f convergent ideal does not have f limit points with different supports etc the relation between the completely hausdorff axiom defined in the paper and other separation axioms is discussed also

semigroup properties and the crandall liggett approximation for a class of differential equations with state dependent delays abstract we present an approach for the resolution of a class of differential equations with state dependent delays by the theory of strongly continuous nonlinear semigroups we show that this class determines a strongly continuous semigroup in a closed subset of c 0 1 we characterize the infinitesimal generator of this semigroup through its domain finally an approximation of the crandall liggett type for the semigroup is obtained in a dense subset of c as far as we know this approach is new in the context of state dependent delay equations while it is classical in the case of constant delay differential equations

a unified theory of elastic degradation and damage based on a loading surface a number of new models with stiffness degradation have been proposd in recent literature in the small strain regime however most of these works represent specific formulations each using its own terminology notation and assumptions and relatively little effort has been spent so far towards achieving a common theoretical framework similar for instance to the theory of elastoplasticity moreover most of the existing damage models are presented with intensive recourse to abstract thermodynamics concepts and they combine stiffness degradation with plasticity which though being ultimately necessary to represent the actual material behavior makes it much more difficult to isolate analyse and understand the properties of the formulation for elastic stiffness degradation as a contribution in this field this paper presents a unifying theoretical framework to describe a class of models for elastic stiffness degradation based on the concept of loading surface the derivation includes two consecutive steps first the constitutive framework for elastic degrading models with evolution laws which are expressed directly in terms of the secant stiffness or compliance tensor and second the elastic damage models in which the scant stiffness or compliance is assumed to depend on a reduced set of damage variables with clearer physical meaning and simpler evolution laws whenever possible terminology is borrowed from the classical formulation of elastoplasticity and thermodynamic concepts are introduced only as needed both stress based and strain based developments are compared throughout the paper and the concept of associativity is reanalysed and generalized within the new unified framework of elastic degradation the most significant scalar damage models found in the literature are reinterpreted in the context of this unified theory finally a general expression is obtained for the tangential stiffness operator of associated scalar models stress and strain based of the 1 d type that includes all the models considered as particular cases more general damage formulations scalar non 1 d vectorial tensorial are reviewed and discussed systematically in a sequel paper

pointwise uniformities in fuzzy set theory a theory of pointwise quasi uniformities is based on fuzzy sets many theorems corresponding to the usual theorems in general topology are generalized on fuzzy sets in particular each fuzzy topological space is pointwise quasi uniformizable a pointwise uniformity is characterized in terms of a kind of complete regularity a uniformity on the fuzzy unit interval is constructed

another look at order homomorphisms on fuzzes abstract order homomorphisms between fuzzy spaces are considered a general result is established which leads to an extension and simplification of earlier work by g j wang fuzzy sets and systems 12 1984 281 288

on energy based coupled elastoplastic damage theories constitutive modeling and computational aspects abstract novel energy based coupled elastoplastic damage theories are presented in this paper the proposed formulation employs irreversible thermodynamics and internal state variable theory for ductile and brittle materials at variance with lemaitre s work on damage elastoplasticity the present formulation renders rational thermodynamic potential and damage energy release rate in contrast to previous work by simo and ju featuring an additive split of the stress tensor current formulation assumes an additive split of the strain tensor it is shown that the strain split damage elastoplasticity formulation leads to more robust tangent moduli than the stress split formulation the plastic flow rule and hardening law are characterized in terms of the effective quantities viz the effective stress space plasticity this mechanism is both physically well motivated and computationally efficient further a fourth order anisotropic damage mechanism is proposed for brittle materials rational mechanisms are also presented to account for the microcrack opening and closing operations as well as the strain rate dependency of microcrack growth efficient computational algorithms for proposed elasloplaslic damage models are subsequently explored by making use of the operator splitting methodology in particular new three step operator split algorithms are presented application is made to a class of inviseid and rate dependent cap damage models for concrete and mortar experimental validations are also given to illustrate the applicability of the proposed damage models

pointwise topology on completely distributive lattices abstract in this paper the author presents a kind of pointwise topology theory on complete completely distributive lattices which is both a generalization of fuzzy topology and a further generalization of the author s papers 14 15

srn continuous order homomorphism and its characterizations in this paper the concept of semi regular continuity of order homomorphism is introduced and characterized by molecular nets and ideals in l topological spaces furthermore several properties of this continuity including hereditability and multiplicable properties are studied

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

initial l fuzzy topologies determined by the family of l fuzzy linear order homomorphisms in this paper the properties of initial l fuzzy topologies determined by a family of l fuzzy linear order homomorphisms fang jin xuan 1997 and its properties are investigated as an application of these results we prove that the product of the family of l ftvses is l ftvs

generalization of kolmogoroff s theorem to l topological vector spaces in this paper the concept of l fuzzy normed linear spaces is introduced and some of its properties are studied then we give a necessary and sufficient condition for l topological vector spaces to be l fuzzy normable this is a generalization of kolmogoroff s theorem in the classical topological vector spaces to l topological vector spaces

separation axioms in l fuzzy topological spaces i t0 and t1 abstract using the notion of remote neighborhood we define the separation axioms t 0 and t 1 in l fuzzy topological spaces l fts the relations between our definitions hutton and reilly s and wang s are discussed and the separations of hutton s fuzzy unit interval and gantner s fuzzy real line are examined characterizations of these l fts are proved and a series of properties of them are investigated moreover some results on minimal t 0 l fts and t 1 l fts are established which will be used immediately in our subsequent discussion

sr convergence theory in fuzzy lattices abstract convergence theory and order homomorphisms theory are two important objects of study in fuzzy lattices in this paper sr convergence theory for molecular nets and ideals is established and the concepts of r irresolute sr continuous and almost irresolute order homomorphisms in topological molecular lattices are introduced and systematically characterized some mutual relations between these concepts and others are obtained

l fuzzy smirnov compactifications in this paper we get the pointwise characterization of the l fuzzy topology induced by an l fuzzy proximity space and study some important properties of l fuzzy proximity induced spaces also we discuss the n compactness separated relations and separation axioms of l fuzzy proximity spaces on the base of the method of induced spaces and above conclusions we establish the l fuzzy smirnov compactification and construct an example for l fuzzy smirnov compactifications

existence of periodic solutions for delay differential equations with state dependent delay abstract in this paper we study the existence of periodic solutions of a delay differential equation with delay depending indirectly on the state a fixed point problem related to a poincare operator is constructed and solved using an ejective fixed point theorem

generalized zadeh function in 1986 he ming introduced the concept of biinduced mapping between two arbitrary l fuzzes in this paper we consider the order homomorphisms between two lattices on the basis of biinduced mapping and give the concept of generalized zadeh function the generalized zadeh function has almost all the fine properties of the zadeh function furthermore it has overcome the limitations of the zadeh function in applications and the shortcomings of order homomorphisms

fuzzy sets and de morgan algebras abstract this paper examines some relations between on the one hand the concept of fuzzy sets and fuzzy topologies and on the other hand the concept of complete de morgan algebras and the topologies associated herewith

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

on retrial queueing model with fuzzy parameters abstract this work constructs the membership functions of the system characteristics of a retrial queueing model with fuzzy customer arrival retrial and service rates the cut approach is used to transform a fuzzy retrial queue into a family of conventional crisp retrial queues in this context by means of the membership functions of the system characteristics a set of parametric non linear programs is developed to describe the family of crisp retrial queues a numerical example is solved successfully to illustrate the validity of the proposed approach because the system characteristics are expressed and governed by the membership functions more information is provided for use by management by extending this model to the fuzzy environment fuzzy retrial queue is represented more accurately and analytic results are more useful for system designers and practitioners

theory of topological molecular lattices abstract the aim of this paper is to bring the theories of point set topology fuzzy topology and l fuzzy topology into a unified theory the theory of topological molecular lattices for this purpose we first introduce the concepts of molecule for completely distributive complete lattice molecular lattice for short the cotopology on it and the concept of remote neighborhoods of molecules therefrom we develop the theory of pointwise topology on molecular lattices

a sufficient and necessary condition for fuzzy functions to be zadeh type functions abstract in this paper for an arbitrary fuzz l a sufficient and necessary condition for fuzz functions to be zadeh type functions is given

some results on i l and r l abstract this paper gives a partial solution to problem 1 in wang and lu 1992 and a suggestion about how to construct a better fuzzy unit interval it defines a new kind of fuzzy real line and investigates a series of its properties

parametric programming approach for batch arrival queues with vacation policies and fuzzy parameters this work constructs the membership functions of the system characteristics of a batch arrival queuing model with vacation policies and fuzzy batch arrival customer service and server vacation rates the cut approach is used to transform a fuzzy queue into a family of conventional crisp queues in this context by means of the membership functions of the system characteristics a set of parametric nonlinear programs is developed to describe the family of crisp queues with a vacationing server two numerical examples are solved successfully to illustrate the validity of the proposed approach because the system characteristics are expressed and governed by the membership functions more information is provided for use by management by extending this model to the fuzzy environment fuzzy queues with a vacationing server are represented more accurately and the analytic results are more useful for system designers and practitioners

generalization of inductive topologies to l topological vector spaces in this paper using the theory of l topological vector spaces we study some properties of inductive topologies determined by the family of l fuzzy linear order homomorphisms defined by fang jin xuan j fuzzy math 4 1 1996 93 and give a characterization of inductive topologies determined by a single l fuzzy linear order homomorphism as an example we point out the quotient l topology of l tvs is an inductive topology

fuzzy analysis of queueing systems with an unreliable server a nonlinear programming approach abstract this work constructs the membership functions of the system characteristics of a queuing model with an unreliable server in which the arrival rate and the service rate of customers as well as the breakdown rate and repair rate of server are all fuzzy numbers the cut approach is used to transform a fuzzy queue with an unreliable server into a family of conventional crisp queues with an unreliable server by means of the membership functions of the system characteristics a set of parametric nonlinear programs is developed to describe the family of crisp queues with an unreliable server an efficient algorithm is provided to find the optimal solutions at a different possibility level three numerical examples are solved successfully to illustrate the validity of the proposed approach due to the system characteristics being expressed and governed by the membership functions more information is provided for use by management by extending the fuzzy environment the fuzzy queues with an unreliable server can be represented more accurately by using the proposed approach and the analysis results for such queuing model will be useful and significant for system designers and practitioners

a two field finite element formulation for elasticity coupled to damage a two field variational formulation is proposed for continuum damage mechanics problems this formulation is applied to the numerical solution via the finite element method of initial boundary value problems arising in elasticity coupled to damage the nodal variables are the displacement and damage fields simple examples are presented to demonstrate the advantages and limitations of this formulation

connectivity in fuzzy topological molecular lattices abstract a new kind of the definitions for connectivity in a fuzzy topological molecular lattice called s connectivity is defined some properties for s connectivity are obtained and the relations between s connectivity and each connectivity given in 1 4 7 are discussed

q convergence of ideals in fuzzy lattices and its applications abstract in this paper we study q convergence and q convergence of ideals in fuzzy lattices by the concept of q remote neighborhood then we introduce the strong s irresoluteness s irresoluteness and s strong semicontinuity on fuzzy lattices we also study some properties of the notions above and strong semicontinuity 2 3 and s irresoluteness 3 4 with the aid of the q convergence q convergence of ideals

fuzzy neighborhood operators and derived fuzzy coverings abstract fuzzy coverings are natural extensions of the coverings by replacing crisp sets with fuzzy sets recently some fuzzy neighborhood operators based on a fuzzy covering were defined and their properties were investigated by d eer et al in this paper we propose four types of fuzzy neighborhood operators by introducing the notions such as neighborhood system fuzzy minimal description and fuzzy maximal description first we propose these notions and investigate their properties then we construct four types of fuzzy neighborhood operators based on the fuzzy coverings properties and relationship among these four types of fuzzy neighborhood operators are studied finally six types of fuzzy coverings were derived by using these four types of fuzzy neighborhood operators and their properties are considered

h l completely regular l fuzzy sets and their applications first we introduce the concept of h completely regular l fuzzy set in l fts and give some characterizations of it then we propose the concept of h complete regularization of l fts and investigate some properties of this complete regularization we also establish the relations between h completely regular l fts completely regular l fts and weakly induced l fts based on these results we obtain several characterizations of h completely regular l fts

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

representation theorem of fuzzy lattices and its applications in fuzzy topology abstract a fuzzy lattice is expressed as a direct product of all its minimal fuzzy sublattices and a pointwise characterization of fuzzy complete regularity is proved

completeness and an extension theorem for continuous fuzzy linear order homomorphisms in this paper the notions of cauchy net and completeness in l topological vector spaces are introduced and some of their properties are studied an extension theorem for continuous fuzzy linear order homomorphisms is proved

i type of strong connectivity in l fuzzy topological spaces in this paper we mainly introduce and study r type of strong connectivity for a given l fuzzy topological space it preserves many good properties of connected sets in general topological spaces for example any union of r type of strongly connected sets with nonempty intersection is r type of strongly connected the images of irresolute order homomorphism of r type of strongly connected sets are r type of strongly connected

damage gradient of damage and principle of virtual power a theory of continuum damage mechanics is developed within the framework of the principle of virtual power because the damage in a solid results from microscopic movements we decided to include the power of these microscopic movements in the power of the internal forces the microscopic velocities are related to the damage rate the power of the internal forces we choose depends on the damage velocity and its gradient to take into account the interactions models issued from this theory are presented they are coherent from the mechanical and mathematical points of view the numerical computations show no mesh sensitivity they describe with good agreement the main experimental properties concrete is chosen as an example to illustrate the theory a model using two damage quantities is also presented it yields the correct description of the unilateral phenomenon observed in concrete finally an extension of the existing models is proposed to describe the fatigue damage behaviour

the characterizations of semi continuous and irresolute order homomorphisms on fuzzes abstract the concepts of semi continuous and irresolute order homomorphisms on fuzzes were introduced in j jianghan petroleum institute 2 1988 96 97 in this paper we first present the theory with respect to s convergence s convergence of molecular nets and ideals on fuzzes secondly we introduce the notions of strong semicontinuity strong irresoluteness and s irresoluteness on fuzzes then we systematically study the characterizations of these notions with the aid of the s convergence s convergence of molecular nets and ideals and give the relations of them

order homomorphisms on fuzzes abstract in this paper basic properties of the concept of order homomorphisms on fuzzes 4 which is a proper generalization of the concept of fuzz functions 1 are studied conditions for fuzz functions to be functions of zadeh s type are obtained moreover the concepts of continuous closed and open order homomorphisms are introduced and studied

nonholonomic elastoplastic analysis involving unilateral frictionless contact as a mixed complementarity problem this paper deals with the elastoplastic analysis of suitably discretized elastoplastic structures under frictionless unilateral contact conditions whilst the mathematical programming formulation we adopt can cater equally for hardening as well as softening path dependent nonholonomic plasticity the state problem involving softening is by far the more difficult to solve in view of the inherent nonconvex nature of the underlying mathematical program we propose a novel description of a fairly general class of piecewise linear softening laws and investigate use of an approximate stepwise holonomic path independent approach for capturing the evolution of the structure with softening and or hardening constitutive laws this finite step problem is formulated in a specific way to take advantage of the use of a robust and industry standard complementarity solver named path from within the gams modeling environment we illustrate its application on truss like structures

local connectedness in l topological spaces this paper studies local strong f1 connectedness and local q connectedness of l topological spaces it is shown that every l interval j l and its weak inducification j l are both local strong f1 connected and local q connected and that the local q connectedness of an l topological space is equivalent to that of its induced i l topological space