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

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

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

a comparison of simulated annealing cooling strategies using computer experiments on a simple three state system and an np complete system of permanents we compare different proposed simulated annealing schedules in order to find the cooling strategy which has the least total entropy production during the annealing process for given initial and final states and fixed number of iterations the schedules considered are constant thermodynamic speed exponential logarithmic and linear cooling schedules the constant thermodynamic speed schedule is shown to be the best we are actually considering two different schedules with constant thermodynamic speed the original one valid for near equilibrium processes and a version based on the natural timescale valid also at higher speeds the latter one delivers better results especially in case of fast cooling or when the system is far from equilibrium also with the lowest energy encountered during the entire optimization the best so far energy as the indicator of merit constant thermodynamic speed is superior finally we have compared two different estimators of the relaxation time one estimator is using the second largest eigenvalue of the thermalized form of the transition probability matrix and the other is using a simpler approximation for small deviations from equilibrium these two different expressions only agree at high temperatures

ps convergence theory of fuzzy nets and its applications the convergence theory not only is an significantly basic theory of fuzzy topology and fuzzy analysis but also has wide applications in fuzzy inference and some other aspects in this paper we introduce the concept of psc remote neighborhood of fuzzy points and establish the moore smith ps convergence theory of fuzzy nets also we discuss the applications of ps convergence of fuzzy nets

on the phase diagram of the discrete z6 spin models we point out some problems with the previously proposed phase diagram of the z6 spin models consideration of the diagram near to the decoupling surface using both exact and approximate arguments suggests a modification which remedies these deficiencies with the aid of a new parametrization of the phase space we study the models numerically with results which support our conjectures

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

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

the sr compactness in l fuzzy topological spaces abstract in this paper we introduce and study the sr compactness in l fuzzy topological spaces it possesses the following properties 1 sr compactness is defined for arbitrary subsets 2 sr compactness is hereditary for strongly semiclosed subsets 3 sr compactness is preserved under s irresolute mapping 4 every set with finite support is sr compact also the sr compact space is described with cover form and family of strongly semiclosed sets having a finite intersection property

effect of random field disorder on the first order transition in p spin interaction model abstract we study the random field p spin model with ising spins on a fully connected graph using the theory of large deviations in this paper this is a good model to study the effect of quenched random field on systems which have a sharp first order transition in the pure state for p 2 the phase diagram of the model for bimodal distribution of the random field has been well studied and is known to undergo a continuous transition for lower values of the random field h and a first order transition beyond a threshold h t p 0 439 we find the phase diagram of the model for all p 2 with bimodal random field distribution using large deviation techniques we also look at the fluctuations in the system by calculating the magnetic susceptibility for p 2 beyond the tricritical point in the regime of first order transition we find that for h t p h 0 447 magnetic susceptibility increases rapidly even though it never diverges as one approaches the transition from the high temperature side on the other hand for 0 447 h 0 5 the high temperature behaviour is well described by the curie weiss law for all p 2 we find that for larger magnitudes of the random field h h o 1 p the system does not show ferromagnetic order even at zero temperature we find that the magnetic susceptibility for p 3 is discontinuous at the transition point for h h o

separation axioms in fuzzy topological spaces abstract in this paper certain fuzzy separation axioms are studied in terms of the notions of quasi coincidence q neighbourhoods and fuzzy closure operators fuzzy t2 and urysohn spaces are defined and fuzzy spaces satisfying these axioms are characterized a fuzzy pointwise formulation of a fuzzy t2 axiom of hutton and reilly 1980 is found fuzzy regularity and almost regularity are investigated yielding various characterizing properties of these spaces certain relationships among all those fuzzy separation axioms are also discussed

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

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

unusual universality of branching interfaces in random media we study the criticality of a potts interface by introducing a froth model which unlike its solid on solid ising counterpart incorporates bubbles of different phases the interface is fractal at the phase transition of a pure system however a position space approximation suggests that the probability of loop formation vanishes marginally at a transition dominated by strong random bond disorder this implies a linear critical interface and provides a mechanism for the conjectured equivalence of critical random potts and ising models

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

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

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

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

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

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

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

critical behavior of the random bond ashkin teller model a monte carlo study the critical behaviour of a bond disordered ashkin teller model on a square lattice is investigated by intensive monte carlo simulations a duality transformation is used to locate a critical plane of the disordered model this critical plane corresponds to the line of critical points of the pure model along which critical exponents vary continuously along this line the scaling exponent corresponding to randomness varies continuously and is positive so that randomness is relevant and different critical behaviour is expected for the disordered model we use a cluster algorithm for the monte carlo simulations based on the wolff embedding idea and perform a finite size scaling study of several critical models extrapolating between the critical bond disordered ising and bond disordered four state potts models the critical behaviour of the disordered model is compared with the critical behaviour of an anisotropic ashkin teller model which is used as a refference pure model we find no essential change in the order parameters critical exponents with respect to those of the pure model the divergence of the specific heat c is changed dramatically our results favor a logarithmic type divergence at tc c logl for the random bond ashkin teller and four state potts models and c log logl for the random bond ising model

irresolute and lmost open functions between fuzzy topological spaces abstract the aim of this paper is to introduce and characterize the concept of fuzzy irresolute functions which is strictly stronger than the concept of fuzzy semi continuous functions and independent of the concept of fuzzy continuous functions the independence of the two definitions of fuzzy almost open functions as introduced in 5 and 3 and some of their characterizations are also established

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

critical behavior of the pure and random bond two dimensional triangular ising ferromagnet we investigate the effects of quenched bond randomness on the critical properties of the two dimensional ferromagnetic ising model embedded in a triangular lattice the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method in the first part of our study we present the finite size scaling behavior of the pure model for which we calculate the critical amplitude of the specific heat s logarithmic expansion for the disordered system the numerical data and the relevant detailed finite size scaling analysis along the lines of the two well known scenarios logarithmic corrections versus weak universality strongly support the field theoretically predicted scenario of logarithmic corrections a particular interest is paid to the sample to sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality

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 weak semicontinuity abstract in this paper we introduce the fuzzy weakly semicontinuous mapping which is the weaker form of both fuzzy semicontinuous and fuzzy almost continuous mappings in fuzzy topological spaces however fuzzy weakly semicontinuous mapping and fuzzy weakly continuous mapping are independent notions then we discuss some characteristic properties of fuzzy semicontinuous fuzzy semiopen fuzzy semiclosed and fuzzy pre semi open mappings

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

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

convergence of an annealing algorithm the annealing algorithm is a stochastic optimization method which has attracted attention because of its success with certain difficult problems including np hard combinatorial problems such as the travelling salesman steiner trees and others there is an appealing physical analogy for its operation but a more formal model seems desirable in this paper we present such a model and prove that the algorithm converges with probability arbitrarily close to 1 we also show that there are cases where convergence takes exponentially long that is it is no better than a deterministic method we study how the convergence rate is affected by the form of the problem finally we describe a version of the algorithm that terminates in polynomial time and allows a good deal of practical confidence in the solution

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

effect of random impurities on fluctuation driven first order transitions we analyse the effect of quenched uncorrelated randomness coupling to the local energy density of a model consisting of n coupled two dimensional ising models for n 2 the pure model exhibits a fluctuation driven first order transition characterized by runaway renormalization group behaviour we show that the addition of weak randomness acts to stabilize these flows in such a way that the trajectories ultimately flow back towards the pure decoupled ising fixed point with the usual critical exponents apart from logarithmic corrections we also show by examples that in higher dimensions such transitions may either become continuous or remain first order in the presence of randomness

localization in a simple multichain catalytic absorption model we consider the phase transition in the ensemble of n polymer chains developing on the halfline all chains are independent of each other in all points except the origin x 1 where the point well is located the well depth depends on the number of beads of different chains simultaneously staying at the point x 1 we show that if the well depth grows faster than with n then all chains become localized simultaneously at the origin in the limit in the conclusion we discuss the connection of the above defined problem with the phase transition in the copolymer chain with a quenched random sequence of monomers using the replica approach

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

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

metropolis biogeography based optimization biogeography based optimization bbo is a new population based evolutionary algorithm ea although the exploitation level of bbo is good researchers found some weaknesses in its exploration this study proposes a new hybridization between bbo and simulated annealing sa to enhance its performance in this proposed algorithm the inferior migrated islands will not be selected unless they pass the metropolis criterion of sa and so the new algorithm is called mpbbo the performance of mpbbo is evaluated using 36 benchmark functions with five different cooling strategies of sa and then compared with the original and essentially modified bbo models the results show the exponential inverse and inverse linear cooling strategies provide best solutions but they are the slowest among these three strategies the exponential cooling rate can compromise between the solution quality and cpu time compared with the others also the inverse cooling rate is competitive and wins when the mutation stage is completely disabled the f test and t test show that mpbbo has significant differences further it has been observed through sensitivity analysis that mpbbo behaves like bbo and sa the parameters of sa and bbo can affect the performance of mpbbo which has more immunity against trapping into local optimums moreover the superiority of mpbbo appears when it is compared with non simplified migration based bbo models as well as other hybrid non hybrid eas

criticality in the randomness induced second order phase transition of the triangular ising antiferromagnet with nearest and next nearest neighbor interactions abstract using a wang landau entropic sampling scheme we investigate the effects of quenched bond randomness on a particular case of a triangular ising model with nearest j n n and next nearest neighbor j n n n antiferromagnetic interactions we consider the case r j n n n j n n 1 for which the pure model is known to have a columnar ground state where rows of nearest neighbor spins up and down alternate and undergo a weak first order phase transition from the ordered to the paramagnetic state with the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first order phase transition to a second order phase transition and using the lee kosterlitz method we quantitatively verify this conversion the emerging under random bonds continuous transition shows a strongly saturating specific heat behavior corresponding to a negative exponent and belongs to a new distinctive universality class with 1 135 11 1 744 9 and 0 124 8 thus our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent but a different thermal critical exponent as a wide variety of two dimensional 2d systems without and with quenched disorder

quenched randomness at first order transitions abstract a rigorous theorem due to aizenman and wehr asserts that there can be no latent heat in a two dimensional system with quenched random impurities we examine this result and its possible extensions to higher dimensions in the context of several models for systems whose pure versions undergo a strong first order transition we show that there is an asymptotically exact mapping to the random field ising model at the level of the interface between the ordered and disordered phases this provides a physical explanation for the above result and also implies a correspondence between the problems in higher dimensions including scaling relations between their exponents the particular example of the q state potts model in two dimensions has been considered in detail by various authors and we review the numerical results obtained for this case turning to weak fluctuation driven first order transitions we describe analytic renormalization group calculations which show how the continuous nature of the transition is restored by randomness in two dimensions

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

fuzzy strongly semiopen sets and fuzzy strong semicontinuity abstract in this paper we first introduce and study the fuzzy strongly semiopen and fuzzy strongly semiclosed sets in fuzzy space then we introduce the strong semi interior and strong semiclosure of a fuzzy set and kuratowski s 14 sets theorem of general topology is generalized finally we introduce the fuzzy strongly semicontinuous fuzzy strongly semiopen and fuzzy strongly semiclosed mappings on fuzzy topological spaces and also establish some of their characteristic properties and discuss relations between fuzzy continuous fuzzy semicontinuous and fuzzy strongly semicontinuous mappings

renormalisation group study of a disordered model we study the potts model on a diamond hierarchical lattice with random interactions using weak disorder expansions we calculate analytically the position and the exponents of the random fixed point which appears when the specific heat exponent ap of the pure system becomes positive at ap 0 we find how the logarithmic singularity is modified by the disorder lastly we suggest that this model should present griffiths like singularities

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