fuzzy non continuous mappings and fuzzy pre semi separation axioms the aim of the paper is mainly to introduce and study fuzzy pre semi open mapping fuzzy pre semi irresolute mapping fuzzy pre semi separation axioms and fuzzy pre semi connectedness in fuzzy topological spaces

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

fuzzy initial convergence structure abstract we introduce the notion of fuzzy initial convergence structure induced by family of functions the notion of fuzzy initial convergence structure is shown to be a generalization of fuzzy product convergence structure

a note on lo fuzzy nearly compact spaces in this note we define lo fuzzy nc fuzzy sets and introduce the finite intersection property for fuzzy sets in the sense of lowen lo fip for short we give some equivalent characterizations of lo fuzzy nc spaces and lo fuzzy nc fuzzy sets by using lo fip regular open and regular closed fuzzy sets finally we prove that lo fuzzy nearly compactness is preserved under fuzzy almost continuous and almost open mapping

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

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

a note on compactness in a fuzzy setting abstract the concept of filter basis in a fuzzy setting is defined and investigated fuzzy filter bases are then used to introduce the notion of compactness in fuzzy setting the expected basic properties of compactness are explored

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

on various weak fuzzy pairwise retracts the notion of a fuzzy retract was introduced by rodabaugh j math anal appl 79 1981 273 and this notion was extended to the fuzzy bitopological setting j fuzzy math 9 1 2001 207 in this paper we define the notions of fuzzy pairwise semiretracts fuzzy pairwise preretracts fuzzy pairwise strongly semiretracts fuzzy pairwise less strongly semiretracts and fuzzy pairwise semi preretracts we establish some properties of these concepts moreover the relations between these new concepts are discussed

fuzzy semiregularization topologies and fuzzy submaximal spaces abstract the aim of the paper is to investigate the fuzzy semiregularization spaces associated with fuzzy topological spaces the concept of fuzzy submaximal spaces is introduced and it is proved that corresponding to every fuzzy topological space there always exists a fuzzy submaximal space which is an expansion of the given space fuzzy submaximal and semiregular spaces are shown to be closely associated with those spaces which are minimal or maximal with respect to certain types of properties which we call fuzzy semiregular properties this has induced us to take up different properties for investigation whether these are fuzzy semiregular ones lastly we consider certain mappings between fuzzy topological spaces and study their behaviour when either or both the domain and codomain spaces are replaced by their semiregulatization spaces

a fast algorithm for linear complex chebyshev approximations we propose a new algorithm for finding best minimax polynomial approximations in the complex plane the algorithm is the first satisfactory generalization of the well known remez algorithm for real approximations among all available algorithms ours is the only quadratically convergent one numerical examples are presented to illustrate rapid convergence

regularly open sets in fuzzy topological spaces abstract this paper is devoted to the study of the role of fuzzy regularly open sets we prove some properties of fuzzy almost continuous mappings and define fuzzy almost open mappings we prove that under a fuzzy almost continuous and fuzzy almost open map the inverse image of a fuzzy regularly open set is fuzzy regularly open further we define a new type of fuzzy separation axioms fuzzy almost separation axioms it is interesting that there are some deviations in the behaviour of these axioms as compared to those in general topology for example in a fuzzy almost t1 space not every fuzzy singleton is closed also a fuzzy space which is fuzzy almost t 2 1 2 as well as fuzzy almost t0 is fuzzy almost regular while in general topology we have to take an almost t2 space in place of almost t0 space

modifications of the first remez algorithm this paper proves the convergence of several modifications of the first remez algorithm for the solution of linear and nonlinear chebyshev approximation problems on compact b subset mathbb r s while the first remez algorithm in its original form requires the determination of the global maximum of the error function on all of b in each iteration the algorithms given here are based on its being sufficient to compute the maximum of the kth error function on a grid b k 1 where b k k geqq 0 is a prescribed sequence of finite point sets in b with density tending to zero interpreted differently some results on the discretization of chebyshev approximation problems which do not use full grids b k in b but only small subsets of them are provided the paper concludes with some numerical examples for the solution of linear multivariate problems

on independent statistical decision problems and products of diffusions letzt be a null recurrent diffusion on p with generatorg 1 r r for smooth positiver this note constructs an independent recurrent diffusionz ton 1 such that zt z t is transient in p 1 this resolves negatively an old question in simultaneous estimation is there an admissible but not bayes estimator x of the mean of a multivariate normal distribution for quadratic loss with the property for every admissible x wherex is normal and independent ofx remains admissible in the combined problem obtained by summing the component losses

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

semi open sets and semi continuity in fuzzy bitopological spaces abstract in this paper the concepts of fuzzy semi open sets and fuzzy semi continuous mappings due to azad 1981 have been generalized to fuzzy bitopological spaces and some of their properties are studied

fuzzy product topologies for x y abstract the aim of this paper is to study the product topologies in fuzzy topology the notion and main properties of fk spaces which play an important role in the sequel are introduced sufficient conditions for which the product of fuzzy identification maps is a fuzzy identification map are given

on several types of degree of fuzzy compactness abstract sostak 1985 defined a fuzzy topology on a set x as a fuzzy subset of the family i x of fuzzy subsets of x satisfying some axioms the concept of the degree of compactness of a fuzzy set was first introduced by sostak 1985 in this paper we discuss the degrees of almost compactness near compactness countable compactness light compactness and strong compactness of a fuzzy set also we investigate the behavior of the degrees of compactness under several types of fuzzy continuous functions

semi continous and semi closed mappings and semi connectedness in fuzzy setting abstract the aim of the paper is mainly to study and to find different characterizations of semi continuous and semi closed mappings between fuzzy topological spaces the notion of fuzzy semi open sets is used to define fuzzy ti spaces i 0 1 2 and these spaces are investigated under fuzzy semi continuity finally fuzzy semi connectedness is introduced and studied to some extent

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

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

some remarks on lo rs fuzzy compactness abstract in this paper we define lo rs fuzzy compact fuzzy sets we study some properties of lo rs fuzzy compact spaces and lo rs fuzzy compact fuzzy sets we give some characterizations of these notions by fuzzy regularly open sets and fuzzy regularly closed sets we prove that lo rs fuzzy compactness is preserved under a fuzzy almost continuous and fuzzy almost open mapping

approximation with one or few parameters nonlinear abstract in the case of one or few nonlinear parameters minimax approximation can be done by applying minimization with respect to the nonlinear parameters and reduction to a linear subproblem only the case of a linear subproblem with a haar subspace is considered in which case a linear remez algorithm is used

fuzzy topology and fuzzy multifunctions the fundamental concept of a fuzzy set was first introduced by zadeh in his classical paper 141 since then work has been done by many authors in several directions which has resulted in the formation of a new mathematical field called fuzzy mathematics the theory of fuzzy topological spaces is a branch of such mathematics chang in 2 was the first to introduce the notion of fuzzy topology several others continued the work in this area for example see 12 131 we remark that general point set topology can be regarded as a special case of fuzzy topology where all membership functions are just characteristic functions in this paper we introduce several fuzzy topological concepts and examine their properties our basic tool in that process is the notion of the fuzzy neighborhood of a point introduced by warren in ill we also introduce the notion of fuzzy multifunctions which we strongly believe will be useful in the study of fuzzy games and general fuzzy optimization problems we study the continuity and measurability properties of these multifunctions also we introduce linear fuzzy multifunctions and study their properties in the light of the recent work of katsaras 5 katsaras and liu s and lowen 9 on fuzzy vector spaces

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

a highly accurate trivariate spectral collocation method of solution for two dimensional nonlinear initial boundary value problems abstract in this paper we propose a new numerical method namely the trivariate spectral collocation method for solving two dimensional nonlinear partial differential equations pdes arising from unsteady processes the problems considered are nonlinear pdes defined on regular geometries in the current solution approach the quasi linearization method is used to simplify the nonlinear pdes the solutions of the linearized pdes are assumed to be trivariate lagrange interpolating polynomials constructed using chebyshev gauss lobatto cgl points a purely spectral collocation based discretization is employed on the two space variables and the time variable to yield a system of linear algebraic equations that are solved by iteration the numerical scheme is tested on four typical examples of nonlinear pdes reported in the literature as a single equation or system of equations numerical results confirm that the proposed solution approach is highly accurate and computationally efficient when applied to solve two dimensional initial boundary value problems defined on small time intervals and hence it is a reliable alternative numerical method for solving this class of problems the new error bound theorems and proofs on trivariate polynomial interpolation that we present support findings from the numerical simulations

fuzzy semi preopen sets and fuzzy semi precontinuous mappings abstract the aim of this paper is to introduce and discuss the concepts of fuzzy semi preopen sets and fuzzy semi precontinuous mappings

fuzzy convergence structures abstract we define a fuzzy convergence structure which is a correspondence between the prefilters on a given set x and the fuzzy subsets of x the notion of fuzzy convergence structure is shown to be a generalization of a fuzzy topology

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

a set of new separation axioms in l fuzzy topological spaces in this paper a set of new separation axioms in l fuzzy topological spaces are defined and studied we give several characterizations of these separation axioms and discuss certain relationships among them moreover some of their basic properties are also examined

fuzzy s continuous functions and semilocally connected fuzzy topological spaces abstract the concept of s continuous functions kohli 1978 is translated in fuzzy setting into two concepts fuzzy s continuous functions and fuzzy os continuous functions the concepts of semiconnected functions kohli 1978 and semilocally connected spaces kohli 1978 do the same interactions between those concepts in fuzzy setting and fuzzy continuity chang 1968 are discussed also characterizations of semilocally connected and semilocally o connected fuzzy topological spaces in terms of fuzzy s continuous functions and fuzzy os continuous functions respectively are obtained

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

the poisson compound decision problem revisited the compound decision problem for a vector of independent poisson random variables with possibly different means has a half century old solution however it appears that the classical solution needs smoothing adjustment we discuss three such adjustments we also present another approach that first transforms the problem into the normal compound decision problem a simulation study shows the effectiveness of the procedures in improving the performance over that of the classical procedure a real data example is also provided the procedures depend on a smoothness parameter that can be selected using a nonstandard cross validation step which is of independent interest finally we mention some asymptotic results

on fuzzy compactness in this paper we characterize well known fuzzy compactness see 3 4 9 and 10 using the notion of fuzzy upper limit see 5 also we give and study new fuzzy compactness in fuzzy topological spaces

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 fuzzy t convergences abstract in this paper we introduce and study the notions of fuzzy convergence and weakly convergence on a fuzzy topological space these notions can be considered as generalizations of the convergence defined in georgiou and papadopoulos 1998 also the forementioned convergence does not coincide with the one defined in chen and chenn 1997 the importance of these convergences relies on the fact that they behave equally well as the convergence defined in georgiou and papadopoulos 1998

a compactness in bifuzzy topological spaces abstract compact fuzzy topological spaces were first introduced by chang 3 compact fuzzy topological spaces were introduced by gantner et al 4 abd el monsef et al 1 introduced the notion of almost compact fuzzy topological spaces mashbour et al 8 introduced the notion of bifuzzy topological spaces and defined the notion of compactness in those spaces in this paper we obtain some new results about compact bifuzzy topological spaces we introduce and study the notion of pairwise almost compact bifuzzy topological spaces

admissible estimation dirichlet principles and recurrence of birth death chains on ℤ p we establish a connection between admissible simultaneous estimation and recurrence of reversible markov chains on specifically to each generalized bayes estimator of the mean of a vector of p independent poisson variables for a weighted quadratic loss we associate a variational problem and a reversible birth and death chain on the variational problem is closely related to the dirichlet principle for reversible chains studied recently by griffeath liggett and lyons under side conditions admissibility of the estimator is equivalent to zero infimal energy in the variational problem and to recurrence of the markov chain this yields analytic and probabilistic criteria for inadmissibility which are applied to establish a broad class of results and previous conjectures