vector valued variational principle in fuzzy metric space and its applications a vector valued ekeland s variational principle and its equivalents in fuzzy metric space are presented in this paper our result unifies and extends some of the previous results about single valued and vector valued ekeland s variational principle as an application we obtain a fixed point theorem in fuzzy metric space under a new contractive condition which is a new generalization of well known banach contraction principle all of our results are also new even in usual metric spaces

on the completion of fuzzy metric spaces this paper discusses the completion of a fuzzy metric space in the sense of kaleva and seikkala that is modeled by a pair of two place functions l and r previous work on this question is based on l min r max under the condition that l and r are a generic class of two place functions we characterize the completable fuzzy metric space and show that the corresponding completion is uniquely determined up to isometry furthermore we point out that with more conditions on r including on r max the completion of each fuzzy metric space exists and is unique up to isometry this improves the corresponding result of kaleva the completion of fuzzy metric spaces j math anal appl 109 1985 194 198

φ contractor and the solutions for nonlinear operator equations in fuzzy normed spaces in this paper we introduce the concept of contractor in fuzzy normed spaces and prove the existence and uniqueness theorems of solutions for set and single valued nonlinear operator equations with this kind of contractor as applications of these theorems we obtain some new fixed point theorems in fuzzy normed spaces

the completion of a fuzzy normed linear space abstract the concept of a fuzzy normed linear space was introduced in an earlier paper by the author finite dimensional fuzzy normed linear space fuzzy sets and systems 48 1992 239 248 it was shown therein that any finite dimensional fuzzy normed linear space is necessarily complete there do exist incomplete fuzzy normed linear spaces incompleteness is shown to have handicaps see section 3 there is a need for completion in the sense of enlarging the incomplete space so that the given space is embedded in the enlarged space it is shown in this paper see theorem 3 that this is really possible

a new i vector topology generated by a fuzzy norm this paper is devoted to the research for a topological structure for i vector on the fuzzy normed linear space in the sense of felbin by using a natural method a new i vector topology on the fuzzy normed linear space is constructed we study some of its properties and prove that the fuzzy normed linear space is a locally convex i topological vector space with respect to the i topology under a proper condition we give a necessity and sufficienct condition for a fuzzy normed linear space to be hausdorff and weakly hausdorff with respect to the i vector topology respectively in addition we also discuss the relations between this i vector topology and other two known i vector topologies on the fuzzy normed linear space lastly we give some canonical examples of fuzzy normed linear spaces using this i vector topology

some new sequence spaces of fuzzy numbers defined by orlicz functions using a fuzzy metric using orlicz functions and a fuzzy metric some new sequence spaces are introduced in this paper using the concept that the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number we study some basic properties of the new sequence spaces of fuzzy numbers also we investigate the relations between these spaces

coupled coincidence point results for compatible mappings in partially ordered fuzzy metric spaces coupled fixed point problems have attracted much attention in recent times in this paper we establish coupled coincidence point and coupled fixed point results in the context of fuzzy metric spaces the two mappings considered here are assumed to be compatible hadzic type t norm is used by an application of the coincidence point theorem in fuzzy metric spaces a corresponding result is obtained in metric spaces the main theorem of this paper is illustrated with an example our work extends some existing results

metrization theorems in l topological spaces abstract in this paper some characterizations of a pointwise uniformity are presented in l fuzzy set theory a new hausdorff separation axiom compatible with pointwise metric is introduced urysohn metrization theorem and alexandroff urysohn metrization theorem in general topology are generalized to l topology

fuzzy real numbers abstract the paper gives a contribution to the study of fuzzy real numbers continuing that in eklund and gahler 1988 gahler and gahler 1992 and gahler 1992 we start with investigating algebraic properties using two types of decompositions of fuzzy numbers and the notions of fuzzy norm of symmetric difference and of supplements of fuzzy numbers by means of these notions two special fuzzy metrics on the fuzzy real line are given the fuzzy distance function d and the extended fuzzy distance function d the main interest concerns fuzzy topological properties of the fuzzy real line in particular there are studied the fuzzy topologies t t d and t d t is closely related to the fuzzy topology of hutton s fuzzy unit interval and t d and t d are canonically generated by the fuzzy metrics d and d respectively

common fixed point theorems in fuzzy metric spaces in this paper we prove common fixed point theorems for six mappings in fuzzy metric space our main results extend generalize and fuzzify some known results in fuzzy metric spaces probabilistic metric spaces and uniform spaces

on i topology generated by fuzzy norm abstract in this paper we point out that an i topology t on the fuzzy normed linear space x min max constructed by das and das fuzzy topology generated by fuzzy norm fuzzy sets and systems 107 1999 349 354 is incompatible with the linear structure on x that is x min max is not an i topological vector space with respect to the i topology t therefore we construct a new i topology t on the fuzzy normed linear space x l r by using fuzzy norm we study some of its properties and prove that if r max then x l r is a hausdorff locally convex i topological vector space with respect to the i topology t in addition we also study the relations among three i topologies t t and where is the induced i topology of the crisp vector topology determined by fuzzy norm

the maximal distance between imprecise point objects in this paper we propose a new mathematical model of imprecise point objects and a new algorithm for determining the maximal distance between imprecise point objects results obtained with our model can be used in various applications such as gis imprecise spatial object modelling robotics environment models and image analysis imprecise feature extraction imprecise point objects are modelled as fuzzy points in linear fuzzy space linear fuzzy space is defined over r n where the membership function is convex upper semi continuous symmetric w r t the core and linearly decreasing w r t the core distance where the core is a single point a fuzzy convex hull is defined in linear fuzzy space the distance between objects points is modelled as an imprecise point object in linear fuzzy space defined over r 1 fuzzy ordering relations are defined in distance space the maximal distance is a fuzzy set over a set of distances the maximal distance between a set of imprecise point objects is then determined as the maximal distance of fuzzy convex hull edge points an algorithm for determining the maximal distance between imprecise points belonging to one and two dimensional linear fuzzy space is given for an exact calculation of this maximal distance computational complexity of the algorithm is of polynomial growth of the fourth degree however if the maximal distance is determined approximately then the algorithms computational complexity is of power growth of the quadratic degree with respect to the cardinality of the convex edge

on fuzzy pseudo metric spaces this paper attempts to endow the fuzzy pseudo metric in the sense of george and veeramani with many valued topological structures it is shown that george and veeramani s fuzzy pseudo metric can be characterized by a family of compatible ordinary pseudo metrics called pseudo metric chain in this paper then two kinds of many valued topological structures fuzzifying topology and fuzzifying uniformity are generated by this fuzzy pseudo metric and their properties are also investigated

numerical methods for integral equations of mellin type we present a survey of numerical methods based on piecewise polynomial approximation for integral equations of mellin type including examples arising in boundary integral methods for partial differential equations on polygonal domains

a quadrature based approach to improving the collocation method the collocation method is a popular method for the approximate solution of boundary integral equations but typically does not achieve the high order of convergence reached by the galerkin method in appropriate negative norms in this paper a quadrature based method for improving upon the collocation method is proposed and developed in detail for a particular case that case involves operators with even symbol such as the logarithmic potential operating on 1 periodic functions a smooth spline trial space of odd degree with constant mesh spacingh 1 n and a quadrature rule with 2n points where ann point quadrature rule would be equivalent to the collocation method in this setting it is shown that a special quadrature rule which depends on the degree of the splines and the order of the operator can yield a maximum order of convergence two powers ofh higher than the collocation method

minimization theorems and fixed point theorems in generating spaces of quasi metric family by following the approaches of kada et al 13 we define a family of weak quasi metrics in a generating space of quasi metric family by using a family of weak quasi metrics we prove a takahashi type minimization theorem a generalized ekeland variational principle and a general caristi type fixed point theorem for set valued maps in complete generating spaces of quasi metric family also by following the approach of aubin 11 we prove another fixed point theorem for set valued maps in complete generating spaces of quasi metric family without the assumption of lower semicontinuity from our results in complete generating spaces of quasi metric family we obtain the corresponding theorems for set valued maps in complete fuzzy metric spaces

thompson metric method for solving a class of nonlinear matrix equation based on the elegant properties of the thompson metric we prove that the general nonlinear matrix equation x q a f x a q q 1 always has a unique positive definite solution an iterative method is proposed to compute the unique positive definite solution we show that the iterative method is more effective as q increases a perturbation bound for the unique positive definite solution is derived in the end

on set valued nonlinear equations in menger probabilistic normed spaces we introduce the concept of probabilistic f j contractor couple which allows us to consider set valued nonlinear operator equations in a large class of probabilistic normed spaces our results complete those from cho et al nonlinear equations for fuzzy mappings in probabilistic normed spaces fuzzy sets and systems 110 2000 115 122 and fang on nonlinear equations for fuzzy mappings in probabilistic normed spaces fuzzy sets and systems 131 2002 357 364

on convex and concave fuzzy mappings abstract in this paper we introduce the concepts of convex subsets of f 0 the set of all fuzzy numbers and monotonic fuzzy mappings on r2 and show that a monotonic fuzzy mapping f on a convex set c r1 or r2 is quasi convex and quasi concave we establish two characterizations for convex fuzzy mappings and two characterizations for concave fuzzy mappings we also prove the least upper bound property

a comparative study of fuzzy norms on a linear space in this paper a comparative study among several types of fuzzy norms on a linear space defined by various authors has been made and it is shown that broadly they may be classified into two types one of which is katsaras s type and the other is felbin s type

a note on compactness in a fuzzy metric space we study the compactness in a fuzzy metric space we also give a generalization of niemytzki tychonoff theorem for a fuzzy metric space

high order methods for linear functionals of solutions of second kind integral equations the authors show that linear functionals e g inner products or point functionals of solutions of second kind fredholm integral equations may be found within o 1 n 2r by very simple computational schemes using the nystrom or quadrature method based on piecewise polynomials of order r on an n 1 point mesh our theory covers a class of nonsmooth wiener hopf type equations and applications include the calculation of crack energy and stress intensity factors in certain linear elastic fracture problems and the use of the boundary integral method to compute various superconvergent solutions to boundary value problems in polygonal domains a proof of the uniform convergence of nystrom s method for certain boundary integral equations on polygonal domains is also included

a nystrom method for boundary integral equations in domains with corners we give a convergence and error analysis for a nystrom method on a graded mesh for the numerical solution of boundary integral equations for the harmonic dirichlet problem in plane domains with corners

newton s method for the quadratic matrix equation abstract under suitable condition a quadratic matrix equation is equivalent to a nonlinear matrix equation we apply newton s method to the nonlinear matrix equation for computing the numerical solution of a class of quadratic matrix equations convergence theorems are derived and numerical results are also given

a couple of nonlinear equations with fuzzy mappings in fuzzy normed spaces in this paper we introduce the concept of f contractor couple and study the existence of solutions for a couple of nonlinear equations with fuzzy mappings in fuzzy normed spaces we construct some new iterative algorithms for solving the couple of nonlinear equations with fuzzy mappings and prove the convergence of iterative sequences generated by the algorithms in fuzzy normed spaces as applications we obtain some new common fixed point theorems for fuzzy mappings in fuzzy normed spaces the results presented in this paper improve and generalize corresponding results of cho et al fuzzy sets and systems 110 2000 115 and fang and song fuzzy sets and systems 121 2001 267

approximation methods for singular integral equations with conjugation on curves with corners approximation methods for singular integral operators with continuous coefficients and conjugation as well as for the double layer potential operator on curves with corners are investigated with respect to their stability the methods under consideration include several kinds of quadrature rules and collocation and qualocation methods the approach is based on the thorough use of banach algebra techniques and local principles complete necessary and sufficient stability conditions are derived

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

fuzzy compact operators and topological degree theory in this paper we first prove that the definition of fuzzy norm continuity and fuzzy boundedness of linear operators are equivalent we show that the continuity assumption in the definition of compact linear operator is not necessary we also point out that there is a gap in the proof of a theorem of xiao and zhu and we give a corrected version of the theorem such that all results based on the revised theorem remain true furthermore we define a fuzzy product norm on the cartesian product of two fuzzy normed spaces and prove a multiplicative property for the leray schauder topological degree

fixed point theorems for multivalued mappings in probabilistic metric spaces abstract in this paper we prove a fixed point theorem for multivalued mappings in probabilistic metric spaces some applications in fuzzy metric and random normed spaces are given

two kinds of condition numbers for the quadratic matrix equation in the situation that the quadratic matrix equation has the dominant or minimal solvents the mixed and componentwise condition numbers of the quadratic matrix equation are considered the explicit approximate expressions of two kinds of condition numbers are derived in the uniform manner and the upper bounds are proposed the theoretical results are illustrated by using some simple numerical examples

spline qualocation methods for variable coefficient elliptic equations on curves here the stability and convergence results of oqualocation methods providing additional orders of convergence are extended from the special class of pseudodifferential equations with constant coefficient symbols to general classical pseudodifferential equations of strongly and of oddly elliptic type the analysis exploits localization in the form of frozen coefficients pseudohomogeneous asymptotic symbol representation of classical pseudodifferential operators a decisive commutator property of the qualocation projection and requires qualocation rules which provide sufficiently many additional degrees of precision for the numerical integration of smooth remainders numerical examples show the predicted high orders of convergence

schauder bases and approximation property in fuzzy normed spaces our aim in this article is to introduce and study the notion of weak and strong schauder bases in fuzzy normed spaces further we introduce strong and weak fuzzy approximation properties and set a relationship between these two new notions which may provide an acceleration to the structural analysis of fuzzy normed spaces

minimization theorems for fixed point theorems in fuzzy metric spaces and applications abstract in this paper we establish a minimization theorem in fuzzy metric spaces and make use of the result to obtain a fixed point theorem in fuzzy metric spaces which is similar to the downing kirk fixed point theorem in metric spaces as the consequences we obtain caristi s fixed point theorem and ekeland s variational principle in fuzzy metric spaces and also give a direct simple proof of the equivalence between these two theorems some applications of these results to probabilistic metric spaces are presented

the theory of global fuzzy neighborhood structures iii fuzzy uniform structures in this paper a new notion of fuzzy uniform structure is presented and investigated fuzzy uniform structures are given as special fuzzy filters of special interest are those fuzzy uniform structures which are sup fuzzy filters they can be characterized by a related notion of fuzzy syntopogenous structure as is shown fuzzy metrics gahler and gahler 1994 generate fuzzy uniform structures in our sense each fuzzy uniform structure has an associated global homogeneous fuzzy neighborhood structure and hence also an associated fuzzy topology in case of a 0 1 fuzzy uniform structure and even in a more general case a fuzzy uniform structure of the first type can be associated there are given relation to huttons s and katsaras notions of fuzzy uniform structure hutton 1977 katsaras 1979 and to the notion of fuzzy syntopogenous structure in sense of katsaras and petalas 1984

mellin convolution operators in bessel potential spaces abstract mellin convolution equations acting in bessel potential spaces are considered the study is based upon two results the first one concerns the interaction of mellin convolutions and bessel potential operators bpos in contrast to the fourier convolutions bpos and mellin convolutions do not commute and we derive an explicit formula for the corresponding commutator in the case of mellin convolutions with meromorphic symbols these results are used in the lifting of the mellin convolution operators acting on bessel potential spaces up to operators on lebesgue spaces the operators arising belong to an algebra generated by mellin and fourier convolutions acting on l p spaces fredholm conditions and index formulae for such operators have been obtained earlier by one of the authors and are employed here the results of the present work have numerous applications in boundary value problems for partial differential equations in particular for equations in domains with angular points

some remarks on the topological properties of fuzzy numbers in r n abstract the space of normal upper semicontinuous fuzzy convex and compactly supported fuzzy numbers in r b are considered endowed with different metrics generated by the hausdorff metric a subspace is introduced and properties of the metrics restricted to the subspace are investigated

on linearly topological structure and property of fuzzy normed linear space in this paper the simplified definition of fuzzy normed linear space is introduced the different structure of fuzzy normed linear space with variable right norm r is discussed in terms of topological vector space and its properties such as compactness completeness and density are studied under more general left norm l and right norm r as application the linearly topological structure of menger pn space is obtained

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

on the stability of the nystrom method for the muskhelishvili equation on contours with corners the stability of the nystrom method for the muskhelishvili equation on piecewise smooth simple contours is studied it is shown that in the space l 2 the method is stable if and only if certain operators a j from an algebra of toeplitz operators are invertible the operators a j depend on the parameters of the equation considered on the opening angles j of the corner points j and on parameters of the approximation method mentioned numerical experiments show that there are opening angles where the operators a j are noninvertible therefore for contours with such corners the method under consideration is not stable otherwise the method is always stable numerical examples show an excellent convergence of the method

on generalized fuzzy normed spaces and coincidence point theorems in this paper generalized fuzzy norms are defined on a set of objects endowed with a structure of linear space the relationships between these fuzzy norms and the fuzzy metrics and between these fuzzy norms and the topological structures on the base linear space are analyzed finally coincidence and fixed point theorems for mappings with values in fuzzy metric spaces and in such fuzzy normed spaces are proved

contributions to fuzzy analysis in some sense fuzzy analysis deviates highly from classical analysis needing its own specific notions the main reason which causes this situation consists in the different algebraic and structure theoretic properties of the usual real numbers and fuzzy numbers the paper which is an extended version of 4 is devoted to this problem presenting some of these specific notions in particular examples of proper fuzzy normed vector spaces and proper fuzzy normed algebras are given

finite dimensional fuzzy normed linear space abstract the concept of a fuzzy normed linear space is introduced it is proved that in a finite dimensional fuzzy normed linear space fuzzy norms are the same upto fuzzy equivalence finite dimensional fuzzy subspaces of a fuzzy normed linear space are proved to be necessarily complete fuzzy normed linear spaces

fuzzy bounded operators in this paper we introduce the concepts of fuzzy bounded linear operators on fuzzy normed or banach spaces and give some properties of fuzzy bounded linear operators which are extensions of ordinary operator theories

convergence in the i fuzzy real line infinite sums and sequences in the fuzzy real line have been investigated by wang in this paper a necessary and sufficient condition for a sequence in to be convergent is given in terms of cut set it is proved that fuzzy convergence of sequences in is equivalent to weak convergence as an application convergence of sequences of fuzzy numbers in the sense of chang and zadeh is discussed

fixed point theorems in fuzzy metric spaces using property e a abstract we prove two common fixed point theorems for a pair of weakly compatible maps in fuzzy metric spaces both in the sense of kramosil and michalek and in the sense of george and veeramani by using e a property

on the level convergence of a sequence of fuzzy numbers abstract in this paper we first give a simplified proof of the existence theorem of supremum and infimum in fuzzy number space e 1 established by wu and wu j math anal appl 210 1997 499 and improve the expressions of the supremum and infimum as a straightforward corollary of this result we obtain a necessary and sufficient condition under which for a bounded sequence of fuzzy numbers u n the pair of functions sup n u n and sup n u n can determine a fuzzy number secondly we give a necessary and sufficient condition for a sequence of fuzzy numbers u n to be levelwise convergent in e 1 and generalize some important theorems in real number spaces to fuzzy number spaces finally we prove the existence of supremum and infimum for the level continuous fuzzy valued function on a closed interval and give a necessary and sufficient condition under which its supremum and infimum can be attained

regularity and normality of l m fuzzy topological spaces abstract in this paper regularity and normality axioms are introduced in l m fuzzy topological spaces where l and m are completely distributive lattices with order reversing involution each l m fuzzy topological space can be regarded to be regular and normal to some degree the relations among the four separation axioms are investigated they are equivalent to each other in an l m fuzzy metric space

extension of c algebras and moore penrose stability of sequences of additive operators abstract an extension a of a c algebra a by some element m which has a number of special properties is proposed these properties allow us to introduce some suitable operations of addition multiplication and involution on a after which we are able to study different kinds of moore penrose invertibility in a due to such an approach we obtain necessary and sufficient conditions of weak asymptotic moore penrose invertibility for an algebra arising from spline approximation methods for singular integral equations with conjugation

coincidence point theorems in generating spaces of quasi metric family in this paper we establish some new versions of coincidence point theorems for single valued and multi valued mappings in generating spaces of quasi metric family as applications we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single valued and multi valued mappings in fuzzy metric spaces and probabilistic metric spaces

on fixed degree theorems for fuzzy mappings in menger pm spaces in this paper we establish a new common fixed degree theorem for a sequence of fuzzy mappings in menger pm spaces as an immediate consequence of this theorem we obtain an improvement of a corresponding result of chang et al fuzzy sets and systems 87 1997 325 334 in addition we also obtain some fixed degree and fixed point theorems for fuzzy mappings in fuzzy metric spaces our results unify and generalize the results of heilpern j math anal appl 83 1981 566 569 butnariu fuzzy sets and systems 7 1982 191 207 hadzic fuzzy sets and systems 29 1989 115 125 fang fuzzy sets and systems 48 1992 391 395 lee et al fuzzy sets and systems 61 1994 309 312 j fuzzy math 2 1994 859 870 and chang et al math japon 40 1994 289 293 fuzzy sets and systems 87 1997 325 334

a comment on the completion of fuzzy metric spaces we argue that in some recent papers discussing the completion of fuzzy metric and fuzzy normed spaces proper credit is not given to earlier works on the subject

coincidence theorems for set valued mappings and ekeland s variational principle in fuzzy metric spaces abstract in this paper we establish a coincidence theorem for set valued mappings in fuzzy metric spaces with a view to generalizing downing kirk s fixed point theorem in metric spaces as consequences we obtain caristi s coincidence theorem for set valued mappings and a more general type of ekeland s variational principle in fuzzy metric spaces further we also give a direct simple proof of the equivalence between these two theorems in fuzzy metric spaces some applications of these results to probabilistic metric spaces are presented

the variational principle in fuzzy metric spaces and its applications abstract in this paper we prove a fixed point theorem and a variational principle in fuzzy metric spaces applying these results to some probabilistic metric spaces we obtain a corresponding fixed point theorem and a variational principle

a coloring fuzzy graph approach for image classification one of the main problems in practice is the difficulty in dealing with membership functions many decision makers ask for a graphical representation to help them to visualize results in this paper we point out that some useful tools for fuzzy classification can be derived from fuzzy coloring procedures in particular we bring here a crisp grey coloring algorithm based upon a sequential application of a basic black and white binary coloring procedure already introduced in a previous paper d gomez j montero j yanez c poidomani a graph coloring algorithm approach for image segmentation omega in press in this article the image is conceived as a fuzzy graph defined on the set of pixels where fuzzy edges represent the distance between pixels in this way we can obtain a more flexible hierarchical structure of colors which in turn should give useful hints about those classes with unclear boundaries

fuzzy lipschitz maps and fixed point theorems in fuzzy metric spaces in this paper we introduce the notion of dilation and fuzzy lipschitz of a map from a fuzzy metric space into a fuzzy metric space and we prove continuity properties for such maps we also define the notion of the fuzzy lipschitz distance between two fuzzy metric spaces and show that two compact fuzzy metric spaces whose lipschitz distance is zero is fuzzy isometric to each other on the other hand we introduce the concept of minimal slope of a map between fuzzy metric spaces which is defined by the ratio of two fuzzy metrics and derive some properties on it and relations with the dilation in particular we show that if the dilation of a map from a fuzzy metric space which is complete in george and veeramani sense into itself is less than the minimal slope then the map must have a fixed point in case that a fuzzy metric space is considered in the sense of kramosil and michalek and that the completeness in the sense of grabiec the same result holds

the equivalence of convergences of sequences of fuzzy numbers and its applications to the characterization of compact sets in this paper with the help of the convergence of sequences of fuzzy numbers with respect to the lebesgue measure we study the relationship between convergences of sequences of fuzzy numbers with respect to the endograph metric the sendograph metric and the l p metric we prove that these convergences are equivalent under proper conditions in addition by applying our result we give a new characterization of compact sets in fuzzy number space with the sendograph metric

resonance theorems for family of quasi homogeneous operators in fuzzy normed linear spaces in this paper we establish some resonance theorems for families of point wise bounded semi bounded and non unbounded quasi homogeneous and email protected subadditive operators in fuzzy normed linear spaces as their consequences we obtain the corresponding resonance theorems in classical normed spaces and menger probabilistic normed spaces

graded sets and points a stratified approach to fuzzy sets and points abstract in this paper we define the concepts of graded set and graded point as well as the usual theoretical set operations and relations and the extension of mappings between graded sets these definitions provide a method to extend concepts of classical set theory this method is related to fuzzy set theory and generalizes some properties of the family of cuts moreover the graded points verify the following two properties which cannot happen with fuzzy points

simplification of erceg s fuzzy metric function and its application abstract in this paper we greatly simplify the definition of erceg s p q p metric on a fuzzy lattice l on the basis of this a new pointwise p q p metric is introduced being defined on the set of all non zero join irreducible elements of a fuzzy lattice l meanwhile we prove that it can be directly extended to erceg s p q p metric defined on the fuzzy lattice l these results are exactly what erceg wanted to obtain furthermore we investigate the application of the pointwise metric to fuzzy p metric spaces

on fuzzy valued inequalities abstract in this note a general fuzzy valued inequality is given and some classical inequalities such as the mean value inequality the holder s inequality the minkowski s inequality and the cauchy inequality are extended from ordinary real analysis to the fuzzy valued case

on the convergence of collocation methods for boundary integral equations on polygons the integral equations encountered in boundary element methods are frequently solved numerically using collocation with spline trial functions convergence proofs and error estimates for these approximation methods have been only available in the following cases fredholm integral equations of the second kind 4 7 one dimensional pseudodifferential equations and singular integral equations with piecewise smooth coefficients on smooth curves 2 3 17 26 29 and some special results on the classical neumann integral equation of potential theory for polygonal plane domains 5 8 9 here we give convergence proofs for collocation with piecewise linear trial functions for neumann s integral equation and symm s integral equation on plane curves with corners we derive asymptotic error estimates in sobolev norms and analyze the effect of graded meshes 0 introduction in this paper we give convergence proofs and asymptotic error estimates in sobolev norms for collocation with piecewise linear spline trial func tions applied to two basic integral equations of potential theory on plane polygons namely the integral equation of the second kind with the double layer potential neumann s integral equation and the integral equation of the first kind with the simple layer potential symm s integral equation we use an idea of arnold and wendland 2 namely considering dirac delta functions the test functions in the collocation method as second derivatives of piecewise linear functions therefore similar results as presented here should be possible for splines of higher odd order corresponding results for even order splines are not yet available thus for one of the simplest methods of numerically solving dirichlet s problem on a plane domain with corners the midpoint collocation with piecewise constant trial functions for the first kind integral equation with the simple layer potential convergence is still an open problem the method of fourier series that yields the convergence proof in the case of a smooth boundary 27 cannot be applied in the presence of corners we apply the method of local mellin transformation that has previously been used to derive error estimates for galerkin methods for a wide class of operators including those occurring in boundary element methods in acoustics electromag

condensing operators and topological degree theory in standard fuzzy normed spaces in this paper level cut measures of noncompactness are introduced in standard fuzzy normed spaces and condensing operators are studied using the extensions of nonlinear compact operators topological degree theory with respect to condensing operators is given in standard fuzzy normed spaces as an application of degree theory a fixed point theorem for condensing operators is presented

on fixed point theorems in fuzzy metric spaces we give fixed point theorems for complete fuzzy metric spaces in the sense of george and veeramani and also for kramosil and michalek s fuzzy metric spaces which are complete in grabiec s sense

analysis and efficient implementation of a linguistic fuzzy c means the paper is concerned with a linguistic fuzzy c means fcm algorithm with vectors of fuzzy numbers as inputs this algorithm is based on the extension principle and the decomposition theorem it turns out that using the extension principle to extend the capability of the standard membership update equation to deal with a linguistic vector has a huge computational complexity in order to cope with this problem an efficient method based on fuzzy arithmetic and optimization has been developed and analyzed we also carefully examine and prove that the algorithm behaves in a way similar to the fcm in the degenerate linguistic case synthetic data sets and the iris data set have been used to illustrate the behavior of this linguistic version of the fcm

a class of iteration methods based on the moser formula for nonlinear equations in markov chains abstract many stochastic models in queueing inventory communications and dam theories etc result in the problem of numerically determining the minimal nonnegative solutions for a class of nonlinear matrix equations various iterative methods have been proposed to determine the matrices of interest we propose a new efficient successive substitution moser method and a newton moser method which use the moser formula which originally is just the schulz method these new methods avoid the inverses of the matrices and thus considerable savings on the computational workloads may be achieved moreover they are much more suitable for implementing on parallel multiprocessor systems under certain conditions we establish monotone convergence of these new methods and prove local linear convergence for the substitution moser method and superlinear convergence for the newton moser method

topological stability for fuzzy expansive maps abstract we introduce the definitions of expansivity and topological stability for homeomorphisms on fuzzy metric spaces we show some basic properties of fuzzy expansive homeomorphisms moreover we prove walters s theorem in the context of fuzzy metric spaces i e a fuzzy expansive system with the fuzzy shadowing property is fuzzy topologically stable

fixed points in fuzzy metric spaces abstract in this note the well known fixed point theorems of banach and edelstein are extended to fuzzy metric spaces in the settle of kramosil and michalek