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

determination of point group harmonics for arbitrary j by a projection method i cubic group quantization along an axis of order 4 we give a method for systematically building cubic harmonics i e base vectors of irreducible representations of the group of invariance of a cube applications include solid state physics molecular chemistry spectroscopy etc the only necessary operators are cz4 and ry rotation of 2 around 0y projectors on representations are constructed then their rows are orthogonalized by a schmidt method and normalized simply by dividing by the square root of a diagonal element

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

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

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

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

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

determination of point group harmonics for arbitrary j by a projection method iii cubic group quantization along a ternary axis the method described in a first paper to obtain cubic harmonics quantized on an axis of order 4 is applied to the case of a ternary quantization axis projectors on irreducible representations are expressed with rotation matrices r 0 and r 0 arccos 1 3 acting on subspaces of su 2 invariant under d3 relations between the descriptions on the two axes of quantization are derived

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

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

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

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

triangular differential quadrature and its application to elastostatic analysis of reissner plates the recently proposed triangular differential quadrature method tdqm is further elaborated in the paper explicit formulae to calculate the weighting coefficients for uniform grid are developed the tdqm is applied to the elastostatic analysis of reissner plates in comparison with other available numerical results good accuracy and rapid convergence are achieved indicating that the tdqm has attractive potential as a novel numerical technique

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

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

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

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

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

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

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 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

a topological geometric method for the obtention of symmetry adapted functions for point groups iv the dihedral groups abstract symmetry adapted icosahedral harmonics have been obtained by using a new method based on the geometrical and topological properties of icosaedral spatial arrangements of charged particles this study has allowed us to show that especially for groups of high symmetry our method proved to be more simple and advantageous than others existing in the literature as for instance the projection operator classical method

on fuzzy metric spaces in the present paper the authors define f open sets f closed sets f adherent points f limit points f isolated points f isolated sets f derived sets f closures f interior points f interior f exterior points f exterior f everywhere dense sets f nowhere dense sets and make some characterizations of fuzzy metric spaces

non uniform rational lagrange functions and its applications to isogeometric analysis of in plane and flexural vibration of thin plates abstract new basis functions were developed for isogeometric analysis iga to overcome the difficulties of iga using nurbs non uniform rational b splines on coping with dirichlet boundary conditions the new basis functions were constructed through nesting rational local lagrange interpolations like the t spline and were evaluated in similar procedure as the finite difference method explicit expressions for the new basis functions were presented due to their equivalence to the nurbs the new basis functions were named as non uniform rational lagrange nurl basis iga using nurl includes the finite element method as a special case but the geometry in iga using nurl is exact iga using nurl can carry out p refinement that has the nesting feature of the k refinement of nurbs dirichlet boundary conditions can be directly imposed in iga using nurl because the nurl are interpolation basis functions a method of directly transforming the tensor product basis of triangular patches to area coordinates was presented and the singularity problem at the edge degenerated to a single point was solved the methods developed in this work were applied to in plane and flexural vibration of thin plates comparisons with available results in literatures showed the fast convergence and high accuracy of iga using nurl and the transformation method for triangular patches introduction of a matlab toolbox of the nurl was appended

on the zeros of 3j coefficients polynomial degree versus recurrence order for 3j coefficients of su 2 two quantities the degree n and the order m are defined the first the polynomial degree n is well known as the number of terms in the polynomial part of the single sum expression of the 3j coefficient minus one the second the recurrence order m is new from an exhaustive computer search for non trivial zeros of 3j coefficients it follows that both quantities play an important role in classifying the zeros explicit formulae for all zeros of order 1 are obtained and several new infinite sequences of zeros related to pell equations are presented

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

on a labeling for point group harmonics i cubic group expressions for the 4 6 and 8 representations are derived in terms of the 1 representations for neighboring angular momenta expressions for 5 7 and again for 8 are derived in terms of the 2 representations a third set of expressions for 8 is derived in terms of the 3 representations with an arbitrary choice of orthonormal sets of the 1 2 and 3 representations orthonormal sets of all other kinds of representations are thus well defined and can be entirely labeled using the parent representations all clebsch gordan coefficients are expressed in terms of those between parent representations and a few other ones the 4 and 5 representations defined here are not those conventionally used but they provide a simpler expression for the fictitious spin coefficients tables of the parent representations 1 2 and 3 are given for quaternary and ternary axes of quantization using the usual clebsch gordan coefficients of su 2 these tables allow us to obtain any representation for int

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

differential cubature method for static solutions of arbitrarily shaped thick plates this paper presents the first endeavor to exploit the differential cubature method as an accurate and efficient global technique for fundamental solutions of arbitrarily shaped thick plates the method is examined here for its suitability for solving the boundary value problem of thick plates governing by the first order shear deformation theory using the method the governing differential equations and boundary conditions are transformed into sets of linear algebraic equations boundary conditions are implemented through discrete grid points by constraining displacements bending moments and rotations detailed discussion on the formulation and implementation of the method are presented the applicability efficiency and simplicity of the method are demonstrated through solving example plate problems of different shapes the accuracy of the method is verified by direct comparison with the known values

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

free vibration analysis of isosceles triangular mindlin plates by the triangular differential quadrature method the triangular differential quadrature method is applied to the free flexural vibration of isosceles triangular mindlin plates the first six frequencies are sought and the convergence of triangular differential quadrature method in vibrational analysis of triangular mindlin plates is examined in comparison with available results good to excellent agreement is achieved for triangular plates with combinations of clamped and simply supported boundary conditions the implementation of various other boundary conditions in triangular differential quadrature analysis is also discussed and the sensitivity of solution to the implementation of corner conditions in vibrational analysis is highlighted

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

on a labeling for point group harmonics ii icosahedral group the expressions for the 2 5 6 8 and 9 representations are given in terms of those of 1 representations for neighboring angular momenta the coefficients of the 4 representations are expressed in terms of those of 7 representations therefore with an arbitrary choice of orthonormal sets of 1 3 and 7 representations orthonormal sets of other kinds of representations are well defined and can be labeled with the labels of parent representations all clebsch gordan coefficients are expressed in terms of those between parent representations and a few others tables of all nondegenerate 1 3 and 7 representations are given for the axes of quantization of order 5 with some degenerate 3 and 7 representations which are also given any representation of integer or half integer angular momentum up to 27 can be obtained using some usual clebsch gordan coefficients of su 2

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 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

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

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

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

a differential quadrature hierarchical finite element method using fekete points for triangles and tetrahedrons and its applications to structural vibration abstract a differential quadrature hierarchical finite element method dqhfem using fekete points was formulated for triangles and tetrahedrons and applied to structural vibration analyses first orthogonal polynomials on triangles and tetrahedrons that can be used as bases of the hierarchical finite element method hfem were derived and simple formulas of transforming one dimensional non uniform nodes to simplexes were presented then the non uniform nodes were used as initial guesses to solve the fekete points on simplexes through newton raphson s method together with the orthogonal polynomials new differential quadrature dq rules on simplexes were formulated using the hfem bases and the fekete points the numbers of nodes or bases on different edges and faces and inside the body of the new dq elements do not relate with each other like the hfem that can freely assign different numbers of bases on different edges and faces and inside the body so the new dq method was named as a differential quadrature hierarchical dqh method that uses either interpolation functions or orthogonal polynomials as bases inside the element its weak form was named as the dqhfem besides the dqh method and its weak form a simple method of generating high quality linear and high order triangular and tetrahedral meshes from a single nurbs patch was presented numerical tests of the dqhfem through structural vibration analyses showed that high accuracy results can be obtained using only a few nodes even on curvilinear domains using the dqh bases on both physical and geometric fields it was concluded that wide applications of the dqh method and the dqhfem to science and engineering are possible and commercial codes based on them are deserved to be developed