characterizing completable fuzzy metric spaces recently we showed the existence of a fuzzy metric space in the sense of george and veeramani which is not completable fuzzy sets and systems 130 2002 399 here we present an internal characterization of those fuzzy metric spaces that are completable some applications are derived and some illustrative examples are given

on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy 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

on some results of analysis for fuzzy metric spaces abstract a necessary and sufficient condition for a fuzzy metric space to be complete is given we prove that a subspace of a separable fuzzy metric space is separable and every separable fuzzy metric space is second countable uniform limit theorem is generalized to fuzzy metric spaces

curve arclength in fuzzy metric spaces abstract in the paper an arclength notion of continuous curves in fuzzy metric spaces is proposed and some arclength properties are studied including invariance additivity continuity and boundedness it turns out that these arclength properties imply the corresponding ones in metric spaces

an identification theorem for the completion of the hausdorff fuzzy metric abstract we prove that given a fuzzy metric space in the sense of kramosil and michalek the completion of its hausdorff fuzzy metric space is isometric to the hausdorff fuzzy metric space of its completion when the hausdorff fuzzy metrics are defined on the respective collections of non empty closed subsets as a consequence we deduce the corresponding result for metric spaces by using the standard fuzzy metric an application to the extension of multivalued mappings and some illustrative examples are also given

tripled fuzzy metric spaces and fixed point theorem abstract one of the most important topics of research in fuzzy sets is to get an appropriate notion of fuzzy metric space fms in the paper we propose a new fms tripled fuzzy metric space tfms which is a new generalization of george and veeramani s fms then we present some related examples topological properties convergence of sequences cauchy sequence cs and completeness of the tfms moreover we introduce two kinds of notions of generalized fuzzy contractive f c mappings and derive a fixed point theorem fpt on the mappings in the space

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

product states and c dynamical system of product type abstract a study is made of a special type of c dynamical system consisting of a class n uniformly hyperfinite c algebra a compact lie group and a natural product action of g on by automorphisms in particular a simple class of representations of the fixed point algebra g is examined those induced by restrictions of pure product states of sufficient conditions are obtained for 1 irreducibility and 2 unitary equivalence of such irreducible representations in the case of an arbitrary compact lie group g with continuous unitary representation in c n these are used to produce necessary and sufficient conditions when g u 1 or g su 2 acts by a product type conjugation on the class 2 algebra

the wijsman topology of a fuzzy metric space we introduce and study the notions of lower wijsman topology upper wijsman topology and wijsman topology of a fuzzy metric space in the sense of kramosil and michalek in particular quasi uniformizability uniformizability quasi metrizability and metrizability of these topologies are discussed their relations with other hypertopologies are also analyzed corresponding results to the wijsman topology of a metric space are deduced from our approach with the help of the standard fuzzy metric

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

completeness in probabilistic quasi uniform spaces abstract in this paper we give a kind of cauchy completeness in probabilistic quasi uniform space by using pair filters and prove that this kind of cauchy completeness is equivalent to the completeness of induced probabilistic uniform space introduced by hohle we also give a characterization of cauchy completeness by lawvere completeness then we study the completion of probabilistic quasi uniform space and show that each t 0 separated probabilistic quasi uniform space has a t 0 cauchy completion finally in probabilistic quasi metric space we study the relationship between the completeness of induced quasi uniform space and the completeness of probabilistic quasi metric space

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

fuzzy pseudometric spaces vs fuzzifying structures in this paper we apply the representation theorem established in mardones perez and de prada vicente 2012 12 to define and study the degree in which some topological type properties of fuzzy pseudometric spaces are fulfilled fuzzifying structures which appear naturally are also investigated and the relation between these structures and fuzzy pseudometric spaces is explored

gromov hausdorff convergence of non archimedean fuzzy metric spaces we introduce the notion of the gromov hausdorff fuzzy distance between two non archimedean fuzzy metric spaces in the sense of kramosil and michalek basic properties involving convergence and the fuzzy version of the completeness theorem are presented we show that the topological properties induced by the classic gromov hausdorff distance on metric spaces can be deduced from our approach

the construction of the sh lie algebra of closed bosonic strings we present a construction of the closed string algebra in terms of gaussian processes and crossed products also we give a purely functional analytical prove of the sh lie structure

on completion of fuzzy metric spaces completions of fuzzy metric spaces in the sense of george and veeramani are discussed a complete fuzzy metric space y is said to be a fuzzy metric completion of a given fuzzy metric space x if x is isometric to a dense subspace of y we present an example of a fuzzy metric space that does not admit any fuzzy metric completion however we prove that every standard fuzzy metric space has an up to isometry unique fuzzy metric completion we also show that for each fuzzy metric space there is an up to uniform isomorphism unique complete fuzzy metric space that contains a dense subspace uniformly isomorphic to it

fuzzy quasi metrics for the sorgenfrey line we endow the set of real numbers with a family of fuzzy quasi metrics in the sense of george and veeramani which are compatible with the sorgenfrey topology although these fuzzy quasi metrics are not deduced explicitly from a quasi metric they possess interesting properties related to completeness for instance we prove that they are balanced and complete in the sense of doitchinov and that only one of them is right k sequentially complete we also observe that compatible fuzzy quasi metrics for the sorgenfrey line cannot be left weakly right k sequentially complete

fuzzy uniform structures and continuous t norms we introduce and discuss a notion of fuzzy uniform structure that provides a direct link with the classical theory of uniform spaces more exactly for each continuous t norm we prove that the category of all fuzzy uniform spaces in our sense and fuzzy uniformly continuous mappings is isomorphic to the category of uniform spaces and uniformly continuous mappings by means of a covariant functor moreover we also describe the inverse functor and then we discuss completeness and completion of these fuzzy uniform structures it follows from our results that each fuzzy uniform structure in our sense induces a hutton 0 1 uniformity and conversely each hutton 0 1 uniformity induces a fuzzy uniform structure in our sense

std convergence in fuzzy metric spaces in this note we answer two recent questions posed by morillas and sapena 10 related to standard convergence in fuzzy metric spaces in the sense of george and veeramani the obtained results lead us to establish what conditions must satisfy a concept about sequential convergence to be considered compatible with a concept of cauchyness

meir keeler theorems in fuzzy metric spaces abstract in this paper we propose the concept of fuzzy meir keeler contractive mappings in fuzzy metric spaces which covers fuzzy contractive mappings and fuzzy h contractive mappings as special cases with the aid of the proposed concept we obtain some meir keeler type fixed point theorems the derived theorems improve and extend the corresponding ones developed by d mihet d wardowski and v gregori et al and an example in the end of the paper illustrates the validity of our results

characters of the infinite symplectic group a riesz ring approach we classify both the finite and infinite characters of the inductive limit symplectic group g an important feature of our technique is the systematic use of a multiplicative structure on an ordered completion of the k0 group for the group c algebra a of g we also give explicit examples of the k theory for certain primitive quotients of a

completeness of hutton 0 1 quasi uniform spaces this paper deals with completeness of hutton 0 1 quasi uniform spaces recently the first two authors j gutierrez garcia m a de prada vicente hutton 0 1 quasi uniformities induced by fuzzy quasi metric spaces fuzzy sets and systems 157 2006 755 766 have constructed a hutton 0 1 quasi uniformity induced by a fuzzy metric space in the sense of george and veeramani in this paper we define completeness of hutton 0 1 quasi uniform spaces as convergence of any stratified tight cauchy 0 1 filter our main result states the equivalence between completeness of any fuzzy metric space x m and completeness of the induced hutton 0 1 quasi uniformity u m also it is proved that the hutton 0 1 quasi uniform space x u m has in this context a kind of completion that is unique up to uniform isomorphism the obtained results come from an appropriate definition of cauchy l filter where l stands for a complete lattice with additional properties

an application of a representation theorem for fuzzy metrics to domain theory in this paper we study the interplay between fuzzy metric spaces and domain theory using the representation theorem established in mardones perez and de prada vicente 2012 12 we will prove that suitable restrictions of completeness in fuzzy metric spaces correspond to a structure of domain in the poset of formal balls endowed with appropriate orders

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

short communication some remarks on fuzzy contractive mappings recently a new concept of fuzzy contraction in fuzzy metric spaces in the sense of george and veeramani wardowski 2013 5 has been introduced here we provide some comments to this paper

some properites of fuzzy metric spaces abstract we prove that the topology induced by any complete fuzzy metric space in the sense of george and veeramani is completely metrizable we also show that every separable fuzzy metric space admits a precompact fuzzy metric and that a fuzzy metric space is compact if and only if it is precompact and complete finally we generalize among other classical results the niemytzki tychonoff theorem to fuzzy metric spaces

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

remarks on the analytic hierarchy process the analytic hierarchy process ahp is flawed as a procedure for ranking alternatives in that the rankings produced by this procedure are arbitrary this paper provides a brief review of several areas of operational difficulty with the ahp and then focuses on the arbitrary rankings that occur when the principle of hierarchic composition is assumed this principle requires that the weights on the higher levels of a hierarchy can be determined independently of the weights on the lower levels virtually all of the published examples of the use of the ahp to evaluate alternatives relative to a set of criteria have assumed this principle the key to correcting this flaw is the synthesis of the ahp with the concepts of multiattribute utility theory

multidimensional coincidence point results for compatible mappings in partially ordered fuzzy metric spaces in recent times coupled tripled and quadruple fixed point theorems have been intensively studied by many authors in the context of partially ordered complete metric spaces using different contractivity conditions roldan et al showed a unified version of these results for nonlinear mappings in any number of variables which were not necessarily permuted or ordered introducing the notion of multidimensional coincidence point very recently choudhury et al proved coupled coincidence point results in the context of fuzzy metric spaces in the sense of george and veeramani in this paper using the idea of coincidence point for nonlinear mappings in any number of variables we study a fuzzy contractivity condition to ensure the existence of coincidence points in the framework of fuzzy metric spaces provided with hadzic type t norms then we present an illustrative example in which our methodology leads to the existence of coincidence points but previous theorems cannot be applied

the hausdorff fuzzy quasi metric removing the condition of symmetry in the notion of a fuzzy pseudo metric in kramosil and michalek s sense one has the notion of a fuzzy quasi pseudo metric then for each fuzzy quasi pseudo metric on a set x we construct a fuzzy quasi pseudo metric on the collection of all nonempty subsets of x called the hausdorff fuzzy quasi pseudo metric we investigate several properties of this structure and present several illustrative examples as well as an application to the domain of words the notion of hausdorff fuzzy quasi pseudo metric when quasi pseudo metric fuzziness is considered in the sense of george and veeramani is also discussed

on contractions in probabilistic and fuzzy metric spaces in this paper by means of weakening conditions of the gauge function a new fixed point theorem for probabilistic contraction in menger probabilistic metric spaces with a t norm of h type is established this theorem improves and generalizes the recent results of iric 2010 4 jachymski 2010 12 and xiao et al 2013 25 by using the theorem we also obtain some important corollaries and the fixed point theorems for contraction in fuzzy metric spaces

iterated function systems and attractors in the km fuzzy metric spaces fractal attractors are considered as invariant sets for contraction mappings in hyperspaces of the km fuzzy metric spaces using the properties of hausdorff fuzzy metrics several existence results of attractors are obtained for a finite family and a countable family of nonlinear contractions in particular unbounded invariant sets are also examined for the iterated function systems in km fuzzy metric spaces our results are generalizations in some aspects and analogous to their counterparts in usual metric spaces

l valued bornologies on powersets in m abel and a ostak 2011 1 the concept of an l fuzzy bornology was introduced actually an l fuzzy bornology on a set x is a certain ideal in the family lx of l fuzzy subsets of a set x here we propose an alternative approach to fuzzification of the concept of bornology we define an l valued bornology on a set x as an l fuzzy subset b of the powerset 2x satisfying l valued analogues of the axioms of a bornology basic properties of l valued bornological spaces are studied our special interest concerns l valued bornologies induced by fuzzy metrics and relative compactness type l valued bornologies in changgoguen l topological spaces

some new approaches to modular and fuzzy metric and related best proximity results abstract by using current methods of best proximity point theory we can not establish and prove best proximity point results in modular metric spaces for this purpose we introduce the notion of p d modular metric spaces and then we establish some best proximity point theorems for certain new contraction mappings as an application of the obtained results we establish some best proximity point results in fuzzy metric spaces examples are furnished to demonstrate the validity of the obtained results

the c algebra of bosonic strings we give a rigorous definition of witten sc string algebra to this end we present a new construction ofc algebras associated to special geometric situations kahler foliations and generalize this later construction to the string case through this we get a natural geometrical interpretation of the string of semi infinite forms as well as the fermionic algebra structure using the non commutative geometric concepts for investigating the string algebra we get a natural fredholm module representation of dimension 26

the hausdorff fuzzy metric on compact sets we propose a method for constructing a hausdorff fuzzy metric on the set of the nonempty compact subsets of a given fuzzy metric space in the sense of george and veeramani we discuss several important properties as completeness completion and precompactness some illustrative examples are given

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

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

a soft computing method for multi criteria decision making with dependence and feedback in this paper the decision making problems with the dependence and the feedback effects are considered although the analytic network hierarchy process anp ahp has been proposed to deal with the problems above several problems make the method impractical in this paper we proposed the fuzzy decision maps fdm which incorporates the eigenvalue method the fuzzy cognitive maps fcm and the weighting equation to overcome the problem of preferential independent and the shortcomings of the anp in addition two numerical examples are used to demonstrate the proposed method on the basis of the numerical results we can conclude that the proposed method can soundly deal with the decision making problems with the dependence and the feedback effects

some questions in fuzzy metric spaces the george and veeramani s fuzzy metric defined by m x y t min x y t max x y t on 0 the set of non negative real numbers has shown some advantages in front of classical metrics in the process of filtering images in this paper we study from the mathematical point of view this fuzzy metric and other fuzzy metrics related to it as a consequence of this study we introduce throughout the paper some questions relative to fuzzy metrics also as another practical application we show that this fuzzy metric is useful for measuring perceptual colour differences between colour samples

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

a technique for fuzzifying metric spaces via metric preserving mappings abstract in this paper we develop a new technique for constructing fuzzy metric spaces in the sense of george and veeramani from metric spaces and by means of the lukasievicz t norm in particular such a technique is based on the use of metric preserving functions in the sense of j dobos besides the new generated fuzzy metric spaces are strong and completable and if we add an extra condition they are principal appropriate examples of such fuzzy metric spaces are given in order to illustrate the exposed technique

modelling multicriteria value interactions with reasoning maps idiographic causal maps are extensively employed in operational research to support problem structuring and complex decision making processes they model means end or causal discourses as a network of concepts connected by links denoting influence thus enabling the representation of chains of arguments made by decision makers there have been proposals to employ such structures to support the structuring of multicriteria evaluation models within an additive value measurement framework however a drawback of this multi methodological modelling is the loss of richness of interactions along the means end chains when evaluating options this has led to the development of methods that make use of the structure of the map itself to evaluate options such as the reasoning maps method which employs ordinal scales and ordinal operators for such evaluation however despite their potential reasoning maps cannot model explicitly value interactions nor perform a quantitative ranking of options limiting their applicability and usefulness in this article we propose extending the reasoning maps approach through a multilinear evaluation model structure built with the macbeth multicriteria method the model explicitly captures the value interactions between concepts along the map and employs the macbeth protocol of questioning to assess the strength of influence for each means end link the feasibility of the proposed approach to evaluate options and to deal with multicriteria interactions is tested in a real world application to support the construction of a population health index

on pseudo metric spaces induced by σ decomposable measures in this paper we study the relationship between the pseudo metric and decomposable measures with respect to a triangular conorm decomposable measures for short we first construct a pseudo metric on the measurable sets of a given decomposable measure and then discuss several properties such as completeness and continuity of the constructed pseudo metric space finally we show that the separability and nonatom of the decomposable measure can be characterized in the constructed pseudo metric space our results suggest that the standard approach for obtaining a metric from a given probability measure can be generalized to the setting of decomposable measure

common fixed point theorems in fuzzy metric spaces using the clrg property the main aim of this paper is to obtain some new common fixed point theorems for weakly compatible mappings in fuzzy metric spaces in the sense of kramosil and michalek satisfying new contractive conditions employing the common limit in the range property our results generalize and extend some recent results contained in jain et al 2012 12 to generalized contractive conditions under some control functions in the process some results about multidimensional common fixed points as coupled tripled quadrupled common fixed point results are derived from our main results

fuzzy quasi pseudometrics on algebraic structures abstract in this work we state a number of theorems about fuzzy quasi pseudometrizable algebraic structures our most useful results are 1 a fuzzy semitopological group whose topology is induced by a left invariant fuzzy quasi pseudometric then it is a fuzzy paratopological topological group 2 if the topology on a semigroup s is induced by an invariant fuzzy quasi pseudometric then s is a fuzzy topological semigroup and 3 the same conclusion is valid for a left invariant fuzzy quasi pseudometric on a monoid g such that the left translations are open and the right translations are continuous at the identity e of g by means of the standard fuzzy quasi pseudometric m d associated to a quasi pseudometric d our results apply in the case of semitopological groups semigroups and monoids in order to obtain new results that allow us to generalize and to strengthen previous outcomes

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

probabilistic metric spaces as enriched categories in this paper we investigate cauchy completeness and exponentiablity for quantale enriched categories paying particular attention to probabilistic metric spaces

fixed points in weak non archimedean fuzzy metric spaces mihet fuzzy j contractive mappings in non archimedean fuzzy metric spaces fuzzy sets and systems 159 2008 739 744 proved a theorem which assures the existence of a fixed point for fuzzy j contractive mappings in the framework of complete non archimedean fuzzy metric spaces motivated by this we introduce a notion of weak non archimedean fuzzy metric space and prove that the weak non archimedean fuzzy metric induces a hausdorff topology we utilize this new notion to obtain some common fixed point results for a pair of generalized contractive type mappings

a critical analysis of the eigenvalue method used to derive priorities in ahp abstract a lot of research has been devoted to the critical analysis of the analytic hierarchy process ahp from various perspectives however as far as we know no one has addressed a fundamental problem discussed in this paper concerning the meaning of the priority vector derived from the principal eigenvalue method used in ahp the role of ahp s consistency ratio is also analysed

on fuzzy uniformities induced by a fuzzy metric space abstract different types of fuzzy uniformities have been introduced in the literature standing out the notions due to hutton hohle and lowen the main purpose of this paper is to study several methods to endow a fuzzy metric space x m in the sense of george and veeramani with a probabilistic uniformity and with a hutton 0 1 quasi uniformity we will show the functorial behavior of these constructions as well as its relation with respect to lowen s functors and katsaras s functors which establish a relationship between the categories of probabilistic uniformities and hutton 0 1 quasi uniformities with the category of classical uniformities respectively furthermore we also study the fuzzy topologies associated with these fuzzy uniformities

on n polygonal interval value fuzzy sets and numbers abstract the structure of interval valued fuzzy sets is complex in regard to their arithmetic operations to reduce the computational complexity of arithmetic operations on interval valued fuzzy sets we propose the notion of an n polygonal interval valued fuzzy set considering two 2 n 2 tuple ordered real numbers complete representation of n polygonal interval valued fuzzy sets and numbers is provided moreover we demonstrate that the n polygonal interval valued fuzzy numbers can approximate the general interval value fuzzy numbers with any precision next we introduce arithmetic operations on n polygonal interval valued fuzzy numbers by capitalizing on the good characteristics of n polygonal interval valued fuzzy numbers the properties of the introduced arithmetic operations are also addressed in addition with the aid of a concrete example we verify the effectiveness of the approximation ability of the n polygonal interval valued fuzzy set furthermore we study the properties of the topological space of n polygonal interval valued fuzzy numbers this proves that this space is a complete separable and local compact metric space when endowed with the newly defined distance between two n polygonal interval valued fuzzy numbers by product it shows that arithmetic operations introduced here on n polygonal interval valued fuzzy numbers are continuous finally the practicability of n polygonal interval valued fuzzy numbers is verified by an example

a characterization of bicompletable fuzzy quasi metric spaces we obtain an internal characterization of those fuzzy quasi metric spaces that admit a fuzzy quasi metric bicompletion we also show that such a bicompletion is unique up to isometry

the bicompletion of fuzzy quasi metric spaces extending the well known result that every fuzzy metric space in the sense of kramosil and michalek has a completion which is unique up to isometry we show that every km fuzzy quasi metric space has a bicompletion which is unique up to isometry and deduce that for each km fuzzy quasi metric space the completion of its induced fuzzy metric space coincides with the fuzzy metric space induced by its bicompletion

on the existence and the uniqueness of fixed points of sehgal contractions we discuss the problem of existence and uniqueness of fixed points for fuzzy contraction maps in fuzzy menger spaces and quasi pseudo menger spaces

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

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

examples of fuzzy metrics and applications in this paper we present new examples of fuzzy metrics in the sense of george and veeramani the examples have been classified attending to their construction and most of the well known fuzzy metrics are particular cases of those given here in particular novel fuzzy metrics by means of fuzzy and classical metrics and certain special types of functions are introduced we also give an extension theorem for two fuzzy metrics that agree in its nonempty intersection finally we give an application of this type of fuzzy metrics to color image processing we propose a fuzzy metric that simultaneously takes into account two different distance criteria between color image pixels and we use this fuzzy metric to filter noisy images obtaining promising results this application is also illustrative of how fuzzy metrics can be used in other engineering problems

towards probabilistic partial metric spaces diagonals between distance distributions abstract the quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories motivated by the categorical interpretation of partial metric spaces we are led to investigate the quantaloid of diagonals between distance distributions which is expected to establish the categorical foundation of probabilistic partial metric spaces observing that the quantale of distance distributions w r t an arbitrary continuous t norm is non divisible we precisely characterize diagonals between distance distributions and prove that one step functions are the only distance distributions on which the set of diagonals coincides with the generated down set

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

on completable fuzzy metric spaces in this paper we construct a non completable fuzzy metric space in the sense of george and veeramani which allows to answer an open question related to continuity on the real parameter t in addition the constructed space is not strong non archimedean