on fuzzy valued operations and fuzzy valued fuzzy sets this paper is devoted to investigate fuzzy valued operations and the lattice structures of the algebra of fuzzy values the algebra of fuzzy values is proven to be a complete completely distributive lattice and the list of all join irreducible elements is provided fuzzy valued t norms and t conorms are induced by arbitrary t norms and t conorms regardless of their continuity respectively moreover fuzzy valued fuzzy implications are constructed from fuzzy valued t norms induced by left continuous t norms and residuated lattices are constructed on the algebra of fuzzy values as a consequence fuzzy valued fuzzy rough sets and fuzzy valued fuzzy complete lattices are proposed and investigated in fuzzy valued fuzzy sets

a new approach to l t2 l urysohn and l completely hausdorff axioms in this paper new l t 2 l urysohn and l completely hausdorff axioms are introduced in l topological spaces relations between these axioms are established the l extended real line and its subspaces as well as pointwise metric spaces satisfy these axioms

convergence in topological molecular lattices abstract the theory of topological molecular lattices introduced by wang has general topology and fuzzy topology as special cases in this paper the author establishes the theory of ideal convergence in topological molecular lattices and gives characterizations of some topological notions e g closed elements hausdorffness continuous goh in topological molecular lattices etc in terms of ideals the author establishes the relation between ideal convergence and molecular net convergence introduced by wang

on the accumulation points of fuzzy sets abstract in this paper we first study the stratified structure of the derived sets and the distributional rules of the accumulation points of the f sets then we give some conditions that are equivalent to a b d a d b d for any a b 0 1 x finally we introduce the general f derived operator on x and by which we characterize the general fts x

urysohn closedness on completely distributive lattices the purpose of this paper is to investigate the urysohn closedness of co topology on lattices which are not required to have an order reversing involution the concept of urysohn closedness on lattices is introduced and characterizations of urysohn closedness are given in terms of ideals and nets these characterizations are obtained mainly through the introduction of a kind of convergence for ideals and nets that we call l urysohn convergence

discrete dynamical systems in l topological spaces in this paper we investigate iteration of zadeh image operators and their discrete dynamical systems in l topological spaces some basic concepts such as limit set invariant set periodic point nonwandering point and recurrent point are discussed in weakly induced topological spaces we also study topological mixing topological transitivity and minimality for such dynamical systems while comparing with those corresponding ones in crisp spaces

construct fuzzy lattices from a given symmetric complete lattice abstract fuzzy lattices are the basic objects which l fuzzy topology bases on we study relations of fuzzy lattices and symmetric complete lattices from category points of view a relevant fuzzy lattice l and a relevant symmetric complete heyting algebra l are constructed from a given symmetric complete lattice l we prove that the constructions and are two functors and they have reflective properties over relevant categories

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

reconstruction in a generalized model for translation invariant systems abstract we consider translation invariant ti operators on the set of maps from an abelian group g to called lg fuzzy sets where 0 is a complete lattice ordered group by defining minkowski and morphological operations on and considering order preserving operators we prove a reconstruction theorem this theorem which is called the strong reconstruction theorem srt is similar to the convolution theorem in the theory of linear and shift invariant systems and states that for an order preserving ti operator y one can explicitly compute y a for any a from a specific subset of called the base of y the introduced framework is a general model for the theory of translation invariant systems and srt shows the consistency of it for the special cases when g r z srt implies the results of maragos and schafer

conjugate topology of pointwise metric molecular lattices in this paper the pointwise pseudo metric for molecular lattices introduced by shi is studied a series of expressions concerning neighborhood balls and remote neighborhood balls are obtained some algebraic properties of the pointwise pseudo metric function of molecular lattices are presented and their topological structure are discussed in terms of the conjugate families of mappings these results show that there exist conjugate relations between neighborhoods and remote neighborhoods

a new definition of fuzzy compactness in this paper a new definition of fuzzy compactness is presented in l topological spaces when l is a complete demorgan algebra this definition does not rely on the structure of the basis lattice l and no distributivity in l is required the intersection of a fuzzy compact l set and a closed l set is fuzzy compact the continuous image of a fuzzy compact l set is fuzzy compact if the set of all prime elements of l is order generating then the alexander subbase theorem is true when l is a completely distributive demorgan algebra it is equivalent to lowen s fuzzy compactness and in this case its many characterizations are presented by means of open l sets and closed l sets

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 uniform boundedness principle in l topological vector spaces in this paper we introduce and study the equicontinuity of a family of l fuzzy linear order homomorphisms we prove a generalization of the uniform boundedness principle in the classical topological vector spaces to l topological vector spaces

net theoretical convergence in l m fuzzy cotopological spaces in this paper we introduce the notion of topological l m fuzzy convergence structure and prove that for a given set there exists a bijection between the set of all topological l m fuzzy convergence structures and the set of all l m fuzzy cotopologies on this set this induces an isomorphism between the category of topological l m fuzzy convergence spaces and the category of l m fuzzy cotopological spaces

a new fuzzy compactness defined by fuzzy nets compactness is one of the most important notions in topology and is thoroughly investigated in general topology but it seems that the research about this notion in the area of fuzzy topology is not so effective as in general topology in fact it would seem that there was not even a good definition of compactness in this area until recently indeed soon after the famous article written by zadeh 8 was published chang 1 introduced the notion of fuzzy topological spaces and at the same time a certain fuzzy compactness was given from then on a series of different notions of fuzzy compactness have been discussed 2 3 71 and in 5 they were compared in detail but it seems unsatisfactory that all these fuzzy compactness ideas are defined for the whole fuzzy topological space but not for an arbitrary fuzzy subset therefore they are far from the crisp compactness for example it is impossible to discuss the hereditary property with respect to closed subsets of fuzzy compactness in 1977 pu and liu introduced the notion of fuzzy nets and a new concept of so called q neighborhood was given which could reflect the features of neighborhood structure in fuzzy topological spaces and by this new neighborhood structure the moore smith convergence theory was established spendidly 6 it furnishes us a basic tool to investigate the fuzzy compactness in a more general way to investigate the compactness of arbitrary fuzzy subsets in this paper a new fuzzy compactness defined by fuzzy nets we shall call it n compactness is given but we introduce the notion of r neighborhood see section 2 instead of qneighborhood to establish the moore smith convergence theory for it is perhaps more convennient to use n compactness possesses the following properties 1 n compactness is defined for arbitrary fuzzy subsets 2 for n compactness the hereditary property with respect to closed subsets holds 3 n compactness is a good extension 5 4 the continuous images of ncompact sets are n compact 5 for n compactness the tychonoff product theorem holds 6 if an n compact fuzzy topological space is t2 6 then it will satisfy a stronger separation axiom which will be called t4 in this paper 1 0022 247x 83 3 00

the inverse limit in the category of topological molecular lattices abstract in this paper we first introduce the definition of an inverse system in the category of topological molecular lattices and give the structure of the inverse limit of an inverse system then we establish the concept of a mapping between two inverse systems and induce the concept of a continuous mapping between the inverse limits of two inverse systems finally we discuss a series of properties of continuous mappings therefore the difficult problem in the theory of topological molecular lattices is solved

on the optimality of bayesian change point detection by introducing suitable loss random variables of detection we obtain optimal tests in terms of the stopping time or alarm time for bayesian change point detection not only for a general prior distribution of change points but also for observations being a markov process moreover the optimal minimal average detection delay is proved to be equal to 1 for any possibly large average run length to false alarm if the number of possible change points is finite

an axiomatic approach to bases and subbases in l convex spaces and their applications abstract considering a continuous lattice l as the lattice background an axiomatic approach to bases and subbases in the framework of l convex spaces is provided firstly the concepts of bases and subbases in l convex spaces are introduced and then l convexity base axioms and l convexity subbase axioms are proposed by abstracting the properties of bases and subbases respectively secondly some applications of l convexity base axioms and l convexity subbase axioms are investigated it is shown that l convexity base axioms can be used to demonstrate some relationship between spatial structures with respect to l convex structures and l convexity subbase axioms can be applied to define the join space and the product space of l convex spaces

a variational inequality theory in reflexive smooth banach spaces and applications to p laplacian elliptic inequalities abstract we develop a theory of variational inequality for demicontinuous s contractive maps in reflexive smooth banach spaces variational inequality theorems are proved and applied to study existence of nonzero positive weak solutions for p laplacian elliptic inequalities and a population model of one species arising in mathematical biology

h λ completely hausdorff axiom on l topological spaces this paper defines the new concept of completely hausdorff axiom of an l topological space by means of l continuous mappings from an l topological space to the refined hutton s unit l interval by wang some characterizations of the completely hausdorff axiom defined in this paper are given and many nice properties of this kind of completely hausdorff axiom are proved for example it is hereditary and product invariant the refined hutton s unit l interval satisfy this kind of completely hausdorff axiom and when an l topological space satisfy this kind of completely hausdorff axiom every f convergent ideal does not have f limit points with different supports etc the relation between the completely hausdorff axiom defined in the paper and other separation axioms is discussed also

minimax robust quickest change detection the popular criteria of optimality for quickest change detection procedures are the lorden criterion the pollak criterion and the bayesian criterion in this paper a robust version of these quickest change detection problems is considered when the pre change and post change distributions are not known exactly but belong to known uncertainty classes of distributions for uncertainty classes that satisfy a specific condition it is shown that one can identify least favorable distributions lfds from the uncertainty classes such that the detection rule designed for the lfds is optimal for the robust problem in a minimax sense the condition is similar to that required for the identification of lfds for the robust hypothesis testing problem originally studied by huber an upper bound on the delay incurred by the robust test is also obtained in the asymptotic setting under the lorden criterion of optimality this bound quantifies the delay penalty incurred to guarantee robustness when the lfds can be identified the proposed test is easier to implement than the cusum test based on the generalized likelihood ratio glr statistic which is a popular approach for such robust change detection problems the proposed test is also shown to give better performance than the glr test in simulations for some parameter values

pointwise uniformities in fuzzy set theory a theory of pointwise quasi uniformities is based on fuzzy sets many theorems corresponding to the usual theorems in general topology are generalized on fuzzy sets in particular each fuzzy topological space is pointwise quasi uniformizable a pointwise uniformity is characterized in terms of a kind of complete regularity a uniformity on the fuzzy unit interval is constructed

subcategories of the category of l convex spaces abstract in this paper several types of l convex spaces are introduced including stratified l convex spaces convex generated l convex spaces weakly induced l convex spaces and induced l convex spaces their relations are discussed category theoretically firstly it is shown that there is a galois correspondence between the category sl cs of stratified l convex spaces resp the category wil cs of weakly induced l convex spaces and the category l cs of l convex spaces in particular sl cs and wil cs are both coreflective subcategories of l cs secondly it is proved that there is a galois correspondence between the category cs of convex spaces and the category sl cs resp wil cs specially cs can be embedded into sl cs and wil cs as a coreflective subcategory finally it is shown that the category cgl cs of convex generated l convex spaces the category il cs of induced l convex spaces and cs are isomorphic

urysohn separation property in topological molecular lattices abstract the theory of topological molecular lattices which is a generalization of the theories of point set topology fuzzy topology and l fuzzy topology is established by wang in this paper the concepts of some kinds of urysohn separation axioms in topological molecular lattices are introduced and systematically discussed several important results such as the u i i 1 0 1 2 3 4 urysohn regular and urysohn normal separation properties are both hereditary and topological invariant etc are given

quickest detection in multiple on off processes we consider the quickest detection of idle periods in multiple on off processes at each time only one process can be observed and the observations are random realizations drawn from two different distributions depending on the current state on or off of the chosen process the objective is to catch an idle period in any of the on off processes as quickly as possible subject to a reliability constraint we show that this problem presents a fresh twist to the classic problem of quickest change detection that considers only one stochastic process a bayesian formulation of the problem is developed for both infinite and finite number of processes based on the theory of partially observable markov decision process pomdp while a general pomdp is pspace hard we show that the optimal decision rule has a simple threshold structure for the infinite case for the finite case basic properties of the optimal decision rule are established and a low complexity threshold policy is proposed which converges to the optimal decision rule for the infinite case as the number of processes increases this problem finds applications in spectrum sensing in cognitive radio networks where a secondary user searches for idle channels in the spectrum

a class of expansive type krasnosel skii fixed point theorems abstract in this paper we establish some new fixed point theorems for the sum of two operators in particular one new theorem complements the well known krasnosel skii fixed point theorem in the sense that the mapping t is expansive rather than contractive some previous and related results are extended and developed as an application to one of our main results the existence of periodic solutions for some nonlinear integral equation is considered

asymptotic optimality of mixture rules for detecting changes in general stochastic models the paper addresses a sequential changepoint detection problem for a general stochastic model assuming that the observed data may be non i i d i e dependent and non identically distributed and prior distribution of the change point is arbitrary tartakovsky and veeravalli 2005 baron and tartakovsky 2006 and more recently tartakovsky 2017 developed a general asymptotic theory of changepoint detection for non i i d stochastic models assuming certain stability of the log likelihood ratio process in the case of simple hypotheses when both pre change and post change models are completely specified however in most applications the post change distribution is not completely known in the present paper we generalize previous results to the case of parametric uncertainty assuming that the parameter of the post change distribution is unknown we introduce two detection rules based on mixtures the mixture shiryaev rule and the mixture shiryaev roberts rule and study their asymptotic properties in the bayesian context in particular we provide sufficient conditions under which these rules are first order asymptotically optimal minimizing moments of the delay to detection as the probability of false alarm approaches zero

generalization of kolmogoroff s theorem to l topological vector spaces in this paper the concept of l fuzzy normed linear spaces is introduced and some of its properties are studied then we give a necessary and sufficient condition for l topological vector spaces to be l fuzzy normable this is a generalization of kolmogoroff s theorem in the classical topological vector spaces to l topological vector spaces

a note on urysohn separation property in topological molecular lattices as an extension of urysohn separation axioms in general topology several separation property were introduced by chen and wu urysohn separation property in topological molecular lattices fuzzy sets and systems 123 2001 177 184 in topological molecular lattices in this note it is proved that no 0 1 topological space satisfies chen wu separation axioms s

separation axioms in l fuzzy topological spaces i t0 and t1 abstract using the notion of remote neighborhood we define the separation axioms t 0 and t 1 in l fuzzy topological spaces l fts the relations between our definitions hutton and reilly s and wang s are discussed and the separations of hutton s fuzzy unit interval and gantner s fuzzy real line are examined characterizations of these l fts are proved and a series of properties of them are investigated moreover some results on minimal t 0 l fts and t 1 l fts are established which will be used immediately in our subsequent discussion

sr convergence theory in fuzzy lattices abstract convergence theory and order homomorphisms theory are two important objects of study in fuzzy lattices in this paper sr convergence theory for molecular nets and ideals is established and the concepts of r irresolute sr continuous and almost irresolute order homomorphisms in topological molecular lattices are introduced and systematically characterized some mutual relations between these concepts and others are obtained

categories isomorphic to the kubiak sostak extension of tml abstract in this paper we study wang guo jun s topological molecular lattices wang s tml in a kubiak sostak sense and construct a category the kubiak sostak extension of tml denoted by ftml then we prove that ftml is topological over cd op and tml is bireflective full subcategory of ftml finally we introduce several important categories to characterize ftml

syntopogenous structure on completely distributive lattice and its connectedness abstract in this paper the general theory of syntopogenous structures on completely distributive lattices is established the unified question of cotopology quasi uniformity and t structure is investigated the results of this paper complete the framework of the topological structure on completely distributive lattices and generalize the corresponding theory in general and fuzzy topology finally we examine the connectedness the following main results about connectedness are obtained 1 1 if f l1 s1 l2 s2 is an s1 s2 continuous goh function and d l1 is s1 connected element then f d is s2 connected element 2 2 let c l s be an s connected element and c d c then d is an s connected element 3 3 i li si is connected iff for any i i li si is connected

on the order conditions of fuzzy convergence classes by means of the order structure of the related lattice the liminf condition of fuzzy convergence classes is proposed in this paper which reflects the essential difference between fuzzy convergence classes and ordinary convergence classes the relationship between the liminf condition and two related conditions proposed by liu and wang respectively are discussed the theory of fuzzy convergence classes based on liminf condition is established for topological molecular lattices l topological spaces in the sense of chang or lowen weakly induced spaces and induced spaces

new applications of l nets in l fuzzy multifunctions in this paper we will give new applications of l net in l fuzzy multifunctions using l net we will further study l fuzzy continuous almost continuous and r continuous multifunctions some interesting characterizations are obtained

the category of pointwise s proximity spaces first it is proved that the category of pointwise quasi uniform spaces and pointwise quasi uniformly continuous morphisms is topological then the concept of pointwise s quasi proximity on lattice valued fuzzy set theory is introduced in such a way as to be compatible with pointwise quasi uniformity and pointwise p q metric each co topology can be induced by a pointwise s quasi proximity when a valued lattice is a completely distributive lattices equipped with an order reversing involution the concept of pointwise s proximity can be defined by means of pointwise s quasi proximity the relation between pointwise s quasi proximities and pointwise quasi uniformities is discussed it is proved that the category of pointwise s quasi proximity spaces is isomorphic to the category of totally bounded pointwise quasi uniform spaces the category of pointwise s proximity spaces is isomorphic to a subcategory of totally bounded pointwise uniform spaces hence they are topological

degrees of fuzzy compactness in l fuzzy topological spaces in this paper we introduce the notion of the degree of fuzzy compactness in l fuzzy topological spaces by means of an inequality proposed by shi in 2007 the notion is a generalization of the definition of fuzzy compactness in l topological spaces some properties of this new notion are researched the tychonoff theorem is generalized it is pointed out that our notion is not equivalent to other definition of degree of compactness

minimal hausdorff l fuzzy topological spaces abstract in this paper the author introduced the concept of minimal hausdorff l fuzzy topological spaces investigated basic properties of it by means of fuzzy ideals and fuzzy nets and compared it with the concepts of compactness and h closedness

theory of topological molecular lattices abstract the aim of this paper is to bring the theories of point set topology fuzzy topology and l fuzzy topology into a unified theory the theory of topological molecular lattices for this purpose we first introduce the concepts of molecule for completely distributive complete lattice molecular lattice for short the cotopology on it and the concept of remote neighborhoods of molecules therefrom we develop the theory of pointwise topology on molecular lattices

optimal detection of a change in distribution abstract document discusses a stopping rule that is a limit of bayes rules derived then an almost minimax rule is presented

strong fuzzy compact sets and ultra fuzzy compact sets in l topological spaces abstract in this paper lowen s strong fuzzy compactness and ultra fuzzy compactness of i topological spaces are extended to l subsets for l a complete lattice the properties of strong fuzzy compact l subsets and ultra fuzzy compact l subsets are studied in detail here and comparisons between these notions as well as the notion of n compactness are shown

on asymptotic optimality in sequential changepoint detection non iid case we consider a sequential bayesian changepoint detection problem for a general stochastic model assuming that the observed data may be dependent and non identically distributed and the prior distribution of the change point is arbitrary not necessarily geometric tartakovsky and veeravalli 2005 developed a general asymptotic theory of changepoint detection in the case of non identically distributed and dependent observations and discrete time and baron and tartakovsky 2006 in continuous time assuming the certain stability of the log likelihood ratio process this stability property was formulated in terms of the r quick convergence of the normalized log likelihood ratio process to a positive and finite number which can be interpreted as the limiting kullback leibler information between the change and no change hypotheses in these papers it was conjectured that the r quick convergence can be relaxed in the r complete convergence which is typically much easier to verify in particular examples in the present paper we justify this conjecture by showing that the shiryaev change detection procedure is nearly optimal minimizing asymptotically to first order as the probability of false alarm vanishes moments of the delay to detection up to order r whenever r complete convergence holds we also study asymptotic properties of the shiryaev roberts detection procedure in the bayesian context

l m fuzzy matroids in this paper an extension of matroids is introduced in lattice valued fuzzy set theory such a generalized matroid is a pair made of a finite set and a fuzzy subfamily of its lattice valued fuzzy subsets satisfying three axioms it uses two lattices one for membership grades of elements to fuzzy sets and another for membership degrees of fuzzy sets in a fuzzy family of fuzzy sets it is a logical generalization of the notions of matroids and fuzzifying matroids in our definition of generalized fuzzy matroids each l fuzzy subset can be regarded to be independent of other ones to some degree the relevance of generalized fuzzy matroids is shown in the setting of fuzzy vector spaces and fuzzy graphs

uniform environments as a general framework for metrics and uniformities this paper puts theories of classical uniformity probabilistic uniformity hutton uniformity classical metric probabilistic metric and hutton metric into one framework by introducing the concept of uniform environment which is a functor from the category of sets to the opposite category of involutive unital quantales and involutive closed unital maps subject to certain conditions the results show that uniform environments and their transformations provide a nice framework to study relationships between various notions of uniformity in the literature

l metric on the space of l fuzzy numbers abstract in this article a natural l topology is constructed on the set of l fuzzy numbers which is called the standard l topology it is proved that the standard l topology can be induced by an l metric the space of trapezoidal fuzzy numbers can be regarded as a subspace of the space of l fuzzy numbers an l metric on the set of trapezoidal fuzzy numbers is presented

on afs algebra part ii this paper addresses the properties and structures of ei algebra and ein algebra in the framework of liu fuzzy sets and systems 95 1998 179 the main contribution of the paper is that the expressions of both irreducible elements or irreducible elements in molecular lattice em and ex1 xnm are developed and that the standard minimal family of elements in molecular lattice em and ex1 xnm is formulated it is proved that neither molecular lattice em nor molecular lattice ex1 xnm is a fuzzy lattice

approximation operators on complete completely distributive lattices rough set a tool for data mining deals with the vagueness and granularity in information systems in 2006 chen et al initiated the study of rough approximations on a complete completely distributive lattice ccd lattice for short and brought generalizations of rough sets into a unified framework in this paper we discuss the approximation operators on a ccd lattice based on the concept of neighborhood three kinds of upper approximation operators and a kind of lower approximation operator are constructed basic properties of lower and upper approximation operators are examined furthermore the relationships among these operators are analyzed

l proximities and totally bounded pointwise l uniformities in this paper we shall develop the study of connections between l quasi proximities in the sense of katsaras liu artico moresco and pointwise l quasi uniformities in the sense of shi we shall prove that there exists a one to one correspondence between l quasi proximity spaces and totally bounded pointwise l quasi uniform spaces

on some gross misunderstandings about the theory of topological molecular lattices abstract some gross misunderstandings have arisen since the theory of topological molecular lattices briefly tmls was presented wang 1989 1992 certain scholars think that there is a correspondence between tmls and classical spaces and they could obtain the results in the theory of tmls hence fuzzy topology by simply translating the corresponding results in classical topology the aim of this paper is to clear out such misunderstandings

coincidence theory for multimaps abstract several continuation principles in a variety of settings are presented which guarantee the existence of coincidence points for a general class of multimaps

connectivity in fuzzy topological molecular lattices abstract a new kind of the definitions for connectivity in a fuzzy topological molecular lattice called s connectivity is defined some properties for s connectivity are obtained and the relations between s connectivity and each connectivity given in 1 4 7 are discussed

q convergence of ideals in fuzzy lattices and its applications abstract in this paper we study q convergence and q convergence of ideals in fuzzy lattices by the concept of q remote neighborhood then we introduce the strong s irresoluteness s irresoluteness and s strong semicontinuity on fuzzy lattices we also study some properties of the notions above and strong semicontinuity 2 3 and s irresoluteness 3 4 with the aid of the q convergence q convergence of ideals

average run lengths of an optimal method of detecting a change in distribution abstract suppose one accumulates independent observations from a certain process initially the process is at state 0 at some unknown point in time something occurs e g a breakdown which puts the process in state 1 and consequently the stochastic behavior of the observations changes it is of interest to declare that a change took place to raise an alarm as soon as possible after its occurrence subject to a restriction on the rate of false detections it is assumed that the aforementioned observations are the only information one has about the process and the problem is to construct a good detection scheme practical examples of this problem arise in areas such as health quality control ecological monitoring etc for instance consider surveillance for congenital malformations in newborn infants under normal circumstances the percentage of babies born with a certain type of malformation has a known value should something occur such as an environmental change the introduction of a new drug to the market etc the percentage may increase one would want to raise an alarm as quickly as possible after a change would have taken place subject to an acceptable rate of false alarms

h l completely regular l fuzzy sets and their applications first we introduce the concept of h completely regular l fuzzy set in l fts and give some characterizations of it then we propose the concept of h complete regularization of l fts and investigate some properties of this complete regularization we also establish the relations between h completely regular l fts completely regular l fts and weakly induced l fts based on these results we obtain several characterizations of h completely regular l fts

ditopological texture spaces and fuzzy topology ii topological considerations this is the second of three papers which develop various fundamental aspects of the theory of ditopological texture spaces in a categorical setting and present important links with the theory of l topological spaces in the first paper in this series subtitled basic concepts the authors presented the notions of direlation and difunction between textures and introduced the category dftex the construct ftex and several related categories in this paper the category dfditop of ditopological texture spaces and bicontinuous difunctions is defined and the forgetful functor u dfditop dftex shown to be topological several properties are discussed including the existence of products and coproducts an equivalence with the category of classical hutton spaces is presented and the paper ends with a consideration of l valued sets and topologies from the viewpoint of ditopological texture spaces

a note on optimal detection of a change in distribution suppose x 1 x 2 dots x nu 1 are iid random variables with distribution f 0 and x nu x nu 1 dots are are iid with distributed f 1 the change point nu is unknown the problem is to raise an alarm as soon as possible after the distribution changes from f 0 to f 1 detect the change but to avoid false alarms pollak found a version of the shiryayev roberts procedure to be asymptotically optimal for the problem of minimizing the average run length to detection over all stopping times which satisfy a given constraint on the rate of false alarms here we find that this procedure is strictly optimal for a slight reformulation of the problem he considered explicit formulas are developed for the calculation of the average run length both before and after the change for the optimal stopping time

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

a variational inequality theory for demicontinuous s contractive maps with applications to semilinear elliptic inequalities abstract a variational inequality theory for demicontinuous s contractive maps in hilbert spaces is established by employing the ideas of granas topological transversality such a variational inequality theory has many properties similar to those of fixed point theory for demicontinuous weakly inward s contractive maps and to those of fixed point index for condensing maps the variational inequality theory will be applied to study the existence of positive weak solutions and eigenvalue problems for semilinear second order elliptic inequalities with nonlinearities which satisfy suitable lower bound conditions involving the critical sobolev exponent there has been little discussion for such elliptic inequalities involving the critical sobolev exponent in the literature

on optimality of the shiryaev roberts procedure for detecting a change in distribution in 1985 for detecting a change in distribution pollak introduced a specific minimax performance metric and a randomized version of the shiryaev roberts procedure where the zero initial condition is replaced by a random variable sampled from the quasi stationary distribution of the shiryaev roberts statistic pollak proved that this procedure is third order asymptotically optimal as the mean time to false alarm becomes large the question of whether pollak s procedure is strictly minimax for any false alarm rate has been open for more than two decades and there were several attempts to prove this strict optimality in this paper we provide a counterexample which shows that pollak s procedure is not optimal and that there is a strictly optimal procedure which is nothing but the shiryaev roberts procedure that starts with a specially designed deterministic point

on stratiform l fuzzy topologies and their application for a given l fuzzy topological space and a fixed prime element r of fuzzy lattice l the concept of l fuzzy r open sets is introduced and it is proved that all r open sets for l fuzzy topological space form a new l fuzzy topology which is called stratiform l fuzzy topology making use of the stratiform l fuzzy topology a series of new characterizations of l fuzzy continuous mapping and l fuzzy open mapping and three kinds of separateness hausdorff regular and normal are presented

approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory ii in this paper the representations of fuzzy concepts based on raw data have been investigated within the framework of afs axiomatic fuzzy set theory first a brief review of afs theory is presented and a completely distributive lattice the e i algebra is proposed secondly two kinds of e i algebra representations of fuzzy concepts are derived in detail in order to represent the membership functions of fuzzy concepts in the interval 0 1 the norm of afs algebra is defined and studied finally the relationships of various representations with their advantages and drawbacks are analyzed

connectedness in l fuzzy topological spaces based on the consideration to the layer structures of fuzzy lattices and the level topologies of l fuzzy topological spaces a connectedness is defined for an arbitrary l fuzzy set in this paper this definition reflects the degree of connectivity of an l fuzzy set it is shown that the connectedness of l fuzzy topological spaces is an l good extension multiplicative and preserved under continuous l valued zadeh functions and that the inverse limit of continuums is a continuum general l fuzzy intervals and h intervals are defined and connectedness of them are proved it is also shown that the connectedness of an l fuzzy topological space is equivalent to the connectedness of its induced i l fuzzy topological space

pointwise pseudo metrics in l fuzzy set theory a theory of pointwise pseudo metrics is based on l fuzzy sets a pointwise pseudo metric is characterized by its remote neighborhood maps many theorems in general topology are generalized on l fuzzy sets the l fuzzy real line and the l fuzzy unit interval are pointwise pseudo metrizable a pseudo metrization theorem of pointwise uniformity is obtained relations between erceg s p metric pseudometric and pointwise p metric are discussed

extension of shi s quasi uniformities in a kubiak sostak sense abstract the aim of this paper is to study the extension of shi fu gui s quasi uniformities in a kubiak sostak sense the relationship between this extension of shi fu gui s quasi uniform molecular lattices shi s quml and the corresponding kubiak sostak extension of wang guo jun s topological molecular lattices wang s tml is discussed quml and tml denote the categories of shi s quml and wang s tml respectively cd is the category of completely distributive lattices with complete lattice morphisms as morphisms we prove that fquml the category of fuzzy quasi uniform molecular lattices the extension of shi s quml is a topological category over cd op and ftml the category of fuzzy topological molecular lattices the extension of wang s tml can be embedded in fquml we also prove that fquml is isomorphic to quml c m when m is a completely distributive lattice with multiplicative property where quml c m is the co tower extension of quml finally we study the kubiak sostak extension of hutton s quasi uniformities

lattice theoretic contexts and their concept lattices via galois ideals this paper introduces a concept of lattice theoretic contexts as well as their concept lattices a lattice theoretic context is a triple g m i with two complete lattices g m and their galois ideal i a lattice theoretic context and its concept lattice are a common generalization of classical fca pocs s formal fuzzy context one sided concept lattices generalized concept lattices and l fuzzy concept lattices with hedges when the lattices g m are completely distributive a reduction of the relation i in the lattice theoretic context g m i can be obtained related algorithms to construct concept lattices of l fuzzy contexts considered as lattice theoretic contexts are presented in the case of l being a completely distributive lattice we can reduce the number of elements objects or and attributes before computing the whole concept lattice then the related algorithm has lower complexity

the characterizations of semi continuous and irresolute order homomorphisms on fuzzes abstract the concepts of semi continuous and irresolute order homomorphisms on fuzzes were introduced in j jianghan petroleum institute 2 1988 96 97 in this paper we first present the theory with respect to s convergence s convergence of molecular nets and ideals on fuzzes secondly we introduce the notions of strong semicontinuity strong irresoluteness and s irresoluteness on fuzzes then we systematically study the characterizations of these notions with the aid of the s convergence s convergence of molecular nets and ideals and give the relations of them

order homomorphisms on fuzzes abstract in this paper basic properties of the concept of order homomorphisms on fuzzes 4 which is a proper generalization of the concept of fuzz functions 1 are studied conditions for fuzz functions to be functions of zadeh s type are obtained moreover the concepts of continuous closed and open order homomorphisms are introduced and studied

concept analysis via rough set and afs algebra formal concept analysis fca was originally proposed by wille 1982 which is an important theory for data analysis and knowledge discovery afs axiomatic fuzzy set algebra was proposed by liu x liu the fuzzy theory based on afs algebras and afs structure journal of mathematical analysis and applications 217 1998 459 478 x liu the topology on afs algebra and afs structure journal of mathematical analysis and applications 217 1998 479 489 which is a semantic methodology relating to the fuzzy theory combining above two theories we propose afs formal concept which can be viewed as the generalization and development of monotone concept proposed by deogun and saquer 2003 moreover we show that the set of all afs formal concepts forms a complete lattice afs formal concept can be applied to represent the logic operations of queries in information retrieval furthermore we give an approach to find the afs formal concepts whose intents extents approximate any element of afs algebra by virtue of rough set theory

on compactness of induced i l fuzzy topological spaces abstract the induced i l fuzzy topological spaces for l fuzzy topological spaces introduced by wang geping is a kind of important fuzzy topological space in this paper the author studies the fuzzy compactness of induced i l fuzzy topological spaces some available relations between molecular nets of an l fuzzy topological space and that of its induced i l fuzzy topological space are firstly presented by using these relations the author obtains that the induced i l fuzzy topological space is strong fuzzy compact resp fuzzy compact n compact if and only if the l fuzzy topological space is strong fuzzy compact resp fuzzy compact n compact the author also proves that the induced i l fuzzy topological space is paracompact if and only if the l fuzzy topological space is paracompact

a new approach to the fuzzification of matroids in this paper the concept of closed fuzzy pre matroids is generalized to l fuzzy set theory when l is a complete lattice it is also called an l fuzzifying matroid in the definition of l fuzzifying matroids each subset can be regarded as an independent set to some degree when l is completely distributive an l fuzzifying matroid can be characterized by means of its l fuzzifying rank function an l fuzzifying matroid and its l fuzzifying rank function are one to one corresponding

a variational inequality index for condensing maps in hilbert spaces and applications to semilinear elliptic inequalities a variational inequality index for condensing maps is established in hilbert spaces new results on existence of nonzero positive solutions of variational inequalities for such maps are proved by using the theory of variational inequality index applications of such a theory are given to existence of nonzero positive weak solutions for semilinear second order elliptic inequalities where previous results of variational inequalities for s contractive maps cannot be applied

limit structures over completely distributive lattices the notion of a limit molecular lattice a completely distributive lattice with some kinds of convergence of ideals on it is introduced it is proved that the category of limit molecular lattices is a cartesian closed category containing the category of topological molecular lattices as a bireflective full subcategory and the category of limit spaces as a reflective and coreflective subcategory respectively noteworthy is the distinctive order property of the convergence of ideals on the limit molecular lattice compared to that of limit spaces the l fuzzy version of fuzzy limit space is introduced and it is proved that the category of l fuzzy limit spaces is a nonfull coreflective subcategory of the category of limit molecular lattices