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

fuzzy t net theory abstract in this paper we define the convergence of fuzzy nets in a fuzzy topological space x by means of the family of its level topologies l t t 0 1 introduced in 4 by lowen fuzzy t nets and fuzzy t ultranets are also characterized and relations between t prefilters and fuzzy t nets are studied getting analogous results to those of general topology

the characterizations of h hemiregular hemirings and h intra hemiregular hemirings in this paper the concepts of fuzzy h bi ideals and fuzzy h quasi ideals of a hemiring are introduced and related properties are investigated the notion of h intra hemiregularity of a hemiring which is a generalization of the notion of intra regularity of a ring is provided some characterizations of h hemiregular hemirings h intra hemiregular hemirings and hemirings that are both h hemiregular and h intra hemiregular are derived in terms of fuzzy left fuzzy right h ideals fuzzy h bi ideals and fuzzy h quasi ideals

t prefilter theory abstract in the first part of this paper the notion of t prefilter is introduced and studied as are the applications t and t their properties and relations between them we characterize the minimal prime t prefilters finer than a given t prefilter by using ultrafilters on x and we give equivalents conditions of the t maximality in the second part we define t convergence and we obtain a characterization of t compactness gantner steinlage by means of the maximal t prefilters finally some applications of these concepts related to the continuity separation axioms and fuzzy compactness are studied

the based ring of the lowest two sided cell of an affine weyl group we show that lusztig s homomorphism from an affine hecke algebra to the direct summand of its asymptotic hecke algebra corresponding to the lowest two sided cell is related to the homomorphism constructed by chriss and ginzburg using equivariant k theory by a matrix over the representation ring of the associated algebraic group

fuzzy ideals and semiprime fuzzy ideals in semigroups in this paper we investigate relationships between different definitions of fuzzy ideals of a fuzzy semigroup the equivalence of different definitions of fuzzy ideals of a fuzzy semigroup is obtained we show that the lattice of all f fuzzy ideals of a fuzzy semigroup x is a complete sublattice of the lattice of all fuzzy sets in x when f is an infinitely distributive weak pseudo t norm on l a definition of f semiprime fuzzy ideal of a fuzzy semigroup is given a description of all f semigroups in which every f fuzzy ideal is f semiprime is obtained

a new approach to fuzzy bitopological spaces abstract given a fuzzy bitopological space x 1 2 we have used the operator c12 ix ix defined by c 12 1 cl 2 cl i x which is a supra fuzzy closure operator fuzzy sets and systems 74 1995 353 to generate a family s which is a supra fuzzy topology loc cit 1995 so the space x s is a supra fuzzy topological space associated to the fuzzy bitopological space x 1 2 we extend the notions of fti strong fti and ultra fti due to fuzzy sets and system 43 1991 95 to the space x s the properties of fuzzy bitopological spaces have been studied by using their associated supra fuzzy topological spaces we introduce the notions of fp ti s fp ti and u fp ti by using the level supratopology s of s we investigate the relationship between these notions the notions fp ti loc cit 1995 i 1 2 3 4 and the notions fpti resp s fpti u fpti fuzzy sets and systems 105 1999 459 we give a number of examples which illustrate that these concepts are not equivalent also we extend the notions of f continuous open strong f continuous open and ultra f continuous open due to fuzzy sets and systems 38 1990 115 to the class of supra fuzzy topological spaces associated to the class of fuzzy bitopological spaces we study some properties of fp ti resp s fp ti u fp ti under these mappings

fuzzy radicals and prime fuzzy ideals of ordered semigroups let s be an ordered semigroup a fuzzy subset of s is by definition an arbitrary mapping f s 0 1 where 0 1 is the usual interval of real numbers motivated by studying prime fuzzy ideals in rings semigroups and ordered semigroups and as a continuation of kehayopulu and tsingelis s works in ordered semigroups in terms of fuzzy subsets in this paper we introduce the notion of ordered fuzzy points of an ordered semigroup s and give a characterization of prime fuzzy ideals of an ordered semigroup s we also introduce the concepts of weakly prime fuzzy ideals completely prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of an ordered semigroup s and establish the relationship between the five classes of ideals furthermore we characterize weakly prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of s by their level ideals finally we introduce and investigate the fuzzy radicals of ordered semigroups by means of ordered fuzzy points and prove that the fuzzy radical of every completely semiprime fuzzy ideal of an ordered semigroup s can be expressed as the intersection of all weakly completely prime fuzzy ideals containing it as an application of the results of this paper the corresponding results of semigroups without order are also obtained

fuzzy multiplication semigroup the notion of fuzzy multiplication semigroup is introduced using fuzzy ideal in a fuzzy multiplication semigroup with identity i every fuzzy ideal with sup property whose radical is prime is primary and ii every primary fuzzy ideal with sup property is some power of its fuzzy radical conditions i and ii are also found to be sufficient for a commutative semigroup with identity and satisfying some other conditions to be a fuzzy multiplication semigroup

prime fuzzy ideals in rings abstract in this paper give a characterization of prime fuzzy ideals we introduce weakly completely prime fuzzy ideals and establish a relation between completely prime fuzzy ideals and weakly completely prime fuzzy ideals

homology of the zero set of a nilpotent vector field on a flag manifold 0 1 let x be a linear transformation of a finite dimensional vector space v the configuration of flags in v which are fixed by x has rather remarkable properties when x is unipotent though this case is especially interesting the proper generality in which to study such configurations is in the theory of reductive algebraic groups where their definition can be reformulated in the language of borel subalgebras as follows let g be a connected reductive group over c with lie algebra g and let n e g be a nilpotent element let q be the variety of all borel subalgebras of g and let

fuzzy ideals and fuzzy semiprime ideals some ring theoretic analogues abstract an attempt is made to examine the algebraic nature of fuzzy semiprime ideals under homomorphisms also the fuzzy nil radical of the nth power of a fuzzy prime ideal is studied and a sufficient condition for a fuzzy ideal to be fuzzy maximal is given

characteristic varieties and vanishing cycles on presente une etude systematique des varietes caracteristiques des systemes holonomes a singularites regulieres ce sont des sous varietes lagrangiennes coniques dans le fibre cotangent t x

fuzzy sylow subgroups abstract an attempt is made to define a fuzzy sylow p subgroup of a finite group some basic results regarding sylow p subgroups are extended to the fuzzy setting in particular fuzzy versions of sylow s theorems are obtained

some strong separation in fuzzy topological spaces abstract recently macho stadler et al fuzzy sets and systems 43 1991 95 116 introduced the notion of fuzzy separation using the family of its level topologies lt t t i1 the present work deals with introducing and studying the operations on ri fuzzy topological spaces i 0 1 moreover the notion of fuzzy separation which is well defined as a fuzzy topological concept is described a comparison between the above notions with the analogous fuzzy ones are discussed an acceptable clue which indicates that these notions are equivalent is offered

the embedding of an ordered groupoid into a poe groupoid in terms of fuzzy sets in this paper we prove that if s is an ordered groupoid resp ordered semigroup then the set f of all fuzzy subsets of s is a poe groupoid resp poe semigroup and s is embedded in f a poe groupoid is an ordered groupoid having a greatest element e i e e a a s

strong and ultra separation axioms of fuzzy bitopological spaces given a fuzzy bitopological space x 1 2 we introduce a new notion of fuzzy pairwise separation axioms by using the family of its level bitopologies 1 2 0 1 we prove that these concepts are good extension and we compare them with its corresponding fpt kandil and ei shafee 1991 and fpt1 abu safiya et al 1994 i 0 1 2 3 4 respectively we show that these notions are not equivalent and we give a number of examples which illustrate this fact

regular ordered semigroups in terms of fuzzy subsets given a set s a fuzzy subset of s or a fuzzy set in s is by definition an arbitrary mapping f s 0 1 where 0 1 is the usual interval of real numbers if the set s bears some structure one may distinguish some fuzzy subsets of s in terms of that additional structure this important concept of a fuzzy set was first introduced by zadeh fuzzy groups have been first considered by rosenfeld fuzzy semigroups by kuroki a theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed some results on ordered groupoids semigroups have been already given by the same authors in n kehayopulu m tsingelis fuzzy sets in ordered groupoids semigroup forum 65 2002 128 132 n kehayopulu m tsingelis the embedding of an ordered groupoid into a poe groupoid in terms of fuzzy sets inform sci 152 2003 231 236 n kehayopulu m tsingelis fuzzy bi ideals in ordered semigroups inform sci 171 2004 13 28 where s has been endowed with the structure of an ordered semigroup and defined fuzzy analogous for several notions that have been proved to be useful in the theory of ordered semigroups the characterization of regular rings in terms of right and left ideals is well known the characterization of regular semigroups and regular ordered semigroups in terms of left and right ideals or in terms of left right ideals and quasi ideals is well known as well the characterization of regular le semigroups that is lattice ordered semigroups having a greatest element in terms of right ideal elements and left ideal elements or right left and quasi ideal elements is also known in the present paper we first give the main theorem which characterizes the regular ordered semigroups by means of fuzzy right and fuzzy left ideals then we characterize the regular ordered semigroups in terms of fuzzy right fuzzy left ideals and fuzzy quasi ideals the paper serves as an example to show that one can pass from the theory of ordered semigroups to the theory of fuzzy ordered semigroups some of our results are true for ordered groupoids in general

fuzzy bi ideals in ordered semigroups given a set s a fuzzy subset of s is by definition an arbitrary mapping f s 0 1 where 0 1 is the unit segment of the real line if the set s bears some structure one may distinguish some fuzzy subsets of s in terms of that additional structure this important concept was first introduced by zadeh fuzzy groups have been first considered by rosenfelt fuzzy semigroups by kuroki a theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed in the present paper we endow s with the structure of an ordered semigroup and define fuzzy analogous for several notions that have been proved to be useful in the theory of ordered semigroups we define the fuzzy bi ideals in ordered semigroups and we give the main theorem which characterizes the bi ideals in terms of fuzzy bi ideals then we characterize the left and right simple the completely regular and the strongly regular ordered semigroups by means of fuzzy bi ideals we also study the decomposition of left and right simple ordered semigroups and of ordered semigroups having the property a a2 for all a in terms of fuzzy bi ideals this decomposition is uniquely defined

fuzzy nil radicals and fuzzy primary ideals abstract the purpose of this paper is to extend the concept of a fuzzy set by introducing the concept of a fuzzy nil radical of a fuzzy ideal in a ring using this concept a fuzzy primary ideal is defined some fundamental results concerning these notions are proved

fuzzy subgroups fuzzy ideals and fuzzy cosets some properties abstract as an application of fuzzy subgroups a necessary and sufficient condition for a p group to be cyclic is obtained a procedure to construct the fuzzy subgroup generated by a fuzzy subset of a group is provided also the effect of a homomorphism on the sum product intersection of two fuzzy ideals is studied some elementary properties of the ring fuzzy cosets of a fuzzy ideal are also obtained

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

rough ideals under relations associated to fuzzy ideals in this paper we deal with the theory of rough ideals started in davvaz 2004 we show that the approximation spaces built from an equivalence relation compatible with the ring structure i e associated to a two sided ideal are too naive in order to develop practical applications we propose the use of certain crisp equivalence relations obtained from fuzzy ideals these relations make available more flexible approximation spaces since they are enriched with a wider class of rough ideals furthermore these are fully compatible with the notion of primeness semiprimeness the theory is illustrated by several examples of interest in engineering and mathematics

fuzzy ideals and fuzzy bi ideals in fuzzy semigroups abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra such as fuzzy left right ideal and fuzzy bi ideal in fuzzy semigroup through the new approach of fuzzy space and fuzzy group introduced by dib 1994 our notion of fuzzy ideal and fuzzy bi ideal includes the classical concepts of fuzzy ideal and fuzzy bi ideal of ordinary semigroup many counterexamples are also given

fuzzy normal subgroups and fuzzy quotients abstract in case of groups a mormal subgroup n of a group g can be defined with three equivalent approaches namely i as a kernel of some group homomorphism ii as a subgroup commuting with every element of g and iii as the subgroup n closed with respect to conjugates of elements of n in case of generalizations of this concept to fuzzy sets the elementwise third approach is found more suitable and hence is widely adopted by many authors in this paper we further study this concept of fuzzy subgroups and introduce fuzzy quotients called fuzzy quotient groups for all 0 1 two different definitions of these fuzzy quotients have been given which are shown to lead to isomorphic structures we also study the direct products of fuzzy normal subgroups min product as per the terminology of sherwood 1983 and the problem of writing a fuzzy normal subgroups of a direct product of some groups as a direct product of certain fuzzy normal subgroups has been discussed in detail

characterizations of ordered semigroups by the properties of their fuzzy ideals in this paper we characterize different classes of ordered semigroups by the properties of their ideals quasi ideals and bi ideals we also characterize these classes by the properties of their fuzzy ideals fuzzy quasi ideals and fuzzy bi ideals

rings with chain conditions abstract the aim of this paper is to find out some new results about fuzzy ideals to characterise artinian rings and noetherian rings by fuzzy ideals and to give alternative proofs of some well known results of artinian and noetherian rings by fuzzy ideal theoretic techniques

fuzzy ideals generated by fuzzy sets in semigroups abstract in this paper the definition of a fuzzy left right udeal a fuzzy ideal a fuzzy bi ideal a fuzzy interior ideal generated by a fuzzy set in semigroups is given the depictions of them are then examined

fuzzy ideals and fuzzy prime ideals of a ring abstract besides obtaining certain ring theoretic analogues some peculiarities of the fuzzy setting are also discussed in particular a study of i the conditions under which a given fuzzy ideal can or cannot be expressed as a union of two proper fuzzy ideals ii the algebraic nature of images and preimages of fuzzy prime ideals under homomorphisms and iii the ring of all the fuzzy cosets of a fuzzy prime fuzzy maximal ideal is carried out

a metatheorem for deriving fuzzy theorems from crisp versions a metatheorem is developed that allows theorems containing references to crisp substructures to be reformulated to refer to fuzzy substructures theorems concerning fuzzy substructures in semigroups rings and lattices are derived in concise fashion from analogous theorems that concern crisp substructures the modularity of the lattice of fuzzy normal subgroups of a group is concisely derived from the modularity of its lattice of crisp normal subgroups the fundamental tool used is a function that represents the algebra of fuzzy subsets of a set as a subdirect product of copies of the algebra of crisp subsets

fuzzy regular subsemigroups in semigroups abstract in this paper we define the fuzzy regular subsemigroups and fuzzy left right intra regular subsemigroup in semigroups also some properties of them are studied

lagrangian construction for representations of hecke algebras 1 let k be a non archimedean local field with the residue field consisting of q elements according to langlands philosophy irreducible complex representations of a reductive k group g should roughly speaking correspond to homomorphisms of the weil deligne group into the socalled l group let zc g be the iwahori subgroup the category of admissible gkmodules generated by z fixed vectors is known to be equivalent to the category of finite dimensional representations of the hecke algebra h z g z langlands philosophy suggests via that equivalence the following classification of irreducible hecke algebra modules stated in purely complex terms and not involving any local held

fuzzy ideals and congruences of lattices general theory of algebraic fuzzy systems developed earlier by the authors is applied to extend the stone s prime ideal theorem to fuzzy ideals of distributive lattices a correspondence between fuzzy ideals and fuzzy congruences in a distributive lattice is obtained and certain important properties of these are discussed

fuzzy ideals in semigroups abstract the set of all fuzzy ideals of a semigroup is shown to be a convex set having the crisp ideals as extreme points some connections between fuzzy ideals and green s relations are discussed

on pointwise depiction of fuzzy regularity of semigroups abstract in this paper we introduce the notion of a fuzzy regular point and we give a pointwise depiction of fuzzy regularity meanwhile we show an error in j z shen s paper by a counterexample and simplify some proofs of shen finally we propose the concept of a fuzzy weakly left right intra regular subsemigroup and research some of their algebraic properties

generalised filters 1 we continue the study started in 8 of generalised filters prime prefilters have played a central role in the theory of lowen fuzzy uniform spaces and lowen discovered a characterisation of the set of all minimal prime prefilters finer than a given prefilter in terms of ultrafilters we define the notion of a prime generalised filter and describe the set of all minimal prime g filters finer than a given g filter in terms of ultrafilters the relationship between prime prefilters and prime g filters is revealed the behaviour of the images and preimages of g filters are investigated

on fuzzy ideals and fuzzy bi ideals in semigroups abstract in this paper we give some properties of fuzzy ideals and fuzzy bi ideals of semigroups and characterize semigroups that are left duo left simple and semilattices of subsemigroups in terms of fuzzy ideals and fuzzy bi ideals

fuzzy semiprimary ideals of rings abstract the concept of fuzzy ideals is extended by introducing fuzzy semiprimary ideals in rings this class of fuzzy ideals generalizes the class of fuzzy semiprimary ideals it is shown that there do exist fuzzy ideals which are fuzzy semiprimary but not fuzzy primary a study of i the level ideals of a fuzzy semiprimary ideal ii the characteristic function of a semiprimary ideal iii the zero divisors in the ring of all fuzzy cosets of a fuzzy semiprimary ideal and iv the algebraic nature of direct and inverse images of fuzzy semiprimary ideals under homomorphisms is carried out

on fuzzy regular subsemigroups of a semigroup abstract since a rosenfeld proposed the concept of fuzzy subgroup in 1971 there has been considerable development of fuzzy algebra in particular n kuraki discussed fuzzy biideals and the fuzzy semiprime ideal of a semigroup we introduce the concepts of fuzzy regular subsemigroups fuzzy weakly regular subsemigroups fuzzy completely regular subsemigroups and fuzzy weakly completely regular subsemigroups and investigate some of their algebraic properties

strong separation and strong countability in fuzzy topological spaces given a fuzzy topological space x we introduce new notions of fuzzy separation and fuzzy countability using the family of its level topologies t t 0 1 we check that these are well defined fuzzy topological concepts and we compare them with the analogous fuzzy ones introduced in the literature we verify that these notions are not equivalent and we give a large number of examples which illustrate this fact

fuzzy irreducible ideals in rings abstract in this paper the concept of a fuzzy set is extended by introducing the concept of a fuzzy irreducible ideal in a ring the characteristic function of an irreducible ideal and the level ideals of a fuzzy irreducible ideal are studied the algebraic nature of homomorphic images and preimages of fuzzy irreducible ideals is also examined some other fundamental results pertaining to this concept are discussed

fuzzy regular and inverse subsemigroups abstract regular and inverse a b e a e a v q a b fuzzy subsemigroups are defined the concept of fuzzy analogue of normal subsemigroup is introduced using a type of fuzzy congruence relation a fuzzy quotient subgroup of a fuzzy inverse subsemigroup is constructed some results concerning the interrelationship between fuzzy analogues of unitary subsemigroup inverse subsemigroup and closed subsemigroup of an inverse semigroup are obtained

level subgroups and union of fuzzy subgroups abstract in this paper we investigate the conditions under which a given fuzzy subgroup of a given group can or can not be realized as a union of two proper fuzzy subgroups moreover we formulate the notion of fuzzy subgroup generated by a given fuzzy subset by level subgroups we also give characterizations of fuzzy conjugate subgroups and fuzzy characteristic subgroups by their level subgroups also we discuss the relationship between level subgroups of a given fuzzy subgroup and the level subgroups of its homomorphic image

fuzzy prime spectrum of a ring ii abstract various topological properties of the fuzzy prime spectrum of a ring and certain of its subspaces as well as its functorial nature are discussed

nil radical of fuzzy ideal abstract the concepts of nil radical of a fuzzy ideal and primary fuzzy ideal are introduced and some fundamental propositions proved in particular a structural theorem for a primary fuzzy ideal and the associated prime fuzzy ideal

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

the relationship between various filter notions on agl monoid abstract the notion of a generalised filter is extended to the setting of a gl monoid it is shown that there exists a one to one correspondence between the collection of generalised filters on a set x and the collection of strongly stratified l filters on x specialising to the case where l is the closed unit interval 0 c viewed as a heyting algebra we show that any strongly stratified 0 c filter on x can be uniquely identified with a saturated filter on i x with characteristic value c in this way the notion of a generalised filter unifies various filter notions in particular necessity measures and finitely additive probability measures are specific examples of generalised filters

fuzzy semiprime ideals in semigroups abstract in this paper we shall introduce the notion of fuzzy semiprimality in a semigroup which is an extension of semiprimality in it and characterize a semigroup that is a semilattice of simple semigroups in terms of fuzzy semiprimality

fuzzy nil radicals and fuzzy semiprimary ideals of rings abstract an attempt is made to define a fuzzy semiprimary ideal by using the idea of the fuzzy nil radical of a fuzzy ideal the level ideals of a such a fuzzy ideal are examined and the ring of fuzzy cosets of such a fuzzy ideal is studied the algebraic nature of such fuzzy ideals under homomorphisms is also ascertained

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

on fuzzy right topological semigroups on etend des resultats de foster sur les images homomorphes et les images inverses aux semigroupes topologiques a droite flous

on fuzzy semigroups abstract we give some propertes of fuzzy ideals and fuzzy biideals of a semigroup and characterize a regular semigroup a semigroup that is a semilattice of left right simple semigroups a semigroup that is a semilattice of left right groups and a semigroup that is a semilattice of groups in terms of fuzzy left right and two sided ideals and biideals

on fuzzy rings abstract an internal description of the fuzzy subring fuzzy ideal generated by a finite fuzzy subset of a ring is provided also a fuzzy coset of a fuzzy ideal is defined and the set of all fuzzy cosets of a fuzzy ideal is given a ring structure a fuzzy semiprime ideal is also defined and some basic properties of this fuzzy ideal are studied

prime fuzzy ideals over noncommutative rings in this paper we introduce prime fuzzy ideals over a noncommutative ring this notion of primeness is equivalent to level cuts being crisp prime ideals it also generalizes the one provided by kumbhojkar and bapat in 1993 which lacks this equivalence in a noncommutative setting semiprime fuzzy ideals over a noncommutative ring are also defined and characterized as intersection of primes this allows us to introduce the fuzzy prime radical and contribute to establish the basis of a fuzzy noncommutative ring theory

a short note on fuzzy neighbourhood spaces abstract lowen introduced the concept of fuzzy neighbourhood spaces fns s and proved that the family of level topologies of a fns is an antichain wuyts characterized fns s as being those fully stratified fuzzy topological spaces fts s whose level topologies form antichains and whose fuzzy topologies are the finest possible for thier level topologies mashhour et al introduced the axiom of structure a on fts s and derived for it several characterizations and fuzzy topological consequences we use those characterizations of structure a and wuyts characterization of fns s to prove that a fts is a fns iff it is of structure a and fully stratified

uniform type structures on lattice valued spaces and frames by introducing lattice valued covers of a set we present a general framework for uniform structures on very general l valued spaces for l an integral commutative quantale by showing via an intermediate l valued structure of uniformity how filters of covers may describe the uniform operators of hutton we prove that when restricted to girard quantales this general framework captures a significant class of hutton s uniform spaces the categories of l valued uniform spaces and l valued uniform frames here introduced provide in the case l is a complete chain the missing vertices in the commutative cube formed by the classical categories of topological and uniform spaces and their corresponding pointfree counterparts forming the base of the cube and the corresponding l valued categories forming the top of the cube

on fuzzy bitopological spaces abstract in this paper we have used the fuzzy topologies 1 and 2 to generate a family s which is a supra fuzzy topology on x using the family s we introduce and study the concepts of separation axioms continuity resp openness closedness of a mapping and compactness for a fuzzy bitopological space x 1 2 our definitions preserve much of the correspondence between concepts of fuzzy bitopological spaces and the associated fuzzy topological spaces we then investigate the relationship between these concepts and their correspondence with the fuzzy bitopological spaces kandil and el shafee 1991

on n convergence of fuzzy nets abstract in this paper we define the n convergence of fuzzy nets in a fuzzy topological space and we use it to give a characterization of some fuzzy topological concepts we give necessary conditions for the n convergence of fuzzy nets in a fuzzy topological space and we characterize this n convergence in a topologically generated fuzzy topological space we also study some characterizations of fuzzy ultranets and we introduce the concept of subordination between fuzzy nets we associate to each fuzzy net in x a prefilter on x and conversely and we give an exhaustive description of the connections between these two theories we give a theory of fuzzy convergence classes and we characterize fuzzy topologies via some special types of fuzzy convergence classes

fuzzy vector spaces and fuzzy cosets abstract a fuzzy subspace is characterized by its level subspaces the algebraic nature of fuzzy subspaces under homomorphisms is studied certain conditions are obtained under which a given fuzzy subspace can or cannot be realized as a union of two fuzzy subspaces such that none is contained in the other the construction of a fuzzy subspace generated by a given fuzzy subset of a vector space is given the set of all the fuzzy cosets of a fuzzy subspace is shown to be a vector space and the dimension of the same is obtained a fuzzy quotient space is defined and an analogue of a consequence of the fundamental theorem of homomorphisms is obtained

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

fuzzy rees congruences on semigroups fuzzy congruences on semigroups and groups have been introduced and studied by samhan 1993 and samhan and ahsanullah 1994 among others here we introduce fuzzy rees congruences on semigroups and fuzzy rees congruences semigroups using these ideas we establish a relation between fuzzy ideals of a semigroup s and fuzzy ideals of a quotient semigroup of s as an important result we prove that the lattice of all fuzzy congruences on a fuzzy congruences semigroup is a distributive lattice moreover we obtain that a homomorphic image of a fuzzy rees congruences semigroup is a fuzzy rees congruences semigroup as well

strong and ultra separation axioms on l fuzzy topological spaces given an l fuzzy topological space x d we introduce new notions of l fuzzy separation axioms using the family of its level topology i a d a pr l we check that these are well defined l fuzzy topological concepts and we compare them with the analogous l fuzzy ones introduced in the literature we verify that these notations are not equivalent and we give many examples which illustrate this fact furthermore some results concerning the new concepts have been established

generalized fuzzy interior ideals in semigroups using the idea of quasi coincidence of a fuzzy point with a fuzzy set the concept of an a b fuzzy interior ideal which is a generalization of a fuzzy interior ideal in a semigroup is introduced and related properties are investigated

closure systems and l subalgebras abstract let x be a set and l a class of l subsets of x l is a closure system if it is closed with respect to greatest lower bounds if is an l subset then the g l b tf of g l g is said to be generated by we examine closure systems of l subalgebras and propose formulas for the l subalgebra of a required type generated by a given l subset

on prime quasi prime weakly quasi prime fuzzy left ideals of semigroups in this paper we introduce and study the prime quasi prime and weakly quasi prime fuzzy left ideals of a semigroup s we give characterizations of the largest fuzzy ideal i f contained in a fuzzy left ideal f of a semigroup s and the largest fuzzy subsemigroup i f such that f is a fuzzy ideal of i f finally strongly semisimple semigroups are characterized by quasi prime fuzzy left ideals

fuzzy generalized bi ideals in semigroups abstract we introduce the concept of a fuzzy generalized bi ideal of a semigroup which is an extension of the concept of a fuzzy bi ideal and of a nonfuzzy bi ideal and a nonfuzzy ideal of a semigroup and characterize regular semigroups and both intraregular and left quasiregular semigroups in terms of fuzzy generalized bi ideals

fuzzy semiprime quasi ideals in semigroups abstract we give some properties of fuzzy quasi ideals of a semigroup and characterize a completely regular semigroup and a semigroup that is a semilattice of groups in terms of fuzzy semiprime quasi ideals