some kinds of view the fuzzy filters of bl algebras the concepts of view the mathml source fuzzy implicative positive implicative and fantastic filters of bl algebras are introduced and some related properties are investigated some characterizations of these generalized fuzzy filters are derived in particular we describe the relationships among ordinary fuzzy implicative positive implicative and fantastic filters view the mathml source fuzzy implicative positive implicative and fantastic filters and view the mathml source fuzzy implicative positive implicative and fantastic filters of bl algebras finally we prove that a fuzzy set f of a bl algebra l is an view the mathml source fuzzy implicative filter of l if and only if it is both an view the mathml source fuzzy positive implicative filter and an view the mathml source fuzzy fantastic filter

approximations in hypergroups and fuzzy hypergroups the first part of this paper represents a continuation of the study of approximations in a hypergroup we analyse the lower and upper approximations of a subset in a hypergroup with respect to some operators particularly the completeness operator in the last part we introduce and analyse the lower and upper approximation of a subset in a fuzzy hypergroup

fuzzy groups some group theoretic analogs abstract we introduce the concepts of 1 order of a fuzzy subgroup of a finite group 2 a fuzzy abelian group and 3 a fuzzy solvable group we obtain some results involving these notions which are analogs of results from group theory also we prove analogs of two basic theorems of group theory namely cayley s theorem and lagrange s theorem

reduced forms and reduced witt rings of higher level the present paper and its successor s deal with an extension of the socalled reduced theory of quadratic forms over a formally real field k 5 7 lo this theory deals with the reduced witt ring wred k w k nil w k and its natural embedding into c x z the ring of integer valued continuous functions on the space x x k of orderings of k recently it has been found that there is a far reaching generalization of the notion of ordering namely the orderings of higher level 11 the orderings of level s where s divides a given natural number n are related to sums of 2nth powers in the same way as the usual orderings are to sums of squares their intersection is the set of all sums of 2nth powers in k 11 in 6 orderings of levels were replaced by signatures of this level these are those characters x i s of order 2s whose kernels are additively closed where k k o it is exactly this change in point of view which leads to a natural definition of reduced witt rings of higher level let x x k denote the set of all signatures of k whose order divides 2n so that x k x k x being a closed subspace of the compact character group of x the set x k is also a compact topological space each element a e i induces a continuous function a x c in c x c defined by x x a where c is given the discrete topology by analogy with the natural representation of the ordinary reduced witt ring as a subring of 477 0021 8693 85 3 00

fuzzy normal subgroups and fuzzy cosets abstract we introduce here the notion of 1 i a fuzzy normal subgroup and 2 ii a fuzzy coset we prove that for a group g a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of g further we show that the level subgroups of a fuzzy normal subgroup are all normal we obtain several results which are analogs of some basic theorems of group theory in particular a fuzzy version of lagrange s theorem is established

fuzzy h v ideals in γ h v rings in this paper by means of a kind of new idea we consider the q fuzzy h v ideals of a c h v ring the concept of c h v rings which is a generalization of c rings and h v rings is introduced the notion of q fuzzy h v ideals of a c h v ring is provided and some related properties are investigated the concept of implication based fuzzy h v ideals of a c h v ring is studied in particular the implication operators in the lukasiewicz system of continuous valued logic are discussed finally the homomorphism of q fuzzy h v ideals of a c h v ring is explored

e e v q fuzzy normal quasinormal and maximal subgroups abstract the notions of and q fuzzy normality and quasinormality for a q fuzzy subgroup are introduced the notions of an q fuzzy core subgroup and an q fuzzy p sylow subgroup are also introduced and some fundamental properties are dealt with q fuzzy normality and q fuzzy quasinormality are found to be more generalised concepts than those introduced by others a detailed study with a fuzzy maximal subgroup is incorporated with the limitation of this concept

fuzzy h v groups in this paper we introduce the concept of fuzzy subhypergroup of a hypergroup as well as the fuzzy hv group we prove some results in this respect we also consider the fundamental relation defined on an hv group h and for a fuzzy subset of h we define the fuzzy subset of h and prove a fundamental theorem concerning the group h

rosenfeld s fuzzy subgroups with interval valued membership functions abstract in this paper we define interval valued fuzzy subgroups i e i v fuzzy subgroups of rosenfeld s nature a necessary and sufficient condition for an i v fuzzy subset to be an i v fuzzy subgroup is stated intersection of two i v fuzzy subgroups is also an i v fuzzy subgroup the images and inverse images of i v fuzzy subgroups are defined and how the images or inverse images of i v fuzzy subgroups become i v fuzzy subgroups is studied

fuzzy hypervector spaces based on fuzzy singletons we introduce and study fuzzy hypervector spaces based on fuzzy singletons in this regard by considering the notion of fuzzy singletons we characterize a fuzzy hypervector space fuzzily spanned by a fuzzy subset then we use these results to introduce the concept of fuzzy freeness of a fuzzy subset m of a hypervector space v and finally we characterize it in terms of linear independence in the usual sense

a new view of fuzzy hypernear rings in this survey article we first introduce the concept of quasi coincidence of a fuzzy interval value with an interval valued fuzzy set this concept is a generalized concept of quasi coincidence of a fuzzy point within a fuzzy set by using this new idea we consider the interval valued q fuzzy sub hypernear rings hyperideals of a hypernear ring and hence a generalization of a fuzzy sub near ring ideal is given some related properties of fuzzy hypernear rings are described finally we consider the concept of implication based interval valued fuzzy sub hypernear rings hyperideals in a hypernear ring in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

generalizations of fuzzy subalgebras in bck bci algebras more general form of the notion of quasi coincidence of a fuzzy point with a fuzzy set is considered and generalizations of results in the papers y b jun on a b fuzzy subalgebras of bck bci algebras bull korean math soc 42 4 2005 703 711 y b jun fuzzy subalgebras of type a b in bck bci algebras kyungpook math j 47 2007 403 410 are discussed the notions of q k fuzzy subalgebras and email protected q k fuzzy subalgebras in a bck bci algebra x are introduced and several properties are investigated characterizations of email protected q k fuzzy subalgebra in a bck bci algebra x are discussed

some types of generalized fuzzy filters of bl algebras the aim of this paper is to introduce the notions of interval valued q fuzzy boolean implicative positive implicative and fantastic filters in bl algebras and to investigate some related properties some characterizations of these generalized fuzzy filters are derived finally the relations among these generalized fuzzy filters are discussed it is proved that an interval valued q fuzzy filter in bl algebras is an interval valued q fuzzy boolean implicative filter if and only if it is both an interval valued q fuzzy positive implicative filter and an interval valued q fuzzy fantastic filter

a parametrix for the neumann problem on pseudoconvex domains of finite type abstract we construct a parametrix for the neumann problem on any pseudoconvex domain of finite type which reduces completely the study of isotropic lp sobolev and holder estimates to those for b and b we also establish the maximal nonisotropic estimates in the case of d q domains and provide a precise comparison of the bergman and szego projections and of the canonical solutions to with respect to these two operators the argument is substantially simpler than the known ones for the cases of strongly pseudoconvex domains and pseudoconvex domains of finite type in c 2

generalized fuzzy h bi ideals and h quasi ideals of hemirings a new kind of generalized fuzzy h ideals of a hemiring namely the set membership variant set membership variantlogical orq fuzzy h bi ideal resp h quasi ideal is studied and the relationships between these generalized fuzzy h ideals are described some characterization theorems of prime and semiprime set membership variant set membership variantlogical orq fuzzy h bi ideals resp h quasi ideals of a hemiring are also given in particular we show that the h hemiregular hemirings and h intra hemiregular hemirings can be described by using some of their generalized fuzzy h ideals finally the implication based fuzzy h bi ideals resp h quasi ideals of a hemiring are considered

fuzzy hyperrings hv rings based on fuzzy universal sets the aim of this paper is to define and study the concept of a fuzzy hyperring which depends on the concept of a fuzzy universal set a correspondence relation between a fuzzy hyperring based on a fuzzy universal set and both ordinary and fuzzy hyperideal in the sense of davvaz is obtained

the szegő projection sobolev estimates in regular domains the szego projection preserves global smoothness in weakly pseudoconvex domains that are regular in the sense of diederich fornxess and catlin it preserves local smoothness near boundary points of finite type the bergman projection being linked to the 8 problem plays an important role in several complex variables as demonstrated by recent applications to the boundary behavior of holomorphic maps 7 16 the szego projection is interesting both by analogy and by its connection with the ab problem and hence with unsolvable equations of lewy type while in strictly pseudoconvex domains the bergman and szego projections are both well understood in general much more is known about the bergman projection this is no surprise for the theory of the 8 problem is further advanced than the theory of the 8b problem nonetheless i believe that the szego projection ought not be any more mysterious than the bergman projection this paper is intended to support this contention the most important domains for which the bergman projection is known to be regular are domains with a good a neumann operator here it is shown that in such domains the szego projection also is regular more precisely in smooth bounded pseudoconvex domains satisfying catlin s property p the most general condition presently known that guarantees global regularity of the neumann operator the szego projection is shown to be globally regular theorem 4 1 moreover at boundary points of finite type the szego projection is locally regular theorem 5 1 in both cases the szego projection exactly preserves the degree of differentiability measured in sobolev norms the method of proof is not the obvious one of directly generalizing from the strictly peudoconvex case for there are serious obstacles to such a generalization for instance the approach of analysis on the heisenberg group used by phong and stein 29 to derive estimates for both the bergman and szego projections cannot yet be extended because the theory of singular integrals on weakly pseudoconvex surfaces is still in its early stages 28 15 similarly one does not know how to carry over the fourier integral operator approach of boutet de monvel and sjostrand 10 to the weakly pseudoconvex case explicit construction of cauchy fantappie forms received by the editors march 11 1986 paper presented april 11 1986 to the 826th meeting of the american mathematical society indianapolis special session on several complex variables 1980 mathematics subject classification 1985 revision primary 32a25 32h10 partially supported by national science foundation grants mcs 8201063 and dms 8501758 1987 american mathematical society 0002 9947 87 1 00 25 per page

characterizations of hemirings by νq k fuzzy ideals in this paper we define q k fuzzy h sub hemirings q k fuzzy h bi ideals q k fuzzy h quasi ideals we characterize h hemiregular and h intra hemiregular hemirings by the properties of their q k fuzzy h ideals q k fuzzy h bi idealsand q k fuzzy h quasi ideals some of these characterizations are generalizations of the characterizations given in 36 x ma j zhan generalized fuzzyh bi ideals and h quasi ideals of hemirings inform sci 179 2009 1249 1268

fuzzy subrings and ideals redefined abstract v q fuzzy subrings and ideals of a ring are defined the concepts of v q fuzzy semiprime prime semi primary primary and maximal ideals are introduced and characterization of such fuzzy ideals are obtained v q fuzzy cosets determined by v q fuzzy ideals and v q fuzzy radicals of v q fuzzy ideals are discussed

fuzzy krasner m n hyperrings recently krasner m n hyperrings were introduced and analyzed by mirvakili and davvaz krasner m n hyperrings are a suitable generalization of krasner hyperrings this paper concerns a relationship between fuzzy sets and hyperstructure theory it is a continuation of the ideas presented by davvaz et al 2009 b davvaz p corsini v leoreanu fotea fuzzy n ary subpolygroups computers mathematics with applications 57 2009 141 152 the aim of the paper is to introduce the notion of a fuzzy hyperideal of a krasner m n hyperring and to extend the fuzzy results to krasner m n hyperrings

redefined fuzzy hv submodules and many valued implications this paper considers a relationship between fuzzy sets and algebraic hyperstructures a generalization of ideas presented by davvaz b davvaz fuzzy h v submodules fuzzy sets syst 117 2001 477 484 and bhakat and das s k bhakat p das email protected q fuzzy subgroup fuzzy sets syst 80 1996 359 368 is presented in fact the main purpose of this paper is to introduce and study a new sort of fuzzy h v submodule of an h v module called email protected q fuzzy h v submodules these fuzzy h v submodules are characterized by their level h v submodules the concept of a fuzzy h v submodule with thresholds is introduced and some interesting properties are investigated

new types of fuzzy ideals in bck bci algebras a generalization of an email protected q fuzzy ideal of a bck bci algebra is discussed characterizations of an email protected q k fuzzy ideal and an email protected email protected email protected q email protected fuzzy ideal are provided conditions for an email protected q k fuzzy ideal resp email protected email protected email protected q email protected fuzzy ideal to be a fuzzy ideal are provided using the notion of a fuzzy ideal with thresholds characterizations of a fuzzy ideal an email protected q k fuzzy ideal and an email protected email protected email protected q email protected fuzzy ideal are discussed

n real valuations and the higher level version of the krull baer theorem abstract in comm algebra 29 2001 193 201 cimpric gave examples of division rings containing an ordering of level 2m but not of level m for m n his examples were quite complicated we give substantially simplified examples in section 2 in sections 3 and 4 we investigate this phenomenon using valuation theory we define almost real and n real valuations and study liftings of orderings from the residue division ring to the original division ring such liftings are not always possible as is the case in the commutative setting but we give a necessary and sufficient condition for a lifting to exist we also prove a suitable generalization of the baer krull theorem finally in the last section we use our examples and the theory developed to answer a question given by marshall and zhang j algebra 212 1 1999 190 207

α β fuzzy ideals of hemirings we give a characterization of different types of a b fuzzy ideals of hemirings where a b q q q and a q special attention is paid to q fuzzy prime and semiprime ideals

estimates for the bergman and szego kernels in mathbf c 2 the purpose of this paper some of whose conclusions were announced in nrsw is to study the bergman and szegd projection operators on pseudoconvex domains q of finite type in c2 the results we obtain are of three kinds i the size estimates of the bergman and szeg6 kernels and their derivatives ii the cancellation properties of those kernels expressed in terms of the actions of these operators on suitable bump functions these properties have an interest in their own right but are also crucial in iii below iii the sharp mapping properties of these operators on functions spaces such as lp the nonisotropic sobolev spaces and the nonisotropic lipschitz spaces which are naturally attached to the geometry of the boundary this also leads ultimately to sharp results in the regularity properties of solutions of the equation du f in q and 9bu f on the boundary let us describe these matters in more detail our starting points are certain basic geometric constructs associated to q a metric p defined in terms of the vector fields x1 and x2 which are the real and imaginary parts of the tangential levi vector field on d 2 and a function a p 8 a polynomial in 8 for p e d 2 which represents the higher levi invariant attached to d 9 the significance of these to the geometry of d q can be understood from the following facts the ball b p 8 c d q centered at p of radius 8 in the metric p when viewed in the appropriate coordinates has width 8 in the complex tangential directions but its width is a p 8 in the complementary direction thus the volume of the ball is 82a p 8 among other crucial properties

semigroups characterized by c c νqk fuzzy ideals generalizing the notions of q fuzzy ideal q fuzzy quasi ideal and q fuzzy bi ideal the concepts of q k fuzzy ideal q k fuzzy quasi ideal and q k fuzzy bi ideal are defined different classes of semigroups are characterized by the properties of these fuzzy ideals

generalized fuzzy hyperideals of hyperrings the concept of quasi coincidence of a fuzzy interval value with an interval valued fuzzy set is considered in fact this is a generalized concept of the quasi coincidence of a fuzzy point with a fuzzy set by using this new idea the notion of interval valued a b fuzzy hyperideals in a hyperring is introduced and consequently a generalization of a fuzzy hyperideal is defined in this paper we study the related properties of the fuzzy hyperideals and in particular the interval valued q fuzzy hyperideals in a hyperring will be investigated moreover we also consider the concept of implication based interval valued fuzzy hyperideals in a hyperring some recent results obtained by b davvaz and j m zhan on hyperstructures are extended and consolidated

chain signatures and higher level witt rings in many respects becker s theory of orderings of higher level is very much reminiscent of the familiar artin schreier theory of ordered fields a few examples of similarities are fields with higher level orderings have real closures 1 3 orderings of higher level can be used to study sums of powers in fields 3 41 there is a theory of witt rings for fields with higher level preorderings 7 81 however among all these similarities one very obvious difference stands out a field with a higher level ordering has nonisomorphic real closures becker showed that in order to describe the isomorphism classes of real closures a whole sequence of higher level orderings is required 1 p 162 theorem 121 subsequently this has been relined and reformulated through the introduction of chains of higher level orderings 121 and chain signatures 27 see alo 10 11 i in view of this situation one should expect that if results from the usual theory of ordered fields level 1 carry over to the case of orderings of higher level then quite different results will also be brought in by the chains of higher level orderings the purpose of this paper is to look for such results in the theory of higher level witt rings developed recently by becker and rosenberg 7 81 to keep things from getting too complicated this will be done only for the case where all levels are powers of 2 thus throughout the term higher level will be synonymous with level 2 for some n iv w k denotes the witt ring of the field k with respect to the higher level preordering k c k2 nonzero sums of 2 th powers of 9 just as the use of signatures s leads to homomorphisms w 7 chain signatures lead to homomorphisms

on the definition of a fuzzy subgroup abstract using the idea of quasi coincidence of a fuzzy point with a fuzzy set some new concepts of a fuzzy subgroup are introduced and their acceptibility is investigated some fundamental properties of one such viable fuzzy subgroup are obtained

comparing the bergman and szego projections on domains with subelliptic boundary laplacian we prove that the difference between the bergman and szego projections on a bounded pseudoconvex domain with c boundary is smoothing whenever the boundary laplacian is subelliptic an equivalent statement is that the bergman projection can be represented as a composition of the szego and harmonic bergman projections along with the restriction and poisson extension operators modulo an error that is smoothing we give several applications to the study of optimal mapping properties for these projections and their difference

holomorphy rings and higher level orders on skew fields the intimate connections which exist between higher level orders sums of 2n th powers valuation theory and real valued places on a field have been explored extensively craven initiated the study of similar notions for skew fields in 4 in 12 we pursued these ideas but the best results required a 2 primary assumption this paper extends the work of 12 in particular we prove an artin schreier theorem for preordered skew fields namely that a preorder t in a skew field is the intersection of the kernels of all the signatures that contain t this allows us to obtain the results of 12 without the 2 primary assumption in particular we have that preordered skew fields give rise to spaces of signatures mulcahy s abstract setting for the theory of higher level forms and reduced witt rings our main tools are valuation theory and the kadison dubois representation theorem for partially ordered rings as in the field case we make use of the ring a associated to a preorder t which is the intersection of certain valuation rings along the way to our main theorem we prove some facts about noncommutative priifer rings and we show that a is a priifer ring while our study of preordered skew fields follows along lines which are familiar from the field context there are significant differences between the two theories for example there are skew fields which have no orders but admit valuation rings with ordered residue fields

generalized fuzzy groups and many valued implications in this paper we give the definition of a fuzzy subgroup with thresholds which is a generalization of rosenfeld s fuzzy subgroup and bhakat and das s fuzzy subgroup we also give the definition of an implication based fuzzy subgroup and discuss relations between two fuzzy subgroups

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

some kinds of c ccq interval valued fuzzy ideals of bci algebras in this paper we first introduce the notions of positive implicative implicative and commutative interval valued fuzzy ideals of bci algebras which are generalizations of positive implicative implicative and commutative fuzzy ideals respectively and investigate some of their related properties the concept of quasi coincidence of an interval valued fuzzy point within an interval valued fuzzy set is introduced in fact the concept is a generalized concept of quasi coincidence of a fuzzy point within a fuzzy set by using this new idea we further introduce the notions of positive implicative implicative and commutative q interval valued fuzzy ideals of bci algebras and investigate some of their related properties some characterization theorems of these generalized interval valued fuzzy ideals are derived the relationship among these generalized interval valued fuzzy ideals of bci algebras is also considered

characterizations of regular semigroups by α β fuzzy ideals using the ideas of belonging and quasi coincidence of a fuzzy point with a fuzzy set the concepts of a b fuzzy ideals and a b fuzzy generalized bi ideals which are generalization of fuzzy ideals and fuzzy generalized bi ideals in a semigroup are introduced and related properties are investigated we also define the lower and upper parts of fuzzy subsets of a semigroup characterizations of regular semigroups by the properties of the lower part of q fuzzy left ideals q fuzzy quasi ideals and q fuzzy generalized bi ideals are given

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

soft bl algebras based on fuzzy sets by means of soft sets and q soft sets some characterizations of implicative positive implicative and fantastic filteristic soft bl algebras are investigated finally we prove that a soft set is an implicative filteristic soft bl algebra if and only if it is both a positive implicative filteristic soft bl algebra and a fantastic filteristic soft bl algebra

some kinds of fuzzy ideals of bci algebras the concepts of c c q d fuzzy positive implicative implicative and commutative ideals and c c q d fuzzy positive implicative implicative and commutative ideals in bci algebras are introduced some new characterizations are investigated in particular we prove that a fuzzy set m of a bci algebra x is an c c q d fuzzy implicative ideal of x if and only if it is both an c c q d fuzzy positive implicative ideal and an c c q d fuzzy commutative ideal finally we give some characterizations of three particular classes of bci algebras by these generalized fuzzy ideals

redefined fuzzy implicative filters using the belongs to relation and quasi coincidence with relation q between fuzzy points and fuzzy sets the concept of q j fuzzy implicative filters where q j are any two of q email protected q email protected q with q email protected q is introduced and related properties are discussed relations between email protected q email protected q fuzzy implicative filters and email protected q fuzzy implicative filters are investigated and conditions for an email protected q fuzzy implicative filter to be an fuzzy implicative filter are provided characterizations of email protected q fuzzy implicative filters are given and conditions for a fuzzy set to be a q email protected q fuzzy implicative filter are provided

comparison of the bergman and szego kernels abstract the quotient of the szego and bergman kernels for a smooth bounded pseudoconvex domains in c n is bounded from above by a constant multiple of log p for any p n where is the distance to the boundary for a class of domains that includes those of d angelo finite type and those with plurisubharmonic defining functions the quotient is also bounded from below by a constant multiple of log p for any p 1 moreover for convex domains the quotient is bounded from above and below by constant multiples of

fuzzy n ary polygroups related to fuzzy points recently fuzzy n ary sub polygroups were introduced and studied by davvaz corsini and leoreanu fotea b davvaz p corsini v leoreanu fotea fuzzy n ary sub polygroups comput math appl 57 2008 141 152 now in this paper the concept of email protected q fuzzy n ary sub polygroups email protected email protected email protected email protected fuzzy n ary sub polygroups and fuzzy n ary sub polygroup with thresholds of an n ary polygroup are introduced and some characterizations are described also we give the definition of implication based fuzzy n ary sub polygroups in an n ary polygroup in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

ϵ q level subset abstract the notion of q level subset is introduced the study of q level subset of an q fuzzy subgroup subring or ideal are dealt with

valuations and higher level orders in commutative rings valuation theory is one of the main tools for studying higher level orders and the reduced theory of forms over fields see for example br in mw the theory of higher level orders and reduced forms was generalized to rings with many units and many of the results for fields carried over to this setting while it seems desirable to extend these results further the techniques used for rings with many units will not work for general commutative rings at the same time there is a general theory of valuations in commutative rings see lm m and g which in ma was used to study orders and the reduced theory of quadratic forms over general commutative rings thus it seems natural to ask if the connections between valuations and higher level orders in fields exist in commutative rings in this paper we use valuation theory to study the space of orders and the reduced witt ring relative to a higher level preorder in a commutative ring as in ma we first localize our ring at a multiplicative set without changing the space of orders in order to make the valuation theory work better this is a standard idea from real algebraic geometry remarkably many of the notions methods and results for fields carry over to this new setting we define compatiblity between valuations and orders and preorders and the ring a t associated to a preorder t which turns out to be prufer ring as in the field case we define the relation of dependency on the set of valuations associated to a preorder and we use this to prove a decomposition theorem for the space of orders we can then apply this to show that under a certain finiteness condition the space of orders is equivalent to the space of orders of a preordered field

fuzzy subgroups some characterizations the notion of a fuzzy set was first introduced in 1965 by zadeh 12 since then the theory of fuzzy sets has gone through remarkably rapid strides with well over 4000 papers by now see for example the bibliography 3 several textbooks for example 2 and 6 and an international journal solely devoted to it s the theory has found wideranging applications in such diverse fields as automata control theory decision theory and social behavior pattern studies to name just a few for an interesting expository account see rosenfeld lo and also the book review 7 in 9 rosenfeld introduced the notion of a fuzzy group and showed that many concepts of group theory can be extended in an elementary manner to develop the theory of fuzzy groups in particular he characterized all the fuzzy subgroups of cyclic groups of prime order 9 proposition 5 101 fuzzy groups were further investigated by das in 1 where he characterized all the fuzzy subgroups of finite cyclic groups l theorem 4 21 in this connection he introduced the notion of level subgroups of a fuzzy subgroup which is based on the notion of a level subset introduced earlier by zadeh for a finite group das showed that these level subgroups of a fuzzy subgroup form a chain 1 corollary 3 11 and also constructed a fuzzy subgroup whose chain of level subgroups is maximal in the following special cases when the group is i a direct product of cyclic groups of prime orders ii abelian l theorem 3 41 we analyze the level subgroups of a fuzzy subgroup in more detail and investigate whether the family of level subgroups of a fuzzy subgroup deter

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

determinants of r fold symmetric multilinear forms in hi harrison has constructed and investigated higher degree forms and the witt grothendieck ring of forms we speculate that the signature theory of ordered fields may be extended to the signature theory of partially ordered fields which will be needed for higher degree forms cf br k it seems that higher degree forms and the witt grothendieck ring have important meaning for it in this paper we introduce a notion of determinant as an extension of ordinary determinant and an invariant of forms we shall use the terminologies and notations in h let r be a commutative ring with identity 1 for an r module e let 8 e x e x x e r be an r fold symmetric multilinear form that is 0 x x2 x 0 x x x for every permutation p of 1 2 r and 8 ax byl x2 x ao x

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

characterizations of regular ordered semigroups in terms of α β fuzzy generalized bi ideals in this paper the concept of an a b fuzzy generalized bi ideal in an ordered semigroup is introduced which is a generalization of the concept of a fuzzy generalized bi ideal in an ordered semigroup using this concept some characterization theorems are provided the upper lower parts of an q fuzzy generalized bi ideal are introduced and some characterizations of regular ordered semigroups are given also we consider the concept of implication based fuzzy generalized bi ideals in an ordered semigroup in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

fuzzy hv submodules abstract in this paper we define the concept of fuzzy h v submodule of an h v module and study a few results in this respect we also consider the fundamental relation e defined on an h v module m and prove a fundamental theorem concerning the module m e

more on fuzzy lattices in this paper the concept of an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter in a lattice is introduced which is a generalization of the concept as given by davvaz and kazanci 2011 18 characterizations for an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter are provided different classes of lattices are characterized by the properties of these fuzzy sublattices ideals filters using the notions of a fuzzy sublattice ideal filter with thresholds characterization of a fuzzy sublattice ideal filter an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter are discussed

on fuzzy isomorphism theorems of γ hyperrings in this paper we first derive three isomorphism theorems and a jordan holder theorem of c hyperrings by fuzzy c hyperideals we establish three fuzzy isomorphism theorems of c hyperrings

fuzzy subgroup some characterizations ii abstract we consider an analysis of fuzzy subgroups in terms of the corresponding family of level subgroups given a finite chain of subgroups of a group g we prove that there exists a fuzzy subgroup of g whose level subgroups are exactly the subgroups of this chain as a corollary we obtain an interpretation of the number of chains of subgroups of a group g in which a subgroup h is a member when the group g is a supersolvable group some further interpretation of this number is obtained

a representation theorem for higher level reduced witt rings in 6 becker and rosenberg defined the reduced witt ring wak of a formally real field k with respect to a higher level preorder tin k wak is a subring of the ring c x of continuous c valued functions on the space x of signatures of k which are trivial on t and is built up from higher level t forms over k this higher level reduced theory is a natural generalization of the reduced theory of quadratic forms over fields spaces of signatures were introduced in 18 to provide an abstract framework for the higher level reduced theory over fields along the lines of marshall s spaces of orderings 13 h treatment of the classical reduced theory of quadratic forms there are many advantages to this axiomatic approach it allows for a unified study of reduced witt rings over fields and skew fields powers has shown that becker and rosenberg s study of higher level reduced witt rings can also be carried out over skew fields 22 the absence of technical considerations such as valuation theory not only yields simpler proofs of known results but also new results about the theory over fields 183 the space of orderings version 151 of the result which we prove here has found application in real algebraic geometry and we hope that our abstract higher level result might also prove useful in this context the question which concerns us here is the so called representation problem given fe c x how can we tell if f f for some f w x this has been solved for the higher level reduced witt ring of a field by becker and rosenberg 6 see s also and in the case of spaces of orderings by marshall 15 both solutions being generalizations of the original representation theorems of becker and brlicker 4 5 31 and brown and marshall 9 4 21 in the context of the reduced quadratic form theory over fields under a 2 power assumption we simultaneously extend all of these representation theorems to our abstract higher level setting this entails studying fans and more importantly a generalization called quasifans we not only obtain a common proof of the representation 105 0021 8693 88 3 00