rough ideals in semigroups abstract we shall introduce the notion of a rough left right two sided bi ideal in a semigroup which is an extended notion of a left right two sided bi ideal in a semigroup and give some properties of such ideals

fuzzy g congruences on a groupoid abstract the definition of a fuzzy reflexive relation on a set s is generalized by demanding that x y z z 0 for all x y z s fuzzy equivalence relations on a given set and fuzzy congruences on a given groupoid are studied under this generalized setting

fuzzy congruences and compatible fuzzy partitions the main purpose of this paper is to prove that fuzzy congruence relations and compatible fuzzy partitions on a fuzzy algebra f can be described with the help of crisp congruence relations and compatible partitions on the cuts of f

some properties of fuzzy groups on definit des sous groupes flous normaux des sous groupes flous normaux de niveau et leurs homomorphismes et on donne certaines de leurs proprietes

a multivariate two sample mean test for small sample size and missing data we develop a new statistic for testing the equality of two multivariate mean vectors a scaled chi squared distribution is proposed as an approximating null distribution because the test statistic is based on componentwise statistics it has the advantage over hotelling s t2 test of being applicable to the case where the dimension of an observation exceeds the number of observations an appealing feature of the new test is its ability to handle missing data by relying on only componentwise sample moments monte carlo studies indicate good power compared to hotelling s t2 and a recently proposed test by srivastava 2004 technical report university of toronto the test is applied to drug discovery data

fuzzy relations and fuzzy groups abstract given a group s we consider fuzzy relations on s that is maps from s s into 0 1 of particular interest is to investigate conditions under which the fuzzy relation becomes a fuzzy subgroup on s s we prove that if is a fuzzy subset of s and is the strongest fuzzy relation on s that is a fuzzy relation on then is a fuzzy subgroup if and only if is a fuzzy subgroup a number of other results are obtained about the interrelationships between fuzzy relations on s including the weakest fuzzy relation and fuzzy subgroups on s s

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

on t congruence l relations on groups and rings in this paper we further study t congruence l relations on groups and rings and give the formulas for calculating the t congruence l relations generated by l relations where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l

i fuzzy equivalence relations and i fuzzy partitions a t fuzzy equivalence relation is a fuzzy binary relation on a set x which is reflexive symmetric and t transitive for a t norm t recently mesiar et al r mesiar b reusch h thiele fuzzy equivalence relations and fuzzy partitions j multi valued logic soft comput 12 2006 167 181 have generalised the t norm t to any general conjunctor c and investigated the minimal assumptions required on such operations called duality fitting conjunctors such that the fuzzification of the equivalence relation admits any value from the unit interval and also the one one correspondence between the fuzzy equivalence relations and fuzzy partitions is preserved in this work we conduct a similar study by employing a related form of c transitivity viz i transitivity where i is an implicator we show that although every i fuzzy equivalence relation can be shown to be a c fuzzy equivalence relation there exist c fuzzy equivalence relations that are not i fuzzy equivalence relations and hence these concepts are not equivalent most importantly we show that the class of duality fitting implicators i is much richer than the residuals of the duality fitting conjunctors in the study of mesiar et al we also show that the i fuzzy partitions have a constant wise structure

fuzzy sets and sheaves part ii this essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory resp of the theory of complete w valued sets hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect part ii of this series of two papers explains the sheaf theoretic basis of zadeh s operations on fuzzy sets with the exception of the complementation further the quotient problem w r t similarity relations and the quotient problem of fuzzy groups w r t fuzzy congruence relations are solved finally stratified fuzzy topologies are identified with internal topologies on constant sheaves

on fuzzy congruence of a near ring module the aim of this paper is to introduce fuzzy submodule and fuzzy congruence of an r module near ring module to obtain the correspondence between fuzzy congruences and fuzzy submodules of an r module to define quotient r module of an r module over a fuzzy submodule and to obtain correspondence between fuzzy congruences of an r module and fuzzy congruences of quotient r module over a fuzzy submodule of an r module

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

the join of fuzzy algebraic substructures of a group and their lattices this is a continuation of work in previous papers n ajmal and k v thomas fuzzy sets and systems 58 1993 217 inform sci 76 1994 1 here we provide a common technique of constructing the join of fuzzy substructures consequently it leads to the formation of various types of lattices and sublattices of fuzzy substructures of a group including those of normal and quasinormal fuzzy subgroups a lattice theoretic relationship of these sublattices is established moreover we present simple and direct proofs for the fact that the lattice of fuzzy normal subgroups is modular

fuzzy homomorphisms of algebras in this paper we consider fuzzy relations compatible with algebraic operations which are called fuzzy relational morphisms in particular we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations called uniform fuzzy relational morphisms and those which are partially uniform f functions called fuzzy homomorphisms both uniform fuzzy relations and partially uniform f functions were introduced in a recent paper by us uniform fuzzy relational morphisms are especially interesting because they can be conceived as fuzzy congruences which relate elements of two possibly different algebras we give various characterizations and constructions of uniform fuzzy relational morphisms and fuzzy homomorphisms we establish certain relationships between them and fuzzy congruences and we prove homomorphism and isomorphism theorems concerning them we also point to some applications of uniform fuzzy relational morphisms

representation of lattices by fuzzy weak congruence relations fuzzy lattice valued weak congruences of abstract algebras are investigated for an algebra the family of all such fuzzy relations is a complete lattice its structure and cut properties are investigated and fully described these fuzzy weak congruences are applied in representation of complete and algebraic lattices a wider class of lattices can be represented in such a fuzzy framework than in classical algebra we prove that there is a straightforward representation of any complete lattice using it as a co domain in a more general case it is proved that several subdirect powers of lattices are also representable by fuzzy weak congruences

on fuzzy ideals and fuzzy quotient rings of a ring abstract in this paper we define fuzzy quotient rings induced by fuzzy ideals and give the notion of fuzzy nilpotent ideals we give also a characterization of semiprime rings in terms of fuzzy ideals

fuzzy groups with sup property we investigate the inner structure of fuzzy subgroups with sup property we provide a characterization of this type of fuzzy subgroups in terms of their level subsets it is shown that the property of being a fuzzy subgroup with sup property is invariant under homomorphism and the homomorphic preimage of a fuzzy subgroup with sup property is also a fuzzy subgroup with sup property moreover we investigate the lattice structure of the class lnt of fuzzy normal subgroups of a group g each of which assumes the same value t at the identity of g it is proved that the subclass lnst of fuzzy subgroups with sup property of lnt constitutes a sublattice of lnt the modularity of lnst is derived as a consequence of the modularity of lnt

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

distributivity in lattices of fuzzy subgroups the main goal of this paper is to study the finite groups whose lattices of fuzzy subgroups are distributive we obtain a characterization of these groups which is similar to a well known result of group theory

a contribution to the theory of fuzzy subgroups abstract in this paper we continue our study in order to give a partial answer to the question suggested by asaad in 1991 what can be said about the structure of a group g when the information are known about the structure of a fuzzy subgroup a of g and viceversa

fuzzy equivalence relations abstract in this note we define and discuss properties of fuzzy equivalence relations on a set in particular we show that there exists a correspondence between fuzzy equivalence relations and certain classes of fuzzy subsets we also study the cuts of fuzzy equivalence relations finally certain lattice theoretic properties of fuzzy equivalence relations are discussed

on fuzzy equivalence i fuzzy reflexive symmetric and transitive relations on fuzzy subsets are studied various types of reflexivities and corresponding equivalences are considered the possible fuzzy partitioning of a fuzzy subset is investigated

fuzzy subinclines ideals of incline algebras the fuzzification of subinclines ideals in inclines are considered and some related properties are investigated we also state the product of fuzzy subinclines ideals and the projections of fuzzy subinclines ideals we discuss fuzzy relations fuzzy characteristic subinclines ideals

algebras of fuzzy sets in this paper we investigate two kinds of algebras of fuzzy sets which are obtained by using zadeh s extension principle we give conditions under which a homomorphism between two algebras induces a homomorphism between corresponding algebras of fuzzy sets we prove that if the structure of truth values is a complete residuated lattice the induced algebra of a subalgebra of an algebra a can be embedded into the induced algebra of fuzzy sets of a for direct products we give conditions under which the direct product of algebras of fuzzy sets could be embedded into the algebra of fuzzy sets of the direct product in the case of homomorphisms and direct products the two kinds of algebras of fuzzy sets behave in different ways

fuzzy quotient algebras and fuzzy factor congruences fuzzy quotient algebras are defined some homomorphism theorems are given fuzzy factor congruences and fuzzy factorable algebras are defined and some basic theorems are proved

fuzzy γ hypernear rings the concept of c hypernear rings which is a generalization of c near rings and hypernear rings is introduced some related properties of c hypernear rings are described in particular three isomorphism theorems of c hypernear rings are established by using this new idea we consider the fuzzy hyperideals of c hypernear rings finally the fundamental relations between c hypernear rings and c near rings are discussed

on generalized characteristic fuzzy subgroups of a finite group abstract in 1991 asaad 2 suggested the following two questions i what can be said about the structure of a fuzzy subgroup a of a finite group g when information is known about the structure of g ii what can be said about the structure of group g when information is known about the structure of a fuzzy subgroup a of g the purpose of this paper is to continue the investigation of the above questions

diagonal likelihood ratio test for equality of mean vectors in high dimensional data we propose a likelihood ratio test framework for testing normal mean vectors in high dimensional data under two common scenarios the one sample test and the two sample test with equal covariance matrices we derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure in comparison with the diagonal hotelling s tests our proposed test statistics display some interesting characteristics in particular they are a summation of the log transformed squared t statistics rather than a direct summation of those components more importantly to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses we do not need the requirement that the covariance matrices follow a diagonal matrix structure as a consequence our proposed test methods are very flexible and readily applicable in practice simulation studies and a real data analysis are also carried out to demonstrate the advantages of our likelihood ratio test methods

fuzzy sets and sheaves part ii sheaf theoretic foundations of fuzzy set theory with applications to algebra and topology this essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory resp of the theory of complete valued sets hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect part ii of this series of two papers explains the sheaf theoretic basis of zadeh s operations on fuzzy sets with the exception of the complementation further the quotient problem w r t similarity relations and the quotient problem of fuzzy groups w r t fuzzy congruence relations are solved finally stratified fuzzy topologies are identified with internal topologies on constant sheaves

notes on the lower and upper approximations in a fuzzy group and rough ideals in semigroups in this note we show by examples that propositions 2 4 and 2 5 in n kuroki p p wang the lower and upper approximations in a fuzzy group information sciences 90 1996 203 and theorem 2 5 in n kuroki rough ideals in semigroups information sciences 100 1997 139 are incorrect and offer their modified versions c 2007 elsevier inc all rights reserved

fuzzy cosets and fuzzy normal subgroups abstract in this paper besides generalizing some of the results of mukherjee and bhattacharya 9 we investigate conditions under which a homomorphic image of a fuzzy normal subgroup is fuzzy normal we also prove that a fuzzy subgroup of order p n 1 of a group of order p n is a fuzzy normal subgroup if p is a prime

t type regular l relations on a complete brouwerian lattice abstract in this paper using a general infinitely distributive t norm t on a complete brouwerian lattice l we introduce the concept of t type regular l relations study some basic properties of them and give out some methods of calculating the maximal t type generalized inverse l relations of t type regular l relations

the fuzzy normal subgroup using the concept of fuzzy spaces we define the fuzzy normal subgroup in a fuzzy group its relation with the classical fuzzy normal subgroup is studied

a powerful bayesian test for equality of means in high dimensions abstractwe develop a bayes factor based testing procedure for comparing two population means in high dimensional settings in large p small n settings bayes factors based on proper priors require eliciting a large and complex p p covariance matrix whereas bayes factors based on jeffrey s prior suffer the same impediment as the classical hotelling t2 test statistic as they involve inversion of ill formed sample covariance matrices to circumvent this limitation we propose that the bayes factor be based on lower dimensional random projections of the high dimensional data vectors we choose the prior under the alternative to maximize the power of the test for a fixed threshold level yielding a restricted most powerful bayesian test rmpbt the final test statistic is based on the ensemble of bayes factors corresponding to multiple replications of randomly projected data we show that the test is unbiased and under mild conditions is also locally consistent we demonstrate the efficacy of the appro

a two sample test for equality of means in high dimension we develop a test statistic for testing the equality of two population mean vectors in the large p small n setting such a test must surmount the rank deficiency of the sample covariance matrix which breaks down the classic hotelling t2 test the proposed procedure called the generalized component test avoids full estimation of the covariance matrix by assuming that the p components admit a logical ordering such that the dependence between components is related to their displacement the test is shown to be competitive with other recently developed methods under arma and long range dependence structures and to achieve superior power for heavy tailed data the test does not assume equality of covariance matrices between the two populations is robust to heteroscedasticity in the component variances and requires very little computation time which allows its use in settings with very large p an analysis of mitochondrial calcium concentration in mouse cardiac muscles over time and of copy number varia

diagnosis of random effect model misspecification in generalized linear mixed models for binary response summary generalized linear mixed models glmms are widely used in the analysis of clustered data however the validity of likelihood based inference in such analyses can be greatly affected by the assumed model for the random effects we propose a diagnostic method for random effect model misspecification in glmms for clustered binary response we provide a theoretical justification of the proposed method and investigate its finite sample performance via simulation the proposed method is applied to data from a longitudinal respiratory infection study

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

fuzzy cosets and cyclic and abelian fuzzy subgroups abstract here we give some properties of fuzzy cosets normal fuzzy subgroups and s fuzzy subgroups also we introduce the notions of cyclic abelian fuzzy subgroups and prove some of their properties

total variation based convex filters for medical imaging several variational based diffusion filters are applied to measured magnetic resonance images and on this basis are evaluated for their suitability to medical imaging in particular a specific total variation based filter with a convex variational penalty function is introduced here for the enhancement of edge flat and grey image scales in general results reveal that convex total variation based filters can be implemented to perform very well to enhance the visual clarity of medical images as a result further support is provided to establish such methods for medical applications

a complete study of the lattices of fuzzy congruences and fuzzy normal subgroups in this paper we introduce the concepts of t fuzzy congruences and t fuzzy equivalences using these ideas we investigate completely on one hand the lattice structures of the set of fuzzy equivalence relations on a group and the set of fuzzy congruences and on the other hand the lattice structures of the set of fuzzy subgroups and fuzzy normal subgroups our study reveals some finer and interesting facts about these lattices it is proved among other results that the set ct of all t fuzzy congruences of a group g forms lattice and also the set lnt of all those fuzzy normal subgroups which assume the same value t at e the identity of g forms a lattice as an important result we prove that the lattices ct and lnt are isomorphic it is also shown that the lattices ct and lnt are modular moreover we construct various important sublattices of the lattice ct and exhibit their relationship by lattice diagrams in the process we improve and unify many results of earlier authors on fuzzy congruences

the lattices of fuzzy subgroups and fuzzy normal subgroups abstract here we discuss various types of sublattices of the lattice of fuzzy subgroups of a given group we prove that a special class of fuzzy normal subgroups constitutes a modular sublattice of the lattice of fuzzy subgroups

fuzzy congruences on inverse semigroups abstract we introduce the notion of a quotient semigroup s induced by a fuzzy congruence relation on a semigroup s and give homomorphism theorems with respect to the fuzzy congruence we also introduce the notion of an idempotent separating fuzzy congruence a group fuzzy congruence on inverse semigroups and give some of their properties on inverse semigroups

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 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 lattice of fuzzy normal subgroups is modular abstract we have introduced and discussed in a recent paper 2 various sublattices such as lf lt and lfnt of the lattice l of fuzzy subgroups of a given group in particular we proved that the sublattice lfn of fuzzy normal subgroups with finite range and tip t is a modular sublattice of l here we remove all the restrictions on the choice of fuzzy normal subgroups and prove that the class of all fuzzy normal subgroups ln forms the modular sublattice of l as a tool we prove an important result that the fuzzy subgroups generated by a pair of fuzzy normal subgroups of a group is fuzzy normal

fuzzy quotient groups abstract the operation of a group g induces through zadeh s extension principle a semigroup operation on ig we define a fuzzy quotient group of g to be a fuzzy partition of g that is a subsemigroup of ig having a group structure we show that fuzzy quotient groups of g are in one to one correspondence with normal fuzzy subgroups of g and that their associated fuzzy similarity relations are all two sided invariant we study relationships between the level structures of these structures we also give a necessary and sufficient condition for a group homomorphism to factor through fuzzy quotients

isomorphic fuzzy groups abstract we introduce an acceptable definition of isomorphic fuzzy groups which fulfils the basic requirements the fuzzy versions of the first and the second isomorphism theorems become immediate consequences the idea is applied to the sup min product of two fuzzy subgroups of a group as an indispensable tool the characterization of a fuzzy normal subgroup of a group by the so called open level subgroups is brought forth an isomorphism between the cartesian product and the sup min product of two fuzzy subgroups of a group is demonstrated

lattice of fuzzy congruences in inverse semigroups abstract the lattice of fuzzy congruences in an inverse semigroup is developed in the present paper given a fuzzy congruence relation in an inverse semigroup the fuzzy congruence relations min and ax are defined and some important results are obtained a theorem giving the close relation between a fuzzy congruence and its fuzzy trace and kernel is proved

algebras with fuzzy equalities an algebra with fuzzy equality is a set with operations on it that is equipped with similarity i e a fuzzy equivalence relation such that each operation f is compatible with described verbally compatibility says that each f yields similar results if applied to pairwise similar arguments on the one hand algebras with fuzzy equalities are structures for the equational fragment of fuzzy logic and have been studied from this point of view before on the other hand they are the formal counterpart to the intuitive idea of having functions that are not allowed to map similar objects to dissimilar ones the present paper aims at developing fundamental points of algebras with fuzzy equalities we introduce the notion of an algebra with fuzzy equality present natural examples compare the notion with other approaches and introduce and develop basic structural notions subalgebras morphisms products direct unions in a follow up paper vychodil direct limits and reduced products of algebras with fuzzy equalities submitted for publication we deal with advanced topics in algebras with fuzzy equalities direct limits reduced products

generalized fuzzy quotient subgroups abstract in this paper we consider the fuzzy subgroup of a given group defined by generalized triangular norms and conorms introduced by yager 1986 the definitions of a anti fuzzy subgroup and a anti pseudo fuzzy subgroup are reviewed then a generalized fuzzy cayley theorem as well as a partial generalization of fuzzy lagrange theorem are given also a unified approach for studying fuzzy quotient subgroups is discussed some correspondence theorems for several kinds of fuzzy subgroups are proved and examples of generalized triangular norms conorms are given

the lower and upper approximations in a fuzzy group in this paper we shall introduce the notion of a rough subgroup with respect to a normal subgroup of a group and give some properties of the lower and the upper approximations in a group also we will discuss a rough subgroup with respect to a t level subset of a fuzzy normal subgroup

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

living near the edge a lower bound on the phase transition of total variation minimization this work is about the total variation tv minimization which is used for recovering gradient sparse signals from compressed measurements recent studies indicate that tv minimization exhibits a phase transition behavior from failure to success as the number of measurements increases in fact in large dimensions tv minimization succeeds in recovering the gradient sparse signal with high probability when the number of measurements exceeds a certain threshold otherwise it fails almost certainly obtaining a closed form expression that approximates this threshold is a major challenge in this field and has not been appropriately addressed yet in this work we derive a tight lower bound on this threshold in case of any random measurement matrix whose null space is distributed uniformly with respect to the haar measure in contrast to the conventional tv phase transition results that depend on the simple gradient sparsity level our bound is highly affected by generalized notions of gradient sparsity our proposed bound is very close to the true phase transition of tv minimization confirmed by simulation results

lattice of fuzzy subalgebras and closure systems in i x abstract let x be a non empty set and i be the unit interval of real numbers the elements of i x are called fuzzy subsets of x i x is a lattice with the pointwise ordering of i now if a x f is an universal algebra with a specified set f of finitary operations on x then each operation can be extended to a finitary operation on i x an element of i x is defined to be a fuzzy subalgebra of a using these extended operations we also define algebraic closure system in i x we then show that the lattice of fuzzy subalgebras of a is an algebraic closure system in i x

fuzzy congruences and fuzzy normal subgroups abstract a complete description of the congruences on a group in terms of its normal subgroups can be seen in papers by a rosenfeld and w j howie in this paper we shall introduce the concept of fuzzy congruences on a groupoid and a group and characterize fuzzy congruences on a group in terms of fuzzy normal subgroups

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

fuzzy congruence relations abstract if a x f is an universal algebra and if r x denotes the set of all fuzzy subsets of x x i e fuzzy relations on x then the algebraic operations fg f on x are extended to algebraic operations f on r x f is an algebra similar to a it is called relational algebra a fuzzy equivalence relation which is at the same time a fuzzy subalgebra of r x f is called a fuzzy congruence relation on x in this paper we study fuzzy congruence relations amongst other things we prove that the set of all fuzzy congruence relations on an algebra is a complete lattice and an algebraic closure system

operator domains on fuzzy groups abstract the fuzzy subgroups of a group which are invariant under various operator domains are studied in particular the classes of all inner automorphisms automorphisms and endomorphisms are applied on the fuzzy subgroups of a group as a consequence two distinct partitions of a group which are successively coarser than the family of all conjugate classes are discovered

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