rough prime ideals and rough fuzzy prime ideals in semigroups in this paper we shall introduce the notions of rough prime ideals and rough fuzzy prime ideals in a semigroup and give some properties of such ideals also we will discuss the relations between the upper lower rough prime ideals and the upper lower approximations of their homomorphism images

some notes on equivalent fuzzy sets and fuzzy subgroups this paper discusses the problems of equivalent fuzzy sets and fuzzy subgroups first a critical discussion of previous results by murali and makamba is provided second this paper discusses the conditions under which the equivalence relation of fuzzy sets can be equivalently described by their level sets it also suggests that the equivalence approach to the classification of fuzzy subgroups is suitable only for finite groups and proposes a new definition for the classification of fuzzy subgroups s equivalence showing that any two fuzzy subgroups of an infinite cyclic group with infinite membership values are s equivalent

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

global existence and asymptotic convergence of weak solutions for the one dimensional navier stokes equations with capillarity and nonmonotonic pressure abstract we construct global weak solution of the navier stokes equations with capillarity and nonmonotonic pressure the volume variable v 0 is initially assumed to be in h 1 and the velocity variable u 0 to be in l 2 on a finite interval 0 1 we show that both variables become smooth in positive time and that asymptotically in time u 0 strongly in l 2 0 1 and v approaches the set of stationary solutions in h 1 0 1

on the structure of generalized rough sets in this paper we consider some fundamental properties of generalized rough sets induced by binary relations on algebras and show that 1 any reflexive binary relation determines a topology 2 if q is a reflexive and symmetric relation on a set x then o email protected x q a a is a topology such that a is open if and only if it is closed 3 conversely for every topological space x o satisfying the condition that a is open if and only if it is closed there exists a reflexive and symmetric relation r such that o email protected x r a a 4 let q be an equivalence relation on x for any pseudo w closed subset a of x q a is an w closed set if and only if w x x x email protected a for any email protected x moreover we consider properties of generalized rough sets

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

existence and uniqueness of fuzzy ideals let r be a commutative ring the idea of identifying a fuzzy ideal of r with its corresponding chain of level ideals and its range of values although widely used in the literature for the study of fuzzy ideals has never been investigated in a general setting before we investigate in this paper the more general problem of characterization of all those fuzzy ideals that can be identified with a given arbitrary family c of subsets of r together with a given arbitrary subset s of 0 1 necessary and sufficient conditions for the existence and uniqueness of such fuzzy ideals are established in particular we obtain that uniqueness always holds true for artinian rings moreover examples are presented to further support our results and shed more light on the above mentioned problem of identification we finish by raising a natural question that is left as an open problem for further investigation

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

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

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

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

roughness in rings in this paper basic notions of the rough set theory will be given in fact the paper concerns a relationship between rough sets and ring theory we shall introduce the notion of rough subring resp ideal with respect to an ideal of a ring which is an extended notion of a subring resp ideal in a ring and we shall give some properties of the lower and the upper approximations in a ring

on the topological properties of fuzzy rough sets this paper is devoted to the discussion of the relationship between fuzzy rough set models and fuzzy topologies on a finite universe the tc axiom for fuzzy topology is proposed it is proved that the set of all lower approximation sets based on a reflexive and transitive fuzzy relation consists of a fuzzy topology which satisfies tc axiom and conversely a fuzzy topology which obey tc axiom is just the set of all lower approximation sets under a reflexive and transitive fuzzy relation that is to say there exists a one to one correspondence between the set of all reflexive and transitive fuzzy relations and the set of all fuzzy topologies which satisfy tc axiom

the nil radical of a fuzzy ideal abstract we define ab initio the fuzzy nil radical of an ideal of a commutative ring r the definition has been successful in establishing the analogues of most of the fundamental ground results involving radicals in the fuzzy setting the concept of a fuzzy semiprime ideal of a commutative ring r is introduced through the fuzzy nil radical of an ideal a commutative regular ring is characterized by its semiprime ideals at the end we demonstrate that the intersection of all fuzzy semiprime ideals of a commutative ring which contain a given fuzzy ideal is precisely the nil radical of this establishes the vital connection between a fuzzy semiprime ideal and the nil radical of a fuzzy ideal

roughness based on fuzzy ideals the theory of rough set proposed by pawlak and the theory of fuzzy set proposed by zadeh are complementary generalizations of classical set theory many sets are naturally endowed with two binary operations addition and multiplication one concept which does this is a ring this paper concerns a relationship between rough sets fuzzy sets and ring theory it is a continuation of ideas presented by kuroki and wang n kuroki p p wang the lower and upper approximations in a fuzzy group inform sci 90 1996 203 220 we consider a ring as a universal set and we assume that the knowledge about objects is restricted by a fuzzy ideal in fact we apply the notion of fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring some characterizations of the above approximations are made and some examples are presented

tropical geometric interpretation of ultradiscrete singularity confinement using the interpretation of the ultradiscretization procedure as a non archimedean valuation we use results of tropical geometry to show how roots and poles manifest themselves in piece wise linear systems as points of non differentiability this will allow us to demonstrate a correspondence between singularity confinement for discrete integrable systems and ultradiscrete singularity confinement for ultradiscrete integrable systems

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

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

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

on fuzzy ideals in bck bci algebras in the present paper we give a procedure by which we generate a fuzzy ideal resp closed fuzzy ideal by a fuzzy set in a bci algebra as applications we prove the set of all the fuzzy ideals in a bci algebra forms a complete lattice called fuzzy ideal lattice the set of all the closed fuzzy ideals in a bci algebra is a modular sublattice of the fuzzy ideal lattice but it is not distributive in general for commutative bck algebras we establish the prime fuzzy ideal theorem in particular we give some characterizations of noether bck bci algebras by fuzzy ideals

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

on fuzzy subnear rings and ideals abstract the aim of this paper is to introduce the notion of a fuzzy subnear ring to study fuzzy ideals of a near ring and to give some properties of fuzzy prime ideals of a near ring

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

tl filters of integral residuated l monoids in this paper we introduce and discuss the concept of tl filters of integral residuated l monoids first we study some basic properties of tl filters and give the formula for calculating the tl filters generated by l subsets then we discuss some properties of tl filters under homomorphisms and study the relationship between tl filters and t congruence l relations on integral commutative residuated l monoids

fuzzy prime ideals of rings abstract the notions of fuzzy ideal and fuzzy prime ideal of a ring with truth values in a complete lattice satisfying the infinite meet distributive law are introduced which generalize the existing notions with truth values in the unit interval of real numbers a procedure to construct any fuzzy ideal from a family of ideals with certain conditions is established all fuzzy prime maximal ideals of a given ring are determined by establishing a one to one correspondence between fuzzy prime maximal ideals and the pairs p where p is a prime maximal ideal of the ring and is a prime element dual atom in the complete lattice

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

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

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

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

prime l fuzzy ideals and primary l fuzzy ideals abstract in this paper the concepts of a primary l fuzzy ideal and a prime l fuzzy ideal and p primary are introduced and some fundamental propositions proved in particular a structural theorem for a primary l fuzzy ideal belonging to a prime l fuzzy ideal is 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

two new operators in rough set theory with applications to fuzzy sets in this paper two new operators are introduced for the rough set theory using them two inequalities well known in the rough set theory can now be modified to become equalities with this change no information will be lost in the new expressions hence many properties in rough set theory can be improved and in particular the union the intersection and the complement operations can be redefined based on the two equalities furthermore the collection of rough sets of an approximation space forms a boolean algebra under these new operators finally roughness properties of fuzzy sets are analyzed using the new operations

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

fuzzy h ideals of hemirings a characterization of an h hemiregular hemiring in terms of a fuzzy h ideal is provided some properties of prime fuzzy h ideals of h hemiregular hemirings are investigated it is proved that a fuzzy subset z of a hemiring s is a prime fuzzy left right h ideal of s if and only if z is two valued z 0 1 and the set of all x in s such that z x 1 is a prime left right h ideal of s finally the similar properties for maximal fuzzy left right h ideals of hemirings are considered

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