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

roughness in cayley graphs in this paper rough approximations of cayley graphs are studied and rough edge cayley graphs are introduced furthermore a new algebraic definition for pseudo cayley graphs containing cayley graphs is proposed and a rough approximation is expanded to pseudo cayley graphs in addition rough vertex pseudo cayley graphs and rough pseudo cayley graphs are introduced some theorems are provided from which properties such as connectivity and optimal connectivity are derived this approach opens new research fields such as data networks

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 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

on the structure of rough prime primary ideals and rough fuzzy prime primary ideals in commutative rings this paper is a continuation of ideas presented by davvaz roughness in rings inform sci 164 2004 147 163 roughness based on fuzzy ideals inform sci 176 2006 2417 2437 we introduce the notions of rough prime primary ideals and rough fuzzy prime primary ideals in a ring and give some properties of such ideals also we discuss the relations between the upper and lower rough prime primary ideals and the upper and lower approximations of their homomorphism images

rough 3 valued algebras rough set theory is an important tool for dealing with granularity and vagueness in information systems this paper studies a kind of rough set algebra the collection of all the rough sets of an approximation space can be made into a 3 valued lukasiewicz algebra we call the algebra a rough 3 valued lukasiewicz algebra in this paper we focus on the rough 3 valued lukasiewicz algebras which are a special kind of 3 valued lukasiewicz algebras firstly we examine whether the rough 3 valued lukasiewicz algebra is an axled 3 valued lukasiewicz algebra secondly we present the condition under which the rough 3 valued lukasiewicz algebra is also a 3 valued post algebra then we investigate the 3 valued post subalgebra problem of the rough 3 valued lukasiewicz algebra finally this paper studies the relationship between the rough 3 valued lukasiewicz algebra and the boolean algebra constructed by all the exact sets of the corresponding approximation space

the ϑ lower and t upper fuzzy rough approximation operators on a semigroup in this paper we consider a semigroup as a universal set and investigate the properties of q lower and t upper fuzzy rough approximation operators a new fuzzy algebraic structure called a tl fuzzy rough semigroup is introduced and some related properties are studied finally the homomorphism properties of q lower and t upper fuzzy rough approximation operators are investigated

a short note on algebraic t rough sets our aim in this paper is to introduce the concept of a set valued homomorphism for groups which is a generalization of ordinary homomorphism then using the definitions of lower inverse and upper inverse we introduce the definition of uniform set valued homomorphism and prove that every set valued homomorphism is uniform finally the concept of probabilistic t rough set is defined

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

the lower and upper approximations in a hypergroup this paper presents a relationship between rough sets and hypergroup theory we analyze the lower and upper approximations of a subset with respect to an invertible subhypergroup and we consider some particular situations moreover the notion of a rough subhypergroup is introduced finally fuzzy rough subhypergroups are introduced and characterized

roughness in mv algebras in this paper by considering the notion of an mv algebra we consider a relationship between rough sets and mv algebra theory we introduce the notion of rough ideal with respect to an ideal of an mv algebra which is an extended notion of ideal in an mv algebra and we give some properties of the lower and the upper approximations in an mv algebra

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

rough sets induced by ideals in lattices this paper is to study the rough sets within the context of lattices we study the special properties of the rough sets which can be constructed by means of the congruences determined by ideals of lattice also the properties of the generalized rough sets with respect to ideals of lattice are investigated finally we give an example of their application in formal concept analysis

roughness and fuzziness in quantales abstract rough set theory and fuzzy set theory are two useful mathematical tools for dealing with uncertainty and granularity in information systems motivated by the studies of roughness and fuzziness in algebraic systems and partially ordered sets such as semigroups rings and lattices in this paper we introduce first the notions of fuzzy prime semi prime primary ideals of quantales and investigate their properties several characterizations of such ideals are presented then we introduce the concepts of weak fuzzy prime ideals and strong fuzzy prime ideals of quantales and establish relationships between these ideals and fuzzy prime ideals of quantales by applying rough set theory to fuzzy ideals of quantales we furthermore define rough fuzzy prime semi prime primary ideals of quantales generalizing yang and xu s work on quantales to the fuzzy environment finally relationships between the upper resp lower rough fuzzy ideals of quantales and the upper resp lower approximations of their homomorphic images are also discussed

roughness in quantales rough set theory is a useful mathematical tool for dealing with the uncertainty and granularity in information systems in this paper rough approximations are introduced into quantales a kind of partially ordered algebraic structure with an associative binary multiplication the notions of upper lower rough prime semi prime primary ideals of quantales are proposed and verified to be the extended notions of usual prime semi prime primary ideals of quantales respectively global order properties of all lower upper rough ideals of a quantale are also investigated the rough radical of an upper rough ideal in a quantale is defined and the prime radical theorem of rings is generalized to upper rough ideals of quantales some results about homomorphic images of rough ideals and rough prime ideals of semigroups and rings are also generalized and improved in the field of quantales

pawlak s approximations in γ semihypergroups the c semihypergroup is a generalization of a semigroup a generalization of a semihypergroup and a generalization of a c semigroup in this paper we discuss the roughness of c subsemihypergroups and c hyperideals bi c hyperideals in c semihypergroups in addition we consider rough sets with respect to the idempotent regular relations in a quotient c semihypergroup the upper approximations with respect to green s equivalence relations are derived in the context of c subsemihypergroups and c hyperideals

reference points and roughness in this paper we introduce the notion of a reference point and provide local approximations for a subset of the universe the notion of a reference point naturally gives rise to a rough approximations framework wherein several approximations are possible on the same set also we present an extension to the decision theoretic rough set model by using reference points

roughness in modules the theory of rough sets was proposed by pawlak in 1982 the relations between rough sets and algebraic systems have been already considered by many mathematicians important algebraic structures are groups rings and modules rough groups and rough rings have been investigated by biswas and nanda kuroki and wang and davvaz in this paper we consider an r module as a universal set and we introduce the notion of rough submodule with respect to a submodule of an r module which is an extended notion of a submodule in an r module we also give some properties of the lower and the upper approximations in an r module

spectral geometry of singular riemannian spaces on considere la trace du noyau de la chaleur et l application de la methode de l equation de la chaleur au theoreme d indice pour la caracteristique d euler et des complexes signatures

on kahler einstein metrics on certain kahler manifolds with c1 m 0 on demontre qu il existe une metrique de kahler einstein sur une hypersurface de fermat a m dimensions de degre superieur a m 1

on rough set and fuzzy sublattice let l be a lattice with the least element 0 and the greatest element 1 and let be a full congruence relation on l in this paper the notion of upper and lower approximations of a fuzzy subset of l is introduced and some important properties will be studied

non reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow we consider a time harmonic acoustic scattering problem in a 2d infinite waveguide with walls covered with an absorbing material in the presence of a mean flow assumed uniform far from the source to make this problem suitable for a finite element analysis the infinite domain is truncated this paper concerns the derivation of a non reflecting boundary condition on the artificial boundary by means of a dirichlet to neumann dtn map based on a modal decomposition compared with the hard walled guide case several difficulties are raised by the presence of both the liner and the mean flow in particular acoustic modes are no longer orthogonal and behave asymptotically like the modes of a soft walled guide however an accurate approximation of the dtn map can be derived using some bi orthogonality relations valid asymptotically for high order modes numerical validations show the efficiency of the method the influence of the liner with or without mean flow is illustrated

the lower and upper approximations in a quotient hypermodule with respect to fuzzy sets this paper provides a continuation of ideas presented by davvaz and mahdavipour b davvaz m mahdavipour roughness in modules inform sci 176 2006 3658 3674 the notion of hypermodule is a generalization of the notion of module in this paper we consider the quotient hypermodule m a and interpret the lower and upper approximations as subsets of the quotient hypermodule m a then we introduce the concept of quotient rough sub hypermodule also using the concept of fuzzy sets we introduce and discuss the concept of fuzzy rough hypermodules and then we obtain the relation between fuzzy rough sub hypermodules and level rough sets this relation is characterized as a necessary and sufficient condition

θ t fuzzy rough approximation operators and the tl fuzzy rough ideals on a ring in this paper we consider a ring as a universal set and study t fuzzy rough approximation operators with respect to a tl fuzzy ideal of a ring first some new properties of generalized t fuzzy rough approximation operators are obtained then a new fuzzy algebraic structure tl fuzzy rough ideal is defined and its properties investigated and finally the homomorphism of t fuzzy rough approximation operators is studied

ricci curvature bounds and einstein metrics on compact manifolds where f mo m1 is a homeomorphism and dil f is the dilatation of f given by dil f supx x2 dist f x f x2 dist x1 x2 if mo and m1 are not homeomorphic define dl mo mi oo gromov 20 proves the remarkable result that the space of compact riemannian manifolds f a 3 d of sectional curvature iki 3 0 and diameter dm v and diameter dm c iki dm vm1 in particular gromov s compactness theorem may be strengthened to the statement that f a v d is c1 l compact in the lipschitz topology in this paper we study the question of lipschitz convergence of compact riemannian manifolds with bounds imposed on the ricci curvature ric in

transparent boundary conditions for the harmonic diffraction problem in an elastic waveguide this work concerns the numerical finite element computation in the frequency domain of the diffracted wave produced by a defect crack inclusion perturbation of the boundaries etc located in a 3d infinite elastic waveguide the objective is to use modal representations to build transparent conditions on some artificial boundaries of the computational domain this cannot be achieved in a classical way due to non standard properties of elastic modes however a biorthogonality relation allows us to build an operator relating hybrid displacement stress vectors an original mixed formulation is then derived and implemented whose unknowns are the displacement field in the bounded domain and the normal component of the normal stresses on the artificial boundaries numerical validations are presented in the 2d case

roughness in n ary hypergroups this paper is aimed at studying the rough sets within the context of the commutative n ary hypergroups for this approach the presentation of a detailed study of the various types of n ary subhypergroups is of the greatest importance this study was initiated in v leoreanu fotea several types of n ary subhypergroups italian journal of pure and applied mathematics in press subsequently we shall use the findings in this study to define the upper and lower approximation of a subset with respect to an invertible n ary subhypergroup of a commutative n ary hypergroup in the final part the concept of n ary rough subhypergroup is introduced

rough set theory applied to lattice theory in this paper we intend to study a connection between rough sets and lattice theory we introduce the concepts of upper and lower rough ideals filters in a lattice then we offer some of their properties with regard to prime ideals filters the set of all fixed points compact elements and homomorphisms

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

rough variables with values in measurable spaces an x valued rough variable is introduced as a measurable function from a rough space to a measurable space x based on the concept of x valued rough variables some properties of x valued rough variables are studied furthermore the concept of convergence is presented and convergence of x valued rough variables is discussed

artificial boundary conditions for axisymmetric eddy current probe problems we study different strategies for the truncation of computational domains in the simulation of eddy current probes of elongated axisymmetric tubes for axial fictitious boundaries an exact dirichlet to neumann map is proposed and mathematically analyzed via a non selfadjoint spectral problem under general assumptions we show convergence of the solution to an eddy current problem involving a truncated dirichlet to neumann map to the solution on the entire unbounded axisymmetric domain as the truncation parameter tends to infinity under stronger assumptions on the physical parameters of the eddy current problem convergence rates are shown we further validate our theoretical results through numerical experiments for a realistic physical setting inspired by eddy current probes of nuclear reactor core tubes

the time harmonic maxwell equations in a doubly periodic structure abstract consider the diffraction of a beam of particles in r 3 when the dielectric coefficient is a constant e1 above a surface s and a different constant e2 below s and the magnetic permeability is constant throughout r 3 s is assumed to be a doubly periodic surface say z f x y with f x ml1 y nl2 f x y for integers m n the existence and uniqueness of a solution satisfying a radiation condition at infinity is reduced to a system of fredholm equations thus for all but a discrete set of e s there exists a unique solution

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

generalized lower and upper approximations in a ring in this paper the concepts of set valued homomorphism and strong set valued homomorphism of a ring are introduced and related properties are investigated the notions of generalized lower and upper approximation operators constructed by means of a set valued mapping which is a generalization of the notion of lower and upper approximation of a ring are provided we also propose the notion of generalized lower and upper approximations with respect to an ideal of a ring which is an extended notation of rough ideal introduced lately by davvaz b davvaz roughness in rings information science 164 2004 147 163 in a ring and discuss some significant properties of them

a finite element method with overlapping meshes for free boundary axisymmetric plasma equilibria in realistic geometries existing finite element implementations for the computation of free boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients as a consequence the location of critical points of the poloidal flux that are of paramount importance in tokamak engineering is constrained to nodes of the mesh leading to undesired jumps in transient problems moreover recent numerical results for the self consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map in this work we propose a mortar element method that employs two overlapping meshes one mesh with cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside the two meshes overlap in a narrow region this approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma while preserving accurate meshing of the geometric details outside this region the continuity of the numerical solution in the region of overlap is weakly enforced by a mortar like mapping

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