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

axiomatics for fuzzy rough sets abstract a fuzzy t rough set consists of a set x and a t similarity relation r on x where t is a lower semi continuous triangular norm we generalize the farinas prade definition for the upper approximation operator a i x i x of a fuzzy t rough set x r given originally for the special case t min to the case of arbitrary t we propose a new definition for the lower approximation operator a i x i x of x r our definition satisfies the two important identities a a a and a a a as well as a number of other interesting properties we provide axiomatics to fully characterize those upper and lower approximations

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

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

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

rough set theory applied to fuzzy ideal theory we use covers of the universal set to define approximation operators on the power set of the given set in section 1 we determine basic properties of the upper approximation operator and show how it can be used to give algebraic structural properties of certain subsets we define a particular cover on the set of ideals of a commutative ring with identity in such a way that both the concepts of the fuzzy prime spectrum of a ring and rough set theory can simultaneously be brought to bear on the study of fuzzy ideals of a ring

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

iteration complexity of first order augmented lagrangian methods for convex programming this paper considers a special class of convex programming cp problems whose feasible regions consist of a simple compact convex set intersected with an affine manifold we present first order methods for this class of problems based on an inexact version of the classical augmented lagrangian al approach where the subproblems are approximately solved by means of nesterov s optimal method we then establish a bound on the total number of nesterov s optimal iterations i e the inner iterations performed throughout the entire inexact al method to obtain a near primal dual optimal solution we also present variants with possibly better iteration complexity bounds than the original inexact al method which consist of applying the original approach directly to a perturbed problem obtained by adding a strongly convex component to the objective function of the cp problem

roughness of a fuzzy set an integration between the theories of fuzzy sets and rough sets has been attempted by providing a measure of roughness of a fuzzy set several properties of this new measure are established some of the possible applications for handling uncertainties in the field of pattern recognition are mentioned

a comparative study of fuzzy sets and rough sets this paper reviews and compares theories of fuzzy sets and rough sets two approaches for the formulation of fuzzy sets are reviewed one is based on many valued logic and the other is based on modal logic two views of rough sets are presented set oriented view and operator oriented view rough sets under set oriented view are closely related to fuzzy sets which leads to non truth functional fuzzy set operators both of them may be considered as deviations of classical set algebra in contrast rough sets under operator oriented view are different from fuzzy sets and may be regarded as an extension of classical set algebra

exploring isospectral spring mass systems with firefly algorithm this paper investigates in line spring mass systems an fixed at one end and free at the other with n degrees of freedom d f the objective is to find feasible in line systems b n that are isospectral to a given system the spring mass systems a n and b n are represented by jacobi matrices an error function is developed with the help of the jacobi matrices a n and b n the problem of finding the isospectral systems is posed as an optimization problem with the aim of minimizing the error function the approach for creating isospectral systems uses the fact that the trace of two isospectral jacobi matrices a n and b n should be identical a modification is made to the diagonal elements of the given jacobi matrix a n to create the isospectral systems the optimization problem is solved using the firefly algorithm augmented by a local search procedure numerical results are obtained and resulting isospectral systems are shown for 4 d f and 10 d f systems

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

relational interpretations of neighborhood operators and rough set approximation operators this paper presents a framework for the formulation interpretation and comparison of neighborhood systems and rough set approximations using the more familiar notion of binary relations a special class of neighborhood systems called 1 neighborhood systems is introduced three extensions of pawlak approximation operators are analyzed properties of neighborhood and approximation operators are studied and their connections are examined

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

constructive and axiomatic approaches of fuzzy approximation operators this paper presents a general framework for the study of rough set approximation operators in fuzzy environment in which both constructive and axiomatic approaches are used in constructive approach a pair of lower and upper generalized fuzzy rough and rough fuzzy respectively approximation operators is first defined the representations of both fuzzy rough approximation operators and rough fuzzy approximation operators are then presented the connections between fuzzy and crisp respectively relations and fuzzy rough and rough fuzzy respectively approximation operators are further established in axiomatic approach various classes of fuzzy approximation operators are characterized by different sets of axioms the minimal axiom sets of fuzzy approximation operators guarantee the existence of certain types of fuzzy or crisp relations producing the same operators

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

some properties of generalized rough sets some algebraic and topological properties of generalized rough sets associated with generalized lower and upper approximations are studied generalized definable sets give rise to two topological spaces degree of accuracy dag for generalized rough sets induces two types of equivalence relations one is defined on x whereas the other is defined on p y both of these relations strictly manage an order in classes of x and p y it has been shown that dag induces two types of fuzzy subsets one of the set x and the other of p y finally some properties of these fuzzy sets have been discussed

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 approximations on a complete completely distributive lattice with applications to generalized rough sets the generalizations of rough sets considered with respect to similarity relation covers and fuzzy relations are main research topics of rough set theory however these generalizations have shown less connection among each other and have not been brought into a unified framework which has limited the in depth research and application of rough set theory in this paper the complete completely distributive ccd lattice is selected as the mathematical foundation on which definitions of lower and upper approximations that form the basic concepts of rough set theory are proposed these definitions result from the concept of cover introduced on a ccd lattice and improve the approximations of the existing crisp generalizations of rough sets with respect to similarity relation and covers when t similarity relation is considered the existing fuzzy rough sets are the special cases of our proposed approximations on a ccd lattice thus these generalizations of rough sets are brought into a unified framework and a wider mathematical foundation for rough set theory is established

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

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 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

generalized fuzzy rough sets this paper presents a general framework for the study of fuzzy rough sets in which both constructive and axiomatic approaches are used in constructive approach a pair of lower and upper generalized approximation operators is defined the connections between fuzzy relations and fuzzy rough approximation operators are examined in axiomatic approach various classes of fuzzy rough approximation operators are characterized by different sets of axioms axioms of fuzzy approximation operators guarantee the existence of certain types of fuzzy relations producing the same operators

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

inverse vibration problem for un damped 3 dimensional multi story shear building models various researchers have contributed to the identification of the mass and stiffness matrices of two dimensional 2 d shear building structural models for a given set of vibratory frequencies the suggested methods are based on the specific characteristics of the jacobi matrices i e symmetric tri diagonal and semi positive definite matrices however in case of three dimensional 3 d structural models those methods are no longer applicable since their stiffness matrices are not tri diagonal in this paper the inverse problem for a special class of vibratory structural systems i e 3 d shear building models is investigated a practical algorithm is proposed for solving the inverse eigenvalue problem for un damped 3 d shear buildings the problem is addressed in two steps first using the target frequencies a so called normalized eigenvector matrix which is a banded matrix containing the information related to the frequencies and mode shapes of the target structural system is determined in this regard similar to the solution of inverse problem for 2 d shear building structural models in which an auxiliary structure is constructed by adding constraints or springs to the original system three auxiliary structures are proposed to solve the problem for 3 d cases in the second step the normalized eigenvector matrix is utilized to obtain the normalized stiffness matrix in turn this matrix is decomposed into the stiffness and mass matrices of the system finally a numerical example is presented to demonstrate the efficiency of the proposed algorithm in determining the mass and stiffness matrices of a 3 d structural model for a given set of target vibrational frequencies

general isospectral flows for linear dynamic systems the matrix a a0 a1 2a2 kak lal with matrix coefficients a0 a1 a2 al cm n defines a linear dynamic system of dimension m n when m n and when det a 0 for some values of the eigenvalues of this system are well defined a one parameter trajectory of such a system a0 a1 a2 al is an isospectral flow if the eigenvalues and the dimensions of the associated eigenspaces are the same for all parameter values ir this paper presents the most general form for isospectral flows of linear dynamic systems of orders l 2 3 4 and the forms for isospectral flows for even higher order systems are evident from the patterns emerging based on the definition of a class of coordinate transformations called structure preserving transformations the concept of isospectrality and the associated flows is seen to extend to cases where m n

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

an inverse problem for a functionally graded elliptical plate with large deflection and slightly disturbed boundary this paper deals with the inverse problem of a functionally graded material fgm elliptical plate with large deflection and disturbed boundary under uniform load the properties of functionally graded material are assumed to vary continuously through the thickness of the plate and obey a simple power law expression based on the volume fraction of the constituents based on the classical nonlinear von karman plate theory the governing equations of a thin plate with large deflection were derived in order to solve this non classical problem a perturbation technique was employed on displacement terms in conjunction with taylor series expansion of the disturbed boundary conditions the displacements of in plane and transverse are obtained in a non dimensional series expansion form with respect to center deflection of the plate the approximate solutions of displacements are solved for the first three terms and the corresponding internal stresses can also be obtained

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

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

inverse spectral theory of finite jacobi matrices we solve the following physically motivated problem to determine all finite jacobi matrices j and corresponding indices i j such that the green s function is proportional to an arbitrary prescribed function f z our approach is via probability distributions and orthogonal polynomials we introduce what we call the auxiliary polynomial of a solution in order to factor the map j i j where square brackets denote the equivalence class consisting of scalar multiples this enables us to construct the solution set as a fibration over a connected semi algebraic coordinate base the end result is a wealth of explicit constructions for jacobi matrices these reveal precise geometric information about the solution set and provide the basis for new existence theorems

generalized rough sets based on relations rough set theory has been proposed by pawlak as a tool for dealing with the vagueness and granularity in information systems the core concepts of classical rough sets are lower and upper approximations based on equivalence relations this paper studies arbitrary binary relation based generalized rough sets in this setting a binary relation can generate a lower approximation operation and an upper approximation operation but some of common properties of classical lower and upper approximation operations are no longer satisfied we investigate conditions for a relation under which these properties hold for the relation based lower and upper approximation operations

an axiomatic characterization of a fuzzy generalization of rough sets in rough set theory the lower and upper approximation operators defined by a fixed binary relation satisfy many interesting properties several authors have proposed various fuzzy generalizations of rough approximations in this paper we introduce the definitions for generalized fuzzy lower and upper approximation operators determined by a residual implication then we find the assumptions which permit a given fuzzy set theoretic operator to represent a upper or lower approximation derived from a special fuzzy relation different classes of fuzzy rough set algebras are obtained from different types of fuzzy relations and different sets of axioms of fuzzy set theoretic operator guarantee the existence of different types of fuzzy relations which produce the same operator finally we study the composition of two approximation spaces it is proved that the approximation operators in the composition space are just the composition of the approximation operators in the two fuzzy approximation spaces

inverse structural modification using constraints in a structural modification problem the mass and stiffness matrices are modified to obtain a desired spectrum in this paper this is done by imposing constraints on the structure the undamped natural vibrations of a constrained linear structure are calculated by solving a generalized eigenvalue problem derived from the equations of motion for the constrained system involving lagrangian multipliers the coefficients of the constraint matrix are taken as design variables and a set of equations defining the inverse structural modification problem is formulated this modification problem requires an iterative method for its solution an algorithm based on newton s method is employed each iteration step involves the calculation of a rectangular jacobian and the solving of an associated underdetermined system of linear equations the system can be solved by using the moore penrose inverse the method is demonstrated in some numerical examples

on the reconstruction of a damped vibrating system from two complex spectra part 1 theory abstract the paper concerns an n degree of freedom damped vibrating system consisting ofn 1 masses connected in parallel by springs and dampers to an n th mass the paper analyzes the construction of such a system from the given complex eigenvalue data the analysis has two parts the establishment of the conditions on the eigenvalues which ensure that they correspond to an actual system the derivation of the system parameters from the eigenvalues

topological approaches to covering rough sets rough sets a tool for data mining deal with the vagueness and granularity in information systems this paper studies covering based rough sets from the topological view we explore the topological properties of this type of rough sets study the interdependency between the lower and the upper approximation operations and establish the conditions under which two coverings generate the same lower approximation operation and the same upper approximation operation lastly axiomatic systems for the lower approximation operation and the upper approximation operation are constructed

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 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

rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations abstract in this paper we initially present and compile the tools and theories that are necessary for a rough set analysis of a general type of fuzzy data from this study we have developed two original contributions that can enhance the application of fuzzy rough sets techniques to data that may be affected by several sources of uncertainty in its measurement process for this type of analysis we have first considered the construction of homogeneous granules in which reflexivity symmetry and a certain transitivity property are satisfied this has encouraged us to study the application of t similarity relations in this framework and to examine the available theorems that permit us to aggregate this type of relations as a part of this study we have also developed a new theorem that allows us to use the dual of the generalized means as an aggregation operator in the fuzzy rough sets context another theoretical development that tries to respond to a practical problem is the concept of precision aggregation we use this new notion to export ziarko s variable precision rough set model to the analysis of fuzzy data a generalization that becomes a necessity for the fuzzy rough sets analysis of large databases the utility of this approach is demonstrated with an application example in the vehicle database donated by the turing institute

reduction and axiomization of covering generalized rough sets this paper investigates some basic properties of covering generalized rough sets and their comparison with the corresponding ones of pawlak s rough sets a tool for data mining the focus here is on the concepts and conditions for two coverings to generate the same covering lower approximation or the same covering upper approximation the concept of reducts of coverings is introduced and the procedure to find a reduct for a covering is given it has been proved that the reduct of a covering is the minimal covering that generates the same covering lower approximation or the same covering upper approximation so this concept is also a technique to get rid of redundancy in data mining furthermore it has been shown that covering lower and upper approximations determine each other finally a set of axioms is constructed to characterize the covering lower approximation operation

neighborhood operator systems and approximations this paper presents a framework for the study of generalizing the standard notion of equivalence relation in rough set approximation space with various categories of k step neighborhood systems based on a binary relation on a finite universe six families of binary relations are obtained and the corresponding six classes of k step neighborhood systems are derived extensions of pawlak s rough set approximation operators based on such neighborhood systems are proposed properties of neighborhood operator systems and rough set approximation operators are investigated and their connections are examined

rough matroids based on relations rough sets provide an efficient tool for attribute reduction and rule extraction however many important problems in rough set theory including attribute reduction are np hard and therefore the algorithms for solving them are usually greedy as a generalization of linear independence in vector spaces matroids have wide applications in diverse fields particularly in greedy algorithm design in this paper we propose an integration of rough sets and matroids to exploit the advantages of both theories specifically we present definitions of lower and upper rough matroids based on relations from the viewpoint of approximation operators it is interesting that lower rough matroids based on partial orders coincide with poset matroids which are a well known generalization of matroids a matroid is represented by the lower rough matroid based on both a partial order and an equivalence relation lower and upper rough matroids based on equivalence relations coincide with each other finally we present some special types of examples of rough matroids from the viewpoints of approximations and graphs these interesting results demonstrate the potential for the combination between rough sets and matroids

a rst a generalization of rough set theory the paper presents a transition from the crisp rough set theory to a fuzzy one called alpha rough set theory or in short a rst all basic concepts or rough set theory are extended i e information system indiscernibility dependency reduction core definability approximations and boundary the resulted theory takes into account fuzzy data and allows the approximation of fuzzy concepts besides the control of knowledge granularity is natural in a rst which is based on a parameterized indiscernibility relation a rst is developed to recognize non deterministic relationships using notions as a dependency a reduct and so forth on the other hand we introduce a notion of relative dependency as an alternative of the absolute definibility presented in rough set theory the extension a rst leads naturally to the new concept of alpha rough sets which represents sets with fuzzy non empty boundaries 2000 elsevier science inc all rights reserved

on the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean in this paper we analyze the iteration complexity of the hybrid proximal extragradient hpe method for finding a zero of a maximal monotone operator recently proposed by solodov and svaiter one of the key points of our analysis is the use of new termination criteria based on the varepsilon enlargement of a maximal monotone operator the advantage of using these termination criteria is that their definition do not depend on the boundedness of the domain of the operator we then show that korpelevich s extragradient method for solving monotone variational inequalities falls in the framework of the hpe method as a consequence using the complexity analysis of the hpe method we obtain new complexity bounds for korpelevich s extragradient method which do not require the feasible set to be bounded as assumed in a recent paper by nemirovski another feature of our analysis is that the derived iteration complexity bounds are proportional to the distance of the initial point to the solution set the hpe framework is also used to obtain the first iteration complexity result for tseng s modified forward backward splitting method for finding a zero of the sum of a monotone lipschitz continuous map with an arbitrary maximal monotone operator whose resolvent is assumed to be easily computable also using the framework of the hpe method we study the complexity of a variant of a newton type extragradient algorithm proposed by solodov and svaiter for finding a zero of a smooth monotone function with lipschitz continuous jacobian

rough sets and boolean reasoning abstract in this article we discuss methods based on the combination of rough sets and boolean reasoning with applications in pattern recognition machine learning data mining and conflict analysis

rudiments of rough sets abstract worldwide there has been a rapid growth in interest in rough set theory and its applications in recent years evidence of this can be found in the increasing number of high quality articles on rough sets and related topics that have been published in a variety of international journals symposia workshops and international conferences in recent years in addition many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs rough set theory has led to many interesting applications and extensions it seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences especially in research areas such as machine learning intelligent systems inductive reasoning pattern recognition mereology knowledge discovery decision analysis and expert systems in the article we present the basic concepts of rough set theory and point out some rough set based research directions and applications

inverse finite element vibration problems the paper concerns the reconstruction of a consistent fem model of an in line system of 2 dof elements fixed at one end and free at the other such a system has tridiagonal stiffness and mass matrices k m because each element has one rigid body mode khas negative codiagonal and is constrained to have a particular form mhas positive codiagonal it is shown how to construct an infinite family of such models so that each has a specified undamped frequency response at the free end and how to construct a system with a damper at the free end so that the system has specified complex eigenvalues

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

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

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

inheritance examples of algebraic hyperstructures algebraic hyperstructures represent a natural extension of classical algebraic structures in a classical algebraic structure the composition of two elements is an element while in an algebraic hyperstructure the composition of two elements is a set algebraic hyperstructure theory has many applications in other disciplines the main purpose of this paper is to provide examples of hyperstructures associated with inheritance

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