practical reliable bayesian recognition of 2d and 3d objects using implicit polynomials and algebraic invariants we treat the use of more complex higher degree polynomial curves and surfaces of degree higher than 2 which have many desirable properties for object recognition and position estimation and attack the instability problem arising in their use with partial and noisy data the scenario discussed in this paper is one where we have a set of objects that are modeled as implicit polynomial functions or a set of representations of classes of objects with each object in a class modeled as an implicit polynomial function stored in the database then given partial data from one of the objects we want to recognize the object or the object class or collect more data in order to get better parameter estimates for more reliable recognition two problems arising in this scenario are discussed 1 the problem of recognizing these polynomials by comparing them in terms of their coefficients and 2 the problem of where to collect data so as to improve the parameter estimates as quickly as possible we use an asymptotic bayesian approximation for solving the two problems the intrinsic dimensionality of polynomials and the use of the mahalanobis distance are discussed

topologically faithful fitting of simple closed curves implicit representations of curves have certain advantages over explicit representation one of them being the ability to determine with ease whether a point is inside or outside the curve inside outside functions however save for some special cases it is not known how to construct implicit representations which are guaranteed to preserve the curve s topology as a result points may be erroneously classified with respect to the curve the paper offers to overcome this problem by using a representation which is guaranteed to yield the correct topology of a simple closed curve by using homeomorphic mappings of the plane to itself if such a map carries the curve onto the unit circle then a point is inside the curve if and only if its image is inside the unit circle

on some types of fuzzy covering based rough sets fuzzy coverings are a natural extension of the coverings by replacing crisp sets with fuzzy sets recently an excellent introduction to the definition of a fuzzy covering is due to ma and two fuzzy covering based rough set models are presented in this paper by introducing some new definitions of fuzzy covering approximation spaces the properties of fuzzy covering approximation spaces and ma s fuzzy covering based rough set models are studied furthermore three new types of fuzzy covering based rough set models as generalizations of ma s models are first proposed in this paper first some properties of fuzzy covering and its fuzzy neighborhood family are proposed we present a necessary and sufficient condition for fuzzy neighborhood family induced by a fuzzy covering to be equal to the fuzzy covering itself then we study the characterizations of ma s fuzzy covering based rough set models and give a necessary and sufficient condition for two fuzzy coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation finally this paper proposes three new types of fuzzy covering based rough set models by introducing a new notion of a fuzzy complementary neighborhood

a comparison of two kinds of definitions of rough approximations based on a similarity relation in the present paper we investigate the three types of yao s lower and upper approximations of any set with respect to any similarity relation these types based on a right neighborhood also we define and investigate other three types of approximations for any similarity relations these new types based on the intersection of the right neighborhoods moreover we give a comparison between these types lastly the relationship between these definitions is introduced

quantitative analysis for covering based rough sets through the upper approximation number coverings are a useful form of data while covering based rough sets provide an effective tool for dealing with this data covering based rough sets have been widely used in attribute reduction and rule extraction however few quantitative analyses for covering based rough sets have been conducted while many advances for classical rough sets have been obtained through quantitative tools in this paper the upper approximation number is defined as a measurement to quantify covering based rough sets and a pair of upper and lower approximation operators are constructed using the approximation number the operators not only inherit some important properties of existing approximation operators but also exhibit some new quantitative characteristics it is interesting to note that the upper approximation number of a covering approximation space is similar to the dimension of a vector space or the rank of a matrix

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

extensions and intentions in the rough set theory abstract the approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension it is different from the well known approaches in the literature in that the upper approximations and the lower approximations of unknown sets are considered as certain families of known sets this approach makes it possible to formulate necessary and sufficient conditions for the existence of operations on rough sets which are analogous to classical operations on sets the basic results presented in this paper based on certain ideas of the second author were formulated by the first author in his doctoral dissertation prepared under the supervision of the third author

classification of coverings in the finite approximation spaces based on the notions of neighborhood and complementary neighborhood we consider the classification of coverings in the covering rough set theory we present a classification rule under which the coverings on a universe u are classified such that for any given pair of neighborhood or complementary neighborhood based lower and upper approximation operators on u all the different coverings in the same class generate the same pair of lower and upper approximations of each x u we show that there is a one to one correspondence between the equivalence classes of coverings and the topologies of the universe thus the number of the equivalence classes of coverings is equal to the number of topologies of the universe and therefore this number is much smaller than that of the coverings we also give an illustrative example to show how we can classify some given coverings by calculating the topologies moreover based on the relationship between the neighborhood and the complementary neighborhood we find that each class of coverings has a dual class and each pair of approximation operators has a dual pair of approximation operators for a finite universe considering one pair of approximation operators under one equivalence class of coverings is equivalent to considering its dual approximation operator pair under the dual class of coverings finally we also present a sufficient condition under which for any given pair of neighborhood based lower and upper approximation operators two coverings of the universe u generate the same pair of approximations of each x u if and only if they belong to the same equivalence class

graph and matrix approaches to rough sets through matroids abstract rough sets are efficient for attribute reduction and rule extraction in data mining however many important problems including attribute reduction in rough sets are np hard therefore the algorithms to solve them are often greedy matroids generalized from linear independence in vector spaces provide well established platforms for greedy algorithm design in this paper we use graph and matrix approaches to study rough sets through matroids first we construct an isomorphism from equivalence relations to 2 circuit matroids and then propose graph representations of lower and upper approximations through the graphic matroid we also study graph representations of lower and upper approximations by that of the dual of the matroid second in light of the fact that the relational matrix is a representable matrix of the matroid induced by an equivalence relation matrix representations of lower and upper approximations are obtained with the representable matrix of the matroid in a word borrowing from matroids this work presents two interesting views graph and matrix ones to investigate rough sets

impulsive effects on stability of cohen grossberg neural networks with variable delays in this paper a model of impulsive cohen grossberg neural networks is first formulated by establishing some impulsive differential inequalities we investigate impulsive effects on the stability of cohen grossberg neural networks with variable delays and obtain some sufficient conditions ensuring global exponential stability of the impulsive delay system our criteria not only show that the stability still remains under certain impulsive perturbations for some continuous stable neural networks but also present an approach to stabilize the unstable neural networks by utilizing impulsive effects the results extend and improve some recent works for impulsive neural networks as well as non impulsive neural networks some examples and their simulations are given for illustration of the theoretical results

robust segmentation of primitives from range data in the presence of geometric degeneracy this paper addresses a common problem in the segmentation of range images we present methods for the least squares fitting of spheres cylinders cones and tori to 3d point data and their application within a segmentation framework least squares fitting of surfaces other than planes even of simple geometric type has rarely been studied our main application areas of this research are reverse engineering of solid models from depth maps and automated 3d inspection where reliable extraction of these surfaces is essential our fitting method has the particular advantage of being robust in the presence of geometric degeneracy i e as the principal curvatures of the surfaces being fitted decrease the results returned naturally become closer and closer to those surfaces of simpler type i e planes cylinders cones or spheres which best describe the data many other methods diverge because in such cases various parameters or their combination become infinite

relationships among generalized rough sets in six coverings and pure reflexive neighborhood system rough set is a useful tool to deal with partition related uncertainty granularity and incompleteness of knowledge although the classical rough set is constructed on the basis of an indiscernibility relation it can also be generalized by using some weaker binary relations in this paper a systematic approach is used to study the generalized rough sets in six coverings and pure reflexive neighborhood system after two steps relationships among generalized rough sets in six coverings and pure reflexive neighborhood system are obtained the first step is to study the generalized rough sets in six coverings and to get relationships between every two covering rough set models the second step is to study the relationships between generalized rough sets in each covering and in pure reflexive neighborhood system the inclusion relations or equivalence relations among the seven upper lower approximations could be acquired finally the accuracy measures of generalized rough sets in six coverings and that in pure reflexive neighborhood system are compared the relationships among seven accuracy measures are also obtained some illustrative examples are employed to demonstrate our arguments

stability analysis and design of impulsive control systems with time delay a class of impulsive control systems with time varying delays is considered by establishing an impulsive delay differential inequality we analyze the global exponential stability of the impulsive delay systems and estimate the exponential convergence rate on the basis of the analysis a design procedure of impulsive controller is presented the designed impulsive controller not only can globally exponentially stabilize the time delay systems but also can control the exponential convergence rate of the systems two numerical examples are given to illustrate the effectiveness of the method

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

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

characterizations of coverings for upper approximation operators being closure operators in this paper we define two conditions of symmetry for the covering c in a covering based approximation space u c by using these conditions and the triangle chain condition we give general topological and intuitive characterizations of the covering c for three types of covering based upper approximation operators being closure operators we also give descriptions of u c in terms of information exchange systems when these operators are closure operators these results answer an open problem raised in ge et al 2012 as an example application of our characterizations we discuss the problem of implications among conditions for different types of covering based upper approximation operators being closure operators

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

fitting curves and surfaces with constrained implicit polynomials a problem which often arises while fitting implicit polynomials to 2d and 3d data sets is the following although the data set is simple the fit exhibits undesired phenomena such as loops holes extraneous components etc previous work tackled these problems by optimizing heuristic cost functions which penalize some of these topological problems in the fit the paper suggests a different approach to design parameterized families of polynomials whose zero sets are guaranteed to satisfy certain topological properties namely we construct families of polynomials with star shaped zero sets as well as polynomials whose zero sets are guaranteed not to intersect an ellipse circumscribing the data or to be entirely contained in such an ellipse this is more rigorous than using heuristics which may fail and result in pathological zero sets the ability to parameterize these families depends heavily on the ability to parameterize positive polynomials to achieve this we use some powerful results from real algebraic geometry

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

quick attribute reduct algorithm for neighborhood rough set model abstract in this paper we propose an efficient quick attribute reduct algorithm based on neighborhood rough set model in this algorithm we divide the objects records of the whole data set into a series of buckets based on their euclidean distances and then iterate each record by the sequence of buckets to calculate the positive region of neighborhood rough set model we also prove that each record s neighborhood elements can only be contained in its own bucket and its adjacent buckets thus it can reduce the iterations greatly based on the division of buckets we then present a new fast algorithm to calculate the positive region of neighborhood rough set model which can achieve a complexity of o m u m is the number of attributes u is the number of records containing in the data set furthermore with the new fast positive region computation algorithm we present a quick reduct algorithm for neighborhood rough set model and our algorithm can achieve a complexity of o m 2 u at last the efficiency of this quick reduct algorithm is proved by comparable experiments and especially this algorithm is more suitable for the reduction of big data

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

multigranulation rough sets from partition to covering the classical multigranulation rough set mgrs theory offers a formal theoretical framework for solving the complex problem under multigranulation environment however it is noticeable that mgrs theory cannot be applied in multi source information systems with a covering environment in the real world to address this issue we firstly present in this paper three types of covering based multigranulation rough sets in which set approximations are defined by different covering approximation operators then by using two different approximation strategies i e seeking common reserving difference and seeking common rejecting difference two kinds of covering based multigranulation rough set are presented namely a covering based optimistic multigranulation rough set and a covering based pessimistic multigranulation rough sets finally we develop some properties and several uncertainty measures of the covering based multigranulation rough sets these results will enrich the mgrs theory and enlarge its application scope

semi monolayer cover rough set concept property and granular algorithm abstract rough set theory is known as a powerful tool for dealing with incomplete inconsistent and insufficient information in decision making with the constraint that each set of cover has at least one reliable element the semi monolayer cover smc is a special neighborhood system defined on the universe between the partition and regular cover more similar to pawlak approximation operators than cover approximation operators smc approximation operators have some interesting properties such as the equivalent granular forms the cross duality etc in this paper we define four pairs of smc rough approximation operators namely gc gu de and da and then discuss their properties and relations it has been proven that 1 gu is the equivalent granular form approximation operator of de 2 de and da are two pairs of cross dual approximation operators that is to say that upper de and lower da lower de and upper da are two pairs of dual approximation operators the equivalent relation and cross dual relation serve as a bridge connecting granular form approximation operators with the dot form ones 3 a de or da approximation set can be rebuilt by the corresponding gc approximation set and an smc mapping the equivalent granular form of de and da gives rise to some advanced algorithms that improve the efficiency of calculating de and da approximation sets experimental results on a uci data set show the granular algorithm achieves better performance than the basic dot algorithm and the speedup of efficiency tends to be exponential with the size of universe

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

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

stable fitting of 2d curves and 3d surfaces by implicit polynomials this work deals with fitting 2d and 3d implicit polynomials ips to 2d curves and 3d surfaces respectively the zero set of the polynomial is determined by the ip coefficients and describes the data the polynomial fitting algorithms proposed in this paper aim at reducing the sensitivity of the polynomial to coefficient errors errors in coefficient values may be the result of numerical calculations when solving the fitting problem or due to coefficient quantization it is demonstrated that the effect of reducing this sensitivity also improves the fitting tightness and stability of the proposed two algorithms in fitting noisy data as compared to existing algorithms like the well known 3l and gradient one algorithms the development of the proposed algorithms is based on an analysis of the sensitivity of the zero set to small coefficient changes and on minimizing a bound on the maximal error for one algorithm and minimizing the error variance for the second simulation results show that the proposed algorithms provide a significant reduction in fitting errors particularly when fitting noisy data of complex shapes with high order polynomials as compared to the performance obtained by the above mentioned existing algorithms

topological characterizations of covering for special covering based upper approximation operators the relationships among properties of covering approximation operators and their corresponding coverings have attracted intensive research in recent years in particular those among topological properties have drawn special attention because of their important applications in rough set theory in this paper we give topological characterizations of covering c for covering based upper approximation operators fh sh th and rh to be closure operators we also give intuitive characterizations of covering c and describe covering based approximation space u c as certain types of information exchange systems when sh or rh is a closure operator by applying our new characterizations we give inequalities about the relationship between the number of members in c and the number of elements in u and discuss relationships among conditions for different covering based upper approximation operators to be closure operators to the best of our knowledge it is the first time that such characterizations descriptions inequalities and discussions are systematically considered in the literature of rough set theory furthermore in this paper we also give several characterizations of unary coverings an important type of coverings in studying relationships among basic concepts in covering based rough sets by the relationships among different types of covering base approximation operators

using geometric distance fits for 3 d object modeling and recognition addresses the problems of automatically constructing algebraic surface models from sets of 2d and 3d images and using these models in pose computation motion and deformation estimation and object recognition we propose using a combination of constrained optimization and nonlinear least squares estimation techniques to minimize the mean squared geometric distance between a set of points or rays and a parameterized surface in modeling tasks the unknown parameters are the surface coefficients while in pose and deformation estimation tasks they represent the transformation which maps the observer s coordinate system onto the modeled surface s own coordinate system we have applied this approach to a variety of real range computerized tomography and video images

implicit polynomial representation through a fast fitting error estimation this paper presents a simple distance estimation for implicit polynomial fitting it is computed as the height of a simplex built between the point and the surface i e a triangle in 2 d or a tetrahedron in 3 d which is used as a coarse but reliable estimation of the orthogonal distance the proposed distance can be described as a function of the coefficients of the implicit polynomial moreover it is differentiable and has a smooth behavior hence it can be used in any gradient based optimization in this paper its use in a levenberg marquardt framework is shown which is particularly devoted for nonlinear least squares problems the proposed estimation is a generalization of the gradient based distance estimation which is widely used in the literature experimental results both in 2 d and 3 d data sets are provided comparisons with state of the art techniques are presented showing the advantages of the proposed approach

linear programming fitting of implicit polynomials a new implicit polynomial ip fitting method is presented it provides a different way of viewing the ip fitting problem from those of the nonlinear optimization approaches it requires less computation and can be done automatically or interactively linear programming is used to do the fitting the approach can incorporate a variety of distance measures and global geometric constraints

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

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

robust exponential stability of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays this paper is concerned with the problem of exponential stability for a class of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays and known or unknown parameters the jumping parameters are determined by a continuous time discrete state markov chain and the mixed time delays under consideration comprise both time varying delays and continuously distributed delays to the best of the authors knowledge till now the exponential stability problem for this class of generalized neural networks has not yet been solved since continuously distributed delays are considered in this paper the main objective of this paper is to fill this gap by constructing a novel lyapunov krasovskii functional and using some new approaches and techniques several novel sufficient conditions are obtained to ensure the exponential stability of the trivial solution in the mean square the results presented in this paper generalize and improve many known results finally two numerical examples and their simulations are given to show the effectiveness of the theoretical results

on recognizing and positioning curved 3 d objects from image contours an approach for explicitly relating the shape of image contours to models of curved three dimensional objects is presented this relationship is used for object recognition and positioning object models consist of collections of parametric surface patches and their intersection curves this includes nearly all representations used in computer aided geometric design and computer vision the image contours considered are the projections of surface discontinuities and occluding contours elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection this equation is parameterized by the object s position and orientation with respect to the observer determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points the proposed approach readily extends to parameterized models it has been implemented for a simple world composed of various surfaces of revolution and tested on several real images

the fourth type of covering based rough sets as a technique for granular computing rough sets deal with the vagueness and granularity in information systems covering based rough sets have been proposed to generalize this theory for wider application three types of covering based rough sets have been studied for different situations to make the theory more complete this paper proposes a fourth type of covering based rough sets compared with the existing ones the new type shows its special characteristic in the interdependency between its lower and upper approximations we carry out a systematical study of this new theory first we discuss basic properties such as normality contraction and monotone then we investigate the conditions for this type of covering based rough sets to satisfy the properties of pawlak s rough sets and study the interdependency between the lower and upper approximation operations in addition axiomatic systems for the lower and upper approximation operations are established lastly we address the relationships between this type of covering based rough sets and the three existing ones

pinning distributed synchronization of stochastic dynamical networks a mixed optimization approach this paper is concerned with the problem of pinning synchronization of nonlinear dynamical networks with multiple stochastic disturbances two kinds of pinning schemes are considered 1 pinned nodes are fixed along the time evolution and 2 pinned nodes are switched from time to time according to a set of bernoulli stochastic variables using lyapunov function methods and stochastic analysis techniques several easily verifiable criteria are derived for the problem of pinning distributed synchronization for the case of fixed pinned nodes a novel mixed optimization method is developed to select the pinned nodes and find feasible solutions which is composed of a traditional convex optimization method and a constraint optimization evolutionary algorithm for the case of switching pinning scheme upper bounds of the convergence rate and the mean control gain are obtained theoretically simulation examples are provided to show the advantages of our proposed optimization method over previous ones and verify the effectiveness of the obtained results

invariant descriptors for 3d object recognition and pose invariant descriptors are shape descriptors that are unaffected by object pose by perspective projection or by the intrinsic parameters of the camera these descriptors can be constructed using the methods of invariant theory which are briefly surveyed a range of applications of invariant descriptors in 3d model based vision is demonstrated first a model based vision system that recognizes curved plane objects irrespective of their pose is demonstrated curves are not reduced to polyhedral approximations but are handled as objects in their own right models are generated directly from image data once objects have been recognized their pose can be computed invariant descriptors for 3d objects with plane faces are described all these ideas are demonstrated using images of real scenes the stability of a range of invariant descriptors to measurement error is treated in detail

approximation operators on complete completely distributive lattices rough set a tool for data mining deals with the vagueness and granularity in information systems in 2006 chen et al initiated the study of rough approximations on a complete completely distributive lattice ccd lattice for short and brought generalizations of rough sets into a unified framework in this paper we discuss the approximation operators on a ccd lattice based on the concept of neighborhood three kinds of upper approximation operators and a kind of lower approximation operator are constructed basic properties of lower and upper approximation operators are examined furthermore the relationships among these operators are analyzed

estimator design for discrete time switched neural networks with asynchronous switching and time varying delay this brief deals with the estimator design problem for discrete time switched neural networks with time varying delay one main problem is the asynchronous mode switching between the neuron state and the estimator our goal is to design a mode dependent estimator for the switched neural networks under average dwell time switching such that the estimation error system is exponentially stable with a prescribed l2 gain in the h sense from the noise signal to the estimation error a new lyapunov functional is constructed that may increase during the mismatched switchings new results on the stability and l2 gain analysis are then obtained the admissible estimator gains are computed by solving a set of linear matrix inequalities the relations among the switching law the maximal delay upper bound and the optimal h disturbance attenuation level are established the effectiveness of the proposed design method is finally illustrated by a numerical example

constructive and algebraic methods of the theory of rough sets this paper reviews and compares constructive and algebraic approaches in the study of rough sets in the constructive approach one starts from a binary relation and defines a pair of lower and upper approximation operators using the binary relation different classes of rough set algebras are obtained from different types of binary relations in the algebraic approach one defines a pair of dual approximation operators and states axioms that must be satisfied by the operators various classes of rough set algebras are characterized by different sets of axioms axioms of approximation operators guarantee the existence of certain types of binary relations producing the same operators

covering rough set structures for a locally finite covering approximation space abstract the purpose of this paper is to introduce the notion of locally finite covering approximation lfc for brevity space u c which is a generalization of a finite covering approximation space furthermore for a subset x of the universe u we develop two kinds of neighborhood systems derived from the covering c specifically k1 x and k2 x which are not comparable with each other next the paper establishes two topologies on u alexandroff and quasi discrete topologies generated by systems k1 x and k2 x as bases respectively after suggesting many examples explaining the above notions and systems we develop two new types of rough set structures an h rough set operator h h and a khalimsky k for short topological rough set operator d k d k the present paper investigates various properties of these operators and refers to certain advantages of them which can be used in applied science including digital geometry information geometry computer vision pattern recognition image processing and so on in order to accomplish this we use some tools such as granulations neighborhood systems typical pawlak s tools related topologies rough set structures associated with the k topology and so on furthermore through this work we can obtain strong connections between covering rough set theory and applied geometry in the present paper all sets u c and x u need not be finite

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 neighborhood operators and derived fuzzy coverings abstract fuzzy coverings are natural extensions of the coverings by replacing crisp sets with fuzzy sets recently some fuzzy neighborhood operators based on a fuzzy covering were defined and their properties were investigated by d eer et al in this paper we propose four types of fuzzy neighborhood operators by introducing the notions such as neighborhood system fuzzy minimal description and fuzzy maximal description first we propose these notions and investigate their properties then we construct four types of fuzzy neighborhood operators based on the fuzzy coverings properties and relationship among these four types of fuzzy neighborhood operators are studied finally six types of fuzzy coverings were derived by using these four types of fuzzy neighborhood operators and their properties are considered

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

knowledge reduction of dynamic covering decision information systems when varying covering cardinalities in covering based rough set theory non incremental approaches are time consuming for performing knowledge reduction of dynamic covering decision information systems when the cardinalities of coverings change as a result of object immigration and emigration because computing approximations of sets is an important step for knowledge reduction of dynamic covering decision information systems efficient approaches to calculating the second and sixth lower and upper approximations of sets using the type 1 and type 2 characteristic matrices respectively are essential in this paper we provide incremental approaches to computing the type 1 and type 2 characteristic matrices of dynamic coverings whose cardinalities vary with the immigration and emigration of objects we also design incremental algorithms to compute the second and sixth lower and upper set approximations experimental results demonstrate that the incremental approaches effectively improve the efficiency of set approximation computation finally we employ several examples to illustrate the feasibility of the incremental approaches for knowledge reduction of dynamic covering decision information systems when increasing the cardinalities of coverings

parameterized families of polynomials for bounded algebraic curve and surface fitting interest in algebraic curves and surfaces of high degree as geometric models or shape descriptors for different model based computer vision tasks has increased in recent years and although their properties make them a natural choice for object recognition and positioning applications algebraic curve and surface fitting algorithms often suffer from instability problems one of the main reasons for these problems is that while the data sets are always bounded the resulting algebraic curves or surfaces are in most cases unbounded in this paper the authors propose to constrain the polynomials to a family with bounded zero sets and use only members of this family in the fitting process for every even number d the authors introduce a new parameterized family of polynomials of degree d whose level sets are always bounded in particular its zero sets this family has the same number of degrees of freedom as a general polynomial of the same degree three methods for fitting members of this polynomial family to measured data points are introduced experimental results of fitting curves to sets of points in r sup 2 and surfaces to sets of points in r sup 3 are presented

on some stability problems of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract this paper covers the topic of both the p th moment p 2 and almost sure stability of impulsive stochastic cohen grossberg neural networks with mixed time delays we partially use a known result on exponential stability of impulsive stochastic functional differential systems based on the razumikhin type technique and extend it to the case of stochastic neural networks using the lyapunov function method and a gronwall type inequality additionally we consider the stability with respect to a general decay function which includes exponential but also more general lower rate decay functions as the polynomial and the logarithmic ones this fact gives us the opportunity to study general decay almost sure stability even when the exponential one cannot be discussed suitable examples which support the theory are also presented

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

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

a fuzzy covering based rough set model and its generalization over fuzzy lattice in this paper we study a new type of fuzzy covering based rough set model by introducing the notion of fuzzy minimal description we mainly address the following issues in this paper first we present the definition of fuzzy minimal description and study its properties then we define a novel type of fuzzy covering based rough set model and investigate the properties of this model furthermore the axiomizations and matrix representations of the fuzzy covering lower and fuzzy covering upper approximations are the vital problems we investigate in this paper moreover we explore the conditions under which two fuzzy coverings generate the same fuzzy covering lower or fuzzy covering upper approximations finally we generalize the model to l fuzzy covering based rough set which is defined over fuzzy lattices similar to the fuzzy covering based rough set model we also address the issues mentioned above to the l fuzzy covering based rough set

textures and covering based rough sets this paper introduces the relations between covering and dicovering in the framework of rough sets the natural counterpart of a covering in textures is given by a family of pairs of sets which is called a dicovering this leads us to two dual concepts which are called star and co star of a set respectively here we define dicovering approximation space and we discuss on covering and dicovering based rough sets in this context star corresponds to the upper approximation operator defined by zakowski and co star corresponds to the lower approximation operator studied by pomykala yao and zhu and wang

an entropy based uncertainty measurement approach in neighborhood systems abstract uncertainty measures can provide us with principled methodologies to analyze uncertain data and unveil the substantive characteristics of the data sets accuracy and roughness proposed by pawlak are two main tools to deal with uncertainty measurement issue in rough set theory many uncertainty measure methodologies for discrete valued information systems or discrete valued decision systems have been developed however there are only limited on the uncertainty measurement for neighborhood systems in this paper we address the issues of uncertainty of a neighborhood system and extend the traditional accuracy and roughness measures to deal with neighborhood systems in particular a concept called neighborhood entropy is first introduced to evaluate the uncertainty of a neighborhood information system consequently the entropy based roughness and approximation roughness measures of neighborhood system are presented theoretical analysis indicates that entropy based measures can be used to evaluate the uncertainty in neighborhood systems experiments are conducted on artificial data sets and standard uci data sets to test our proposed methodologies results demonstrate that the entropy based measures are effective and valid for evaluating the uncertainty of neighborhood systems

recognition of 3d objects based on implicit polynomials closed form expressions for a new set of 3d rotation invariants that are linear quadratic and angular combinations of implicit polynomial ip coefficients are developed based on these invariants we propose a 3d object recognition method that outperforms recognition based on ip fitting after pose estimation and the mpeg 7 ssd technique

reconstructing surfaces by volumetric regularization using radial basis functions we present a new method of surface reconstruction that generates smooth and seamless models from sparse noisy nonuniform and low resolution range data data acquisition techniques from computer vision such as stereo range images and space carving produce 3d point sets that are imprecise and nonuniform when compared to laser or optical range scanners traditional reconstruction algorithms designed for dense and precise data do not produce smooth reconstructions when applied to vision based data sets our method constructs a 3d implicit surface formulated as a sum of weighted radial basis functions we achieve three primary advantages over existing algorithms 1 the implicit functions we construct estimate the surface well in regions where there is little data 2 the reconstructed surface is insensitive to noise in data acquisition because we can allow the surface to approximate rather than exactly interpolate the data and 3 the reconstructed surface is locally detailed yet globally smooth because we use radial basis functions that achieve multiple orders of smoothness

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

improving the stability of algebraic curves for applications an algebraic curve is defined as the zero set of a polynomial in two variables algebraic curves are practical for modeling shapes much more complicated than conics or superquadrics the main drawback in representing shapes by algebraic curves has been the lack of repeatability in fitting algebraic curves to data usually arguments against using algebraic curves involve references to mathematicians wilkinson and runge the first goal of this article is to understand the stability issue of algebraic curve fitting then a fitting method based on ridge regression and restricting the representation to well behaved subsets of polynomials is proposed and its properties are investigated the fitting algorithm is of sufficient stability for very fast position invariant shape recognition position estimation and shape tracking based on invariants and new representations among appropriate applications are shape based indexing into image databases

pinning consensus in networks of multiagents via a single impulsive controller in this paper we discuss pinning consensus in networks of multiagents via impulsive controllers in particular we consider the case of using only one impulsive controller we provide a sufficient condition to pin the network to a prescribed value it is rigorously proven that in case the underlying graph of the network has spanning trees the network can reach consensus on the prescribed value when the impulsive controller is imposed on the root with appropriate impulsive strength and impulse intervals interestingly we find that the permissible range of the impulsive strength completely depends on the left eigenvector of the graph laplacian corresponding to the zero eigenvalue and the pinning node we choose the impulses can be very sparse with the impulsive intervals being lower bounded examples with numerical simulations are also provided to illustrate the theoretical results

relationship among basic concepts in covering based rough sets uncertainty and incompleteness of knowledge are widespread phenomena in information systems rough set theory is a tool for dealing with granularity and vagueness in data analysis rough set method has already been applied to various fields such as process control economics medical diagnosis biochemistry environmental science biology chemistry psychology and conflict analysis covering based rough set theory is an extension to classical rough sets in covering based rough sets there exist several basic concepts such as reducible elements of a covering minimal descriptions unary coverings and the property that the intersection of any two elements is the union of finite elements in this covering these concepts appeared in the literature of covering based rough sets separately in this paper we study the relationships between them in particular we establish the equivalence of the unary covering and the covering with the property that the intersection of any two elements is the union of finite elements in this covering we also investigate the relationship between the covering lower approximation operation and the interior operator a characterization of the interior operator by the covering lower approximation operation is presented in this paper correspondingly we study the relationship between the covering upper approximation operation and the closure operator in addition we explore the conditions under which the covering upper approximation operation is monotone the study of the relationships between these concepts will help us have a better understanding of covering based rough sets

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

stochastic stability of delayed neural networks with local impulsive effects in this paper the stability problem is studied for a class of stochastic neural networks nns with local impulsive effects the impulsive effects considered can be not only nonidentical in different dimensions of the system state but also various at distinct impulsive instants hence the impulses here can encompass several typical impulses in nns the aim of this paper is to derive stability criteria such that stochastic nns with local impulsive effects are exponentially stable in mean square by means of the mathematical induction method several easy to check conditions are obtained to ensure the mean square stability of nns three examples are given to show the effectiveness of the proposed stability criterion

generalized rough sets over fuzzy lattices this paper studies generalized rough sets over fuzzy lattices through both the constructive and axiomatic approaches from the viewpoint of the constructive approach the basic properties of generalized rough sets over fuzzy lattices are obtained the matrix representation of the lower and upper approximations is given according to this matrix view a simple algorithm is obtained for computing the lower and upper approximations as for the axiomatic approach a set of axioms is constructed to characterize the upper approximation of generalized rough sets over fuzzy lattices

the 3l algorithm for fitting implicit polynomial curves and surfaces to data we introduce a completely new approach to fitting implicit polynomial geometric shape models to data and to studying these polynomials the power of these models is in their ability to represent nonstar complex shapes in two 2d and three dimensional 3d data to permit fast repeatable fitting to unorganized data which may not be uniformly sampled and which may contain gaps to permit position invariant shape recognition based on new complete sets of euclidean and affine invariants and to permit fast stable single computation pose estimation the algorithm represents a significant advancement of implicit polynomial technology for four important reasons first it is orders of magnitude taster than existing fitting methods for implicit polynomial 2d curves and 3d surfaces and the algorithms for 2d and 3d are essentially the same second it has significantly better repeatability numerical stability and robustness than current methods in dealing with noisy deformed or missing data third it can easily fit polynomials of high such as 14th or 16th degree fourth additional linear constraints can be easily incorporated into the fitting process and general linear vector space concepts apply

related family a new method for attribute reduction of covering information systems in terms of attribute reduction of covering based rough sets the discernibility matrix is used as a conventional method to compute all attribute reducts however it is inapplicable to attribute reduction in certain circumstances in this article a new method referred to as the related family is introduced to compute all attribute reducts and relative attribute reducts for covering rough sets its core idea is to remove superfluous attributes while keeping the approximation space of covering information system unchanged the related family method is more powerful than the discernibility matrix method since the former can handle complicated cases that could not be handled by the latter in addition a simplified version of the related family and its corresponding heuristic algorithm are also presented

covering based rough set approximations we propose a framework for the study of covering based rough set approximations three equivalent formulations of the classical rough sets are examined by using equivalence relations partitions and s algebras respectively they suggest the element based the granule based and the subsystem based definitions of approximation operators covering based rough sets are systematically investigated by generalizing these formulations and definitions a covering of universe of objects is used to generate different neighborhood operators neighborhood systems coverings and subsystems of the power set of the universe they are in turn used to define different types of generalized approximation operators within the proposed framework we review and discuss covering based approximation operators according to the element granule and subsystem based definitions

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 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

estimation of planar curves surfaces and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation the author addresses the problem of parametric representation and estimation of complex planar curves in 2 d surfaces in 3 d and nonplanar space curves in 3 d curves and surfaces can be defined either parametrically or implicitly with the latter representation used here a planar curve is the set of zeros of a smooth function of two variables x y a surface is the set of zeros of a smooth function of three variables x y z and a space curve is the intersection of two surfaces which are the set of zeros of two linearly independent smooth functions of three variables x y z for example the surface of a complex object in 3 d can be represented as a subset of a single implicit surface with similar results for planar and space curves it is shown how this unified representation can be used for object recognition object position estimation and segmentation of objects into meaningful subobjects that is the detection of interest regions that are more complex than high curvature regions and hence more useful as features for object recognition

on measurements of covering rough sets based on granules and evidence theory covering rough sets generalize classical rough sets by relaxing partitions of the universe to coverings the existing research of covering rough sets mainly concentrates on comparing of different kinds of approximation operators and designing algorithms for attribute reductions of decision systems less efforts have been made in measurements of covering rough sets to enrich this field in this paper we investigate the measurements of covering rough sets based on granules and evidence theory which can be used to solve more complex practical problems firstly it is shown that the most common sixteen pairs of covering approximation operators can be grouped into five pairs of dual covering approximation operators and six pairs of non dual covering approximation operators according to definitions based on element granule and subsystem secondly we define the rough degree and precision for the purpose of characterizing the uncertainty of these summarized covering approximation operators under a unified framework the underlying uncertainty of covering rough sets results from the roughness of granulation of coverings finally we investigate the relationships between the covering approximation operators and evidence theory it shows that some kinds of covering approximation operators can be characterized by belief and plausibility functions while others do not share this property the sufficient conditions under which covering approximation operators can be measured by belief and plausibility functions are further explored and the corresponding counterexamples are given to illustrate those that cannot be measured based on above discussions we develop a basic framework of numerical characterization on measurements of covering rough sets with granules and evidence theory

ellifit an unconstrained non iterative least squares based geometric ellipse fitting method a novel ellipse fitting method which is selective for digital and noisy elliptic curves is proposed in this paper the method aims at fitting an ellipse only when the data points are highly likely belong to an ellipse this is achieved using the geometric distances of the ellipse from the data points the proposed method models the non linear problem of ellipse fitting as a combination of two operators with one being linear numerically stable and easily invertible while the other being non linear but unique and easily invertible operator as a consequence the proposed ellipse fitting method has several salient properties like unconstrained stable non iterative and computationally inexpensive the efficacy of the method is compared against six contemporary and recent algorithms based on the least squares formulation using five experiments of diverse practical challenges like digitization incomplete ellipses and gaussian noise up to 30 three of the experiments comprise of a total of 44 400 ellipses positive test data while the other two are tested on 320 000 non elliptic conics negative test data the results show that the proposed method is quite selective to elliptic shapes only and provides accurate fitting results indicating potential application in medical robotics object detection and other image processing industrial applications

describing complicated objects by implicit polynomials this paper introduces and focuses on two problems first is the representation power of closed implicit polynomials of modest degree for curves in 2 d images and surfaces in 3 d range data super quadrics are a small subset of object boundaries that are well fitted by these polynomials the second problem is the stable computationally efficient fitting of noisy data by closed implicit polynomial curves and surfaces the attractive features of these polynomials for vision is discussed

a general methodology for the determination of 2d bodies elastic deformation invariants application to the automatic identification of parasites a novel methodology is introduced here that exploits 2d images of arbitrary elastic body deformation instances so as to quantify mechanoelastic characteristics that are deformation invariant determination of such characteristics allows for developing methods offering an image of the undeformed body general assumptions about the mechanoelastic properties of the bodies are stated which lead to two different approaches for obtaining bodies deformation invariants one was developed to spot a deformed body s neutral line and its cross sections while the other solves deformation pdes by performing a set of equivalent image operations on the deformed body images both of these processes may furnish a body undeformed version from its deformed image this was confirmed by obtaining the undeformed shape of deformed parasites cells protozoa fibers and human lips in addition the method has been applied to the important problem of parasite automatic classification from their microscopic images to achieve this we first apply the previous method to straighten the highly deformed parasites and then apply a dedicated curve classification method to the straightened parasite contours it is demonstrated that essentially different deformations of the same parasite give rise to practically the same undeformed shape thus confirming the consistency of the introduced methodology finally the developed pattern recognition method classifies the unwrapped parasites into six families with an accuracy rate of 97 6 percent

knowledge acquisition in incomplete information systems a rough set approach abstract this paper deals with knowledge acquisition in incomplete information systems using rough set theory the concept of similarity classes in incomplete information systems is first proposed two kinds of partitions lower and upper approximations are then formed for the mining of certain and association rules in incomplete decision tables one type of optimal certain and two types of optimal association decision rules are generated two new quantitative measures random certainty factor and random coverage factor associated with each decision rule are further proposed to explain relationships between the condition and decision parts of a rule in incomplete decision tables the reduction of descriptors and induction of optimal rules in such tables are also examined

the approximation number function and the characterization of covering approximation space there is renewed interest in the topic of covering based rough sets it is important to understand the characterization of covering approximation spaces recently zhu et al presented the concept of an approximation number function which can be viewed as a quantitative tool for analyzing the covering approximation spaces we focus on this concept and show that an approximation number function can be characterized by its properties we give the axiomatic definition of an approximation number function and prove that there is a one to one correspondence between the set of all lower approximation number functions and the set of all covering approximation spaces this suggests that the concept is fundamental to the characterization of covering approximation spaces we apply approximation number functions to the existing studies on approximation spaces and a series of matroidal structures are induced in an approximation space