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

rough fuzzy approximations on two universes of discourse in rough set theory the lower and upper approximation operators can be constructed via a variety of approaches various fuzzy generalizations of rough approximation operators have been made over the years this paper presents a framework for the study of rough fuzzy sets on two universes of discourse by means of a binary relation between two universes of discourse a covering and three relations are induced to a single universe of discourse based on the induced notions four pairs of rough fuzzy approximation operators are proposed these models guarantee that the approximating sets and the approximated sets are on the same universes of discourse furthermore the relationship between the new approximation operators and the existing rough fuzzy approximation operators on two universes of discourse are scrutinized and some interesting properties are investigated finally the connections of these approximation operators are made and conditions under which some of these approximation operators are equivalent are obtained

fuzzy rough regression with application to wind speed prediction accurate wind speed prediction is a prerequisite of large scale wind power generation there are several uncertain factors which degrade the performance of the current wind speed prediction systems fuzzy rough sets are considered as a powerful tool to deal with uncertainty and have been widely discussed and applied in classification learning in this work we describe a regression algorithm based on fuzzy rough sets consisting of fuzzy partition fuzzy approximation and estimation of regression values in this algorithm the training set is divided into k fuzzy classes with fuzzy partition and then the predicted values of test samples are determined in the finite intervals with fuzzy rough approximation finally they are estimated with lower and upper limits of the intervals numerical experiments on uci data sets and wind speed prediction show the effectiveness of the proposed algorithm

geometrical interpretation and applications of membership functions with fuzzy rough sets fuzzy rough sets are a generalization of crisp rough sets for measuring inconsistency between conditional attributes and decision attributes for many decision systems in many classification problems a membership function for the training sample belonging to a certain class can be computed by methods in fuzzy rough sets in this paper we present a geometrical interpretation and its applications of this kind of membership functions first we prove that every fuzzy similarity relation in fuzzy rough sets is a reproducing kernel which is related to a krein space thus fuzzy similarity relations can be geometrically explained in a krein space second we will present the interpretation of several types of membership functions geometrically by using the lower approximations in fuzzy rough sets in terms of square distances in krein spaces as practical applications of these membership functions we develop a new algorithm to find reducts and reformulate soft margin support vector machines by taking the membership degree for every training sample into considerations experimental results also demonstrate the effectiveness of the work proposed in this paper

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

min max attribute object bireducts on unifying models of reducts in rough set theory abstract a decision table describes a finite set of objects ob by using a finite set of condition attributes c and a finite set of decision attributes d pawlak defines attribute reducts by considering the entire decision table as a generalization we introduce the notion of min max attribute object bireducts of a sub table restricted by a pair b x of a subset of condition attributes b and a subset of objects x a pair r z is a min max attribute object bireduct of b x if and only if r is a minimal subset of b such that r and b make the same correct decisions for objects in x and z is a maximal subset of x for which b can make the correct decisions we propose the notion of the decidability of objects and introduce the decidable region of a set of objects as a generalization of the positive region of the set we define and interpret a min max attribute object bireduct based on the decidable region min max attribute object bireducts offer a general model and existing models of attribute reducts are special cases the results lead to a unified framework for studying four types of attribute reducts

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

double quantitative rough fuzzy set based decisions as two important expanded quantification rough set models the probabilistic rough set prs model and the graded rough set grs model are used to measure relative quantitative information and absolute quantitative information between the equivalence classes and a basic concept respectively the decision theoretic rough set dtrs model is a special case of prs model which mainly utilizes the conditional probability to express relative quantification since the fuzzy concept is more general than classical concept in real life how to make decision for a fuzzy concept using relative and absolute quantitative information is becoming a hot topic in this paper a couple of double quantitative decision theoretic rough fuzzy set dq dtrfs models based on logical conjunction and logical disjunction operation are proposed furthermore we discuss decision rules and the inner relationship between these two models then an experiment in the medical diagnosis is studied to support the theories finally to apply our methods to solve a pattern recognition problem in big data experiments on data sets downloaded from uci are conducted to test the proposed models in addition we also offer a comparative analysis using two non rough set based methods from the results obtained one finds that the proposed method is efficient for dealing with practical issues

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

on the generalization of fuzzy rough sets rough sets and fuzzy sets have been proved to be powerful mathematical tools to deal with uncertainty it soon raises a natural question of whether it is possible to connect rough sets and fuzzy sets the existing generalizations of fuzzy rough sets are all based on special fuzzy relations fuzzy similarity relations t similarity relations it is advantageous to generalize the fuzzy rough sets by means of arbitrary fuzzy relations and present a general framework for the study of fuzzy rough sets by using both constructive and axiomatic approaches in this paper from the viewpoint of constructive approach we first propose some definitions of upper and lower approximation operators of fuzzy sets by means of arbitrary fuzzy relations and study the relations among them the connections between special fuzzy relations and upper and lower approximation operators of fuzzy sets are also examined in axiomatic approach we characterize different classes of generalized upper and lower approximation operators of fuzzy sets by different sets of axioms the lattice and topological structures of fuzzy rough sets are also proposed in order to demonstrate that our proposed generalization of fuzzy rough sets have wider range of applications than the existing fuzzy rough sets a special lower approximation operator is applied to a fuzzy reasoning system which coincides with the mamdani algorithm

a fuzzy rough set approach for incremental feature selection on hybrid information systems in real applications there may exist many kinds of data e g boolean categorical real valued and set valued data and missing data in an information system which is called as a hybrid information system his a new hybrid distance hd in his is developed based on the value difference metric and a novel fuzzy rough set is constructed by combining the hd distance and the gaussian kernel considering the information systems often vary with time the updating mechanisms for attribute reduction feature selection are analyzed with the variation of the attribute set fuzzy rough set approaches for incremental feature selection on his are presented then two corresponding incremental algorithms are proposed respectively finally extensive experiments on eight datasets from uci and an artificial dataset show that the incremental approaches significantly outperform non incremental approaches with feature selection in the computational time

new approaches to fuzzy rough feature selection there has been great interest in developing methodologies that are capable of dealing with imprecision and uncertainty the large amount of research currently being carried out in fuzzy and rough sets is representative of this many deep relationships have been established and recent studies have concluded as to the complementary nature of the two methodologies therefore it is desirable to extend and hybridize the underlying concepts to deal with additional aspects of data imperfection such developments offer a high degree of flexibility and provide robust solutions and advanced tools for data analysis fuzzy rough set based feature fs selection has been shown to be highly useful at reducing data dimensionality but possesses several problems that render it ineffective for large datasets this paper proposes three new approaches to fuzzy rough fs based on fuzzy similarity relations in particular a fuzzy extension to crisp discernibility matrices is proposed and utilized initial experimentation shows that the methods greatly reduce dimensionality while preserving classification accuracy

class specific attribute reducts in rough set theory abstract the concept of attribute reducts plays a fundamental role in rough set analysis there are at least two possibilities to define an attribute reduct a classification based or global attribute reduct is a minimal subset of condition attributes that preserves the positive region of the decision classification namely the positive regions of all decision classes in a decision table a class specific class dependent or local attribute reduct is a minimal subset of condition attributes that preserves the positive region of a particular decision class while a classification based reduct may not work equally well for every decision class a class specific attribute reduct is optimally tailored to a particular decision class however studies in rough set theory are dominated by classification based reducts there is very limited investigation on class specific reducts an objective of this paper is to draw attention to class specific reducts we systematically compare the two types of reducts and investigate their relationships with respect to both individual reducts and families of all reducts it is possible to derive a class specific reduct from a classification based reduct and to derive a classification based reduct from a family of class specific reducts the families of all class specific reducts provide a pair of lower and upper bounds of the family of all classification based reducts based on a three way classification of attributes into the pair wise disjoint sets of core marginal and nonuseful attributes we examine relationships between the corresponding classes of classification based and class specific attributes the union of the sets of class specific core attributes is the set of classification based core attributes it is only possible to obtain an upper bound for the set of classification based marginal attributes and a lower bound for the set of classification based nonuseful attributes from the family of the class specific corresponding sets of attributes

efficient numerical methods for radiation in gas turbines numerical methods for radiative heat transfer equations coupled to a temperature equation are considered efficient solution methods and approximate equations for this system are investigated and a comparative numerical study of the different approximations is given the approximate equations considered in this paper include moment methods and diffusive approximations fast iterative solvers for the problem like multilevel methods with suitable preconditioning are considered in detail numerical experiments and comparisons in different space dimensions and for various physical situations are presented

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

fuzzy rough sets assisted attribute selection attribute selection as refers to the problem of selecting those input attributes or features that are most predictive of a given outcome a problem encountered in many areas such as machine learning pattern recognition and signal processing unlike other dimensionality reduction methods attribute selectors preserve the original meaning of the attributes after reduction this has found application in tasks that involve datasets containing huge numbers of attributes in the order of tens of thousands which for some learning algorithms might be impossible to process further recent examples include text processing and web content classification as techniques have also been applied to small and medium sized datasets in order to locate the most informative attributes for later use one of the many successful applications of rough set theory has been to this area the rough set ideology of using only the supplied data and no other information has many benefits in as where most other methods require supplementary knowledge however the main limitation of rough set based attribute selection in the literature is the restrictive requirement that all data is discrete in classical rough set theory it is not possible to consider real valued or noisy data this paper investigates a novel approach based on fuzzy rough sets fuzzy rough feature selection frfs that addresses these problems and retains dataset semantics frfs is applied to two challenging domains where a feature reducing step is important namely web content classification and complex systems monitoring the utility of this approach is demonstrated and is compared empirically with several dimensionality reducers in the experimental studies frfs is shown to equal or improve classification accuracy when compared to the results from unreduced data classifiers that use a lower dimensional set of attributes which are retained by fuzzy rough reduction outperform those that employ more attributes returned by the existing crisp rough reduction method in addition it is shown that frfs is more powerful than the other as techniques in the comparative study

attribute reduction based on generalized fuzzy evidence theory in fuzzy decision systems attribute reduction is viewed as an important issue in data mining and knowledge representation this paper studies attribute reduction in fuzzy decision systems based on generalized fuzzy evidence theory the definitions of several kinds of attribute reducts are introduced the relationships among these reducts are then investigated in a fuzzy decision system it is proved that the concepts of fuzzy positive region reduct lower approximation reduct and generalized fuzzy belief reduct are all equivalent the concepts of fuzzy upper approximation reduct and generalized fuzzy plausibility reduct are equivalent and a generalized fuzzy plausibility consistent set must be a generalized fuzzy belief consistent set in a consistent fuzzy decision system an attribute set is a generalized fuzzy belief reduct if and only if it is a generalized fuzzy plausibility reduct but in an inconsistent fuzzy decision system a generalized fuzzy belief reduct is not a generalized fuzzy plausibility reduct in general

induction of fuzzy decision trees abstract most decision tree induction methods used for extracting knowledge in classification problems do not deal with cognitive uncertainties such as vagueness and ambiguity associated with human thinking and perception in this paper cognitive uncertainties involved in classification problems are explicitly represented measured and incorporated into the knowledge induction process a fuzzy decision tree induction method which is based on the reduction of classification ambiguity with fuzzy evidence is developed fuzzy decision trees represent classification knowledge more naturally to the way of human thinking and are more robust in tolerating imprecise conflict and missing information

structure of feature spaces related to fuzzy similarity relations as kernels fuzzy similarity relations have been considered as kernels in the domain of machine learning in previous works as a supplementary of this consideration this paper focuses on construction of feature space related to fuzzy similarity relations as indefinite kernels first we generalize the mercer theorem from positive definite kernels to fuzzy similarity relations with this generalization we construct the feature space related to a fuzzy similarity relation as a particular krein space the proposed feature space is a naturally generalization of the existing pseudo euclidean space from finite to infinite universe of discourses at the end of this paper we develop an open problem to set up the connection between transitivity and the positive definiteness of a fuzzy similarity relation results in this paper complete the mathematical foundation for further applications of fuzzy similarity relations under the framework of kernel tricks

local reduction of decision system with fuzzy rough sets one important and valuable topic in fuzzy rough sets is attribute reduction of decision system the existing attribute reductions with fuzzy rough sets consider all decision classes together and cannot identify key conditional attributes explicitly for special decision class in this paper we introduce the concept of local reduction with fuzzy rough sets for decision system the local reduction can identify key conditional attribute and offer a minimal description for every single decision class approach of discernibility matrix is employed to investigate the structure of local reduction at last several experiments are performed to show that the idea of local reduction is feasible and valid

a linear algebraic analysis of diffusion synthetic acceleration for the boltzmann transport equation a linear algebraic formulation of discretized mono energetic steady state linear boltzmann transport equations in slab geometry is presented the discretization consists of a discrete ordinates collocation in angle and a diamond difference method in space by expressing diffusion synthetic acceleration in this formalism asymptotic results are obtained that prove the effectiveness of the associated preconditioner in various asymptotic regimes including the asymptotic diffusion limit these results hold for problems with nonconstant coefficients and nonuniform spatial zoning posed on finite domains with an incident flux and or reflection prescribed at the boundaries numerical results are also presented which demonstrate these results

minimization of axiom sets on fuzzy approximation operators axiomatic characterization of approximation operators is an important aspect in the study of rough set theory in this paper we examine the independence of axioms and present the minimal axiom sets characterizing fuzzy rough approximation operators and rough fuzzy approximation operators

a novel algorithm for finding reducts with fuzzy rough sets attribute reduction is one of the most meaningful research topics in the existing fuzzy rough sets and the approach of discernibility matrix is the mathematical foundation of computing reducts when computing reducts with discernibility matrix we find that only the minimal elements in a discernibility matrix are sufficient and necessary this fact motivates our idea in this paper to develop a novel algorithm to find reducts that are based on the minimal elements in the discernibility matrix relative discernibility relations of conditional attributes are defined and minimal elements in the fuzzy discernibility matrix are characterized by the relative discernibility relations then the algorithms to compute minimal elements and reducts are developed in the framework of fuzzy rough sets experimental comparison shows that the proposed algorithms are effective

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

fuzzy rough attribute reduction with application to web categorization abstract due to the explosive growth of electronically stored information automatic methods must be developed to aid users in maintaining and using this abundance of information effectively in particular the sheer volume of redundancy present must be dealt with leaving only the information rich data to be processed this paper presents a novel approach based on an integrated use of fuzzy and rough set theories to greatly reduce this data redundancy formal concepts of fuzzy rough attribute reduction are introduced and illustrated with a simple example the work is applied to the problem of web categorization considerably reducing dimensionality with minimal loss of information experimental results show that fuzzy rough reduction is more powerful than the conventional rough set based approach classifiers that use a lower dimensional set of attributes which are retained by fuzzy rough reduction outperform those that employ more attributes returned by the existing crisp rough reduction method

fuzzy rough set based incremental attribute reduction from dynamic data with sample arriving abstract attribute reduction with fuzzy rough set is an effective technique for selecting most informative attributes from a given real valued dataset however existing algorithms for attribute reduction with fuzzy rough set have to re compute a reduct from dynamic data with sample arriving where one sample or multiple samples arrive successively this is clearly uneconomical from a computational point of view in order to efficiently find a reduct from such datasets this paper studies incremental attribute reduction with fuzzy rough sets at the arrival of one sample or multiple samples the relative discernibility relation is updated for each attribute on the basis of the updated relation an insight into the incremental process of attribute reduction with fuzzy rough sets is gained to reveal how to add new attributes into the current reduct and delete existing attributes from the current reduct applying the incremental process two incremental algorithms for attribute reduction with fuzzy rough sets are presented for one incoming sample and multiple incoming samples respectively experimental comparisons with several non incremental algorithms and the proposed incremental algorithm for one incoming sample show that our proposed incremental algorithm for multiple incoming samples can efficiently find one reduct with a comparable classification accuracy

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

an efficient fourth order low dispersive finite difference scheme for a 2 d acoustic wave equation in this paper we propose an efficient fourth order compact finite difference scheme with low numerical dispersion to solve the two dimensional acoustic wave equation combined with the alternating direction implicit adi technique and pade approximation the standard second order finite difference scheme can be improved to fourth order and solved as a sequence of one dimensional problems with high computational efficiency however such compact higher order methods suffer from high numerical dispersion to suppress numerical dispersion the compact and non compact stages are interlinked to produce a hybrid scheme in which the compact stage is based on pade approximation in both y and temporal dimensions while the non compact stage is based on pade approximation in y dimension only stability analysis shows that the new scheme is conditionally stable and superior to some existing methods in terms of the courant friedrichs lewy cfl condition the dispersion analysis shows that the new scheme has lower numerical dispersion in comparison to the existing compact adi scheme and the higher order locally one dimensional lod scheme three numerical examples are solved to demonstrate the accuracy and efficiency of the new method

a graph approach for fuzzy rough feature selection abstract rough sets especially fuzzy rough sets have proven to be a powerful tool for dealing with vagueness and uncertainty in data analysis fuzzy rough feature selection has been shown to be highly useful in data dimensionality reduction however many fuzzy rough feature selection algorithms are still time consuming when dealing with the large scale data sets in this paper the problem of feature selection in fuzzy rough sets is studied in the framework of graph theory we propose a new mechanism for fuzzy rough feature selection it is shown that finding the attribute reduction of a fuzzy decision system can be translated into finding the transversal of a derivative hypergraph based on the graph representation model a novel graph theoretic algorithm for fuzzy rough feature selection is proposed the performance of the proposed method is compared with those of the state of the art methods on various classification tasks experimental results show that the proposed technique outperforms all other known feature selection methods in terms of the computation time especially for the large scale data sets it demonstrates promising performance moreover our proposed method can achieve better classification accuracies with the usage of small number of features

fuzzy rough data reduction with ant colony optimization feature selection refers to the problem of selecting those input features that are most predictive of a given outcome a problem encountered in many areas such as machine learning pattern recognition and signal processing in particular solution to this has found successful application in tasks that involve datasets containing huge numbers of features in the order of tens of thousands which would be impossible to process further recent examples include text processing and web content classification rough set theory has been used as such a dataset pre processor with much success but current methods are inadequate at finding minimal reductions the smallest sets of features possible to alleviate this difficulty a feature selection technique that employs a hybrid variant of rough sets fuzzy rough sets has been developed recently and has been shown to be effective however this method is still not able to find the optimal subsets regularly this paper proposes a new feature selection mechanism based on ant colony optimization in an attempt to combat this the method is then applied to the problem of finding optimal feature subsets in the fuzzy rough data reduction process the present work is applied to complex systems monitoring and experimentally compared with the original fuzzy rough method an entropy based feature selector and a transformation based reduction method pca comparisons with the use of a support vector classifier are also included

attribute reduction for heterogeneous data based on the combination of classical and fuzzy rough set models attribute reduction with rough sets aims to delete superfluous condition attributes from a decision system by considering the inconsistency between condition attributes and the decision labels however heterogeneous condition attributes including symbolic and real valued ones always coexist for most decision systems and different types of attributes induce different kinds of granular structures the existing rough set models do not have explicit mechanisms to address different kinds of granular structures reasonably and effectively in this paper we aim to perform attribute reduction for decision systems with symbolic and real valued condition attributes by composing classical rough set and fuzzy rough set models we first define a discernibility relation for every symbolic and real valued condition attribute to characterize its discernible ability related to the decision labels with these discernibility relations we can develop a dependence function to measure the inconsistency between heterogeneous condition attributes and decision labels and attribute reduction aims to keep this dependence function with a small perturbation the proposed attribute reduction deals with heterogeneous condition attributes from the viewpoint of discernible ability and can consider the mutual effects between two types of attributes without preprocessing into single typed ones an algorithm to find reducts is developed and experiments are performed to demonstrate that the proposed idea is effective

theoretical and numerical analysis of a minimal residual solver for 2d boltzmann transport equation relying on the splitting of the collision operator introduced in m2an 34 2000 1109 m2an 32 1998 341 we prove theoretical convergence for an infinite dimensional adaptation of the minimal residual algorithm for boltzmann transport equation in dimension two then we compare numerically this method with existing nonaccelerated schemes it gives good results which could even be further improved by adding a dsa or sor acceleration

a fast multilevel algorithm for the solution of nonlinear systems of conductive radiative heat transfer equations in two space dimensions in this paper we describe a fast multilevel algorithm for the solution of a system of nonlinear integro differential equations that model steady state combined conductive radiative heat transfer in two space dimensions this extends our previous work in one space dimension we formulate the equations as a compact fixed point problem with the temperature as the unknown the fixed point map requires both a poisson solve and a transport solve for its evaluation as a solver for both the transport problem and the full system we apply the atkinson brakhage algorithm using newton gmres as the solver on the coarse mesh we compare our solver choices with newton gmres under modest stability and convergence assumptions on the transport solver we prove convergence of the multilevel method for the complete system

incremental perspective for feature selection based on fuzzy rough sets feature selection based on fuzzy rough sets is an effective approach to select a compact feature subset that optimally predicts a given decision label despite being studied extensively most existing methods of fuzzy rough set based feature selection are restricted to computing the whole dataset in batch which is often costly or even intractable for large datasets to improve the time efficiency we investigate the incremental perspective for fuzzy rough set based feature selection assuming data can be presented in sample subsets one after another the key challenge for the incremental perspective is how to add and delete features with the subsequent arrival of sample subsets we tackle this challenge with strategies of adding and deleting features based on the relative discernibility relations that are updated as subsets arrive sequentially two incremental algorithms for fuzzy rough set based feature selection are designed based on the strategies one updates the selected features as each sample subset arrives and outputs the final feature subset where no sample subset is left the other updates the relative discernibility relations but only performs feature selection where there is no further subset arriving experimental comparisons suggest our incremental algorithms expedite fuzzy rough set based feature selection without compromising performance

a comparative study of rough sets for hybrid data to discover knowledge from hybrid data using rough sets researchers have developed several fuzzy rough set models and a neighborhood rough set model these models have been applied to many hybrid data processing applications for a particular purpose thus neglecting the issue of selecting an appropriate model to address this issue this paper mainly concerns the relationships among these rough set models investigating fuzzy and neighborhood hybrid granules reveals an important relationship between these two granules analyzing the relationships among rough approximations of these models shows that hu s fuzzy rough approximations are special cases of neighborhood and wang s fuzzy rough approximations respectively furthermore one to one correspondence relationships exist between wang s fuzzy and neighborhood rough approximations this study also finds that wang s fuzzy and neighborhood rough approximations are cut sets of dubois fuzzy rough approximations and radzikowska and kerre s fuzzy rough approximations respectively