a measurement theory view on the granularity of partitions measurement of granularity is one of the foundational issues in granular computing this paper investigates a class of measures of granularity of partitions the granularity of a set is defined by a strictly monotonic increasing transformation of the cardinality of the set the granularity of a partition is defined as the expected granularity of all blocks of the partition with respect to the probability distribution defined by the partition many existing measures of granularity are instances of the proposed class new measures of granularity of partitions are also introduced

etching a two dimensional mathematical approach a mathematical model for the etching of a semi infinite active surface is presented the model assumes that the transport of the active species occurs solely by diffusion it is shown that when the diffusion field propagates much faster than the etched surface the problem can be solved by a singular perturbation technique which distinguishes a near field in the area where the moving surface and the non etchable mask meet and a far field where edge effects may be disregarded to first order the leading terms of a composite expansion are given from which the shape of the moving boundary can be determined at all times

learning the information divergence information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems examples are nonnegative matrix tensor factorization stochastic neighbor embedding topic models and bayesian network optimization the success of such a learning task depends heavily on a suitable divergence a large variety of divergences have been suggested and analyzed but very few results are available for an objective choice of the optimal divergence for a given task here we present a framework that facilitates automatic selection of the best divergence among a given family based on standard maximum likelihood estimation we first propose an approximated tweedie distribution for the beta divergence family selecting the best beta then becomes a machine learning problem solved by maximum likelihood next we reformulate alpha divergence in terms of beta divergence which enables automatic selection of alpha by maximum likelihood with reuse of the learning principle for beta divergence furthermore we show the connections between gamma and beta divergences as well as renyi and alpha divergences such that our automatic selection framework is extended to non separable divergences experiments on both synthetic and real world data demonstrate that our method can quite accurately select information divergence across different learning problems and various divergence families

unified development of multiplicative algorithms for linear and quadratic nonnegative matrix factorization multiplicative updates have been widely used in approximative nonnegative matrix factorization nmf optimization because they are convenient to deploy their convergence proof is usually based on the minimization of an auxiliary upper bounding function the construction of which however remains specific and only available for limited types of dissimilarity measures here we make significant progress in developing convergent multiplicative algorithms for nmf first we propose a general approach to derive the auxiliary function for a wide variety of nmf problems as long as the approximation objective can be expressed as a finite sum of monomials with real exponents multiplicative algorithms with theoretical guarantee of monotonically decreasing objective function sequence can thus be obtained the solutions of nmf based on most commonly used dissimilarity measures such as and divergence as well as many other more comprehensive divergences can be derived by the new unified principle second our method is extended to a nonseparable case that includes e g divergence and renyi divergence third we develop multiplicative algorithms for nmf using second order approximative factorizations in which each factorizing matrix may appear twice preliminary numerical experiments demonstrate that the multiplicative algorithms developed using the proposed procedure can achieve satisfactory karush kuhn tucker optimality we also demonstrate nmf problems where algorithms by the conventional method fail to guarantee descent at each iteration but those by our principle are immune to such violation

variational regularized 2 d nonnegative matrix factorization a novel approach for adaptive regularization of 2 d nonnegative matrix factorization is presented the proposed matrix factorization is developed under the framework of maximum a posteriori probability and is adaptively fine tuned using the variational approach the method enables 1 a generalized criterion for variable sparseness to be imposed onto the solution and 2 prior information to be explicitly incorporated into the basis features the method is computationally efficient and has been demonstrated on two applications that is extracting features from image and separating single channel source mixture in addition it is shown that the basis features of an information bearing matrix can be extracted more efficiently using the proposed regularized priors experimental tests have been rigorously conducted to verify the efficacy of the proposed method

asymptotic and numerical solutions for the two dimensional solidification of a liquid half space this paper concerns the twodimensional inward solidification of a halfspace filled with molten material at its fusion temperature the temperature along half of the boundary surface is instantaneou

a quasi likelihood approach to nonnegative matrix factorization a unified approach to nonnegative matrix factorization based on the theory of generalized linear models is proposed this approach embeds a variety of statistical models including the exponential family within a single theoretical framework and provides a unified view of such factorizations from the perspective of quasi likelihood using this framework a family of algorithms for handling signal dependent noise is developed and its convergence proved using the expectation maximization algorithm in addition a measure to evaluate the goodness of fit of the resulting factorization is described the proposed methods allow modeling of nonlinear effects using appropriate link functions and are illustrated using an application in biomedical signal processing

interval ordered information systems interval information systems are generalized models of single valued information systems by introducing a dominance relation to interval information systems we propose a ranking approach for all objects based on dominance classes and establish a dominance based rough set approach which is mainly based on substitution of the indiscernibility relation by the dominance relation furthermore we discuss interval ordered decision tables and dominance rules to simplify knowledge representation and extract much simpler dominance rules we propose attribute reductions of interval ordered information systems and decision tables that eliminate only the information that are not essential from the viewpoint of the ordering of objects or dominance rules the approaches show how to simplify an interval ordered information system and find dominance rules directly from an interval ordered decision table these results will be helpful for decision making analysis in interval information systems

a class of manifold regularized multiplicative update algorithms for image clustering multiplicative update algorithms are important tools for information retrieval image processing and pattern recognition however when the graph regularization is added to the cost function different classes of sample data may be mapped to the same subspace which leads to the increase of data clustering error rate in this paper an improved nonnegative matrix factorization nmf cost function is introduced based on the cost function a class of novel graph regularized nmf algorithms is developed which results in a class of extended multiplicative update algorithms with manifold structure regularization analysis shows that in the learning the proposed algorithms can efficiently minimize the rank of the data representation matrix theoretical results presented in this paper are confirmed by simulations for different initializations and data sets variation curves of cost functions and decomposition data are presented to show the convergence features of the proposed update rules basis images reconstructed images and clustering results are utilized to present the efficiency of the new algorithms last the clustering accuracies of different algorithms are also investigated which shows that the proposed algorithms can achieve state of the art performance in applications of image clustering

rough set approach to multi attribute decision analysis abstract we review the methodology of the rough set analysis of multi attribute decision problems rough set theory proved to be a useful tool for analysis of a vague description of decision situations it answers two basic questions related to multi attribute decision problems one about explanation of a decision situation and another about prescription of some decisions basing on analysis of a decision situation we define four classes of multi attribute decision problems depending on the structure of their representation its interpretation and the kind of questions related then we characterize the rough set methodology for each particular class of decision problems we use simple practical examples to illustrate this presentation a review of related literature is made throughout the paper

degrees of conditional in dependence a framework for approximate bayesian networks and examples related to the rough set based feature selection bayesian networks provide the means for representing probabilistic conditional independence conditional independence is widely considered also beyond the theory of probability with linkages to e g the database multi valued dependencies and at a higher abstraction level of semi graphoid models the rough set framework for data analysis is related to the topics of conditional independence via the notion of a decision reduct to be considered within a wider domain of the feature selection given probabilistic version of decision reducts equivalent to the data based markov boundaries the studies were also conducted for other criteria of the rough set based feature selection e g those corresponding to the multi valued dependencies in this paper we investigate the degrees of approximate conditional dependence which could be a topic corresponding to the well known notions such as conditional mutual information and polymatroid functions however with many practically useful approximate conditional independence models unmanageable within the information theoretic framework the major paper s contribution lays in extending the means for understanding the degrees of approximate conditional dependence with appropriately generalized semi graphoid properties formulated and with the mathematical soundness of the bayesian network like representation of the approximate conditional independence statements thoroughly proved as an additional contribution we provide a case study of the approximate conditional independence model which would not be manageable without the above mentioned extensions

asymptotic solutions to the stefan problem with a constant heat source at the moving boundary in 1989 huppert formulated mathematical models of the melting and or freezing that occurs when a hot fluid begins to flow turbulently over a cold substrate he solved the resulting stefan problems numerically and presented certain asymptotic results this note revisits one of his problems and adds to the mathematical analysis of its asymptotic structure generalizations and relationships with other results are also noted

a generalized divergence measure for nonnegative matrix factorization this letter presents a general parametric divergence measure the metric includes as special cases quadratic error and kullback leibler divergence a parametric generalization of the two different multiplicative update rules for nonnegative matrix factorization by lee and seung 2001 is shown to lead to locally optimal solutions of the nonnegative matrix factorization problem with this new cost function numeric simulations demonstrate that the new update rule may improve the quadratic distance convergence speed a proof of convergence is given that as in lee and seung uses an auxiliary function known from the expectation maximization theoretical framework

stability analysis of multiplicative update algorithms and application to nonnegative matrix factorization multiplicative update algorithms have proved to be a great success in solving optimization problems with nonnegativity constraints such as the famous nonnegative matrix factorization nmf and its many variants however despite several years of research on the topic the understanding of their convergence properties is still to be improved in this paper we show that lyapunov s stability theory provides a very enlightening viewpoint on the problem we prove the exponential or asymptotic stability of the solutions to general optimization problems with nonnegative constraints including the particular case of supervised nmf and finally study the more difficult case of unsupervised nmf the theoretical results presented in this paper are confirmed by numerical simulations involving both supervised and unsupervised nmf and the convergence speed of nmf multiplicative updates is investigated

statistical inference of rough set dependence and importance analysis statistical inference about dependence degree dd and importance degree id of variables in an information system is crucial for variables appraisement and model reconstruction however in rough set data analysis rsda the literature is restricted to validate independence or test whether the degree is significantly big while the fixed value test and interval estimation for related measurements have been ignored because these important issues have not been addressed we cannot determine whether the data support expert opinions and compare the features in depth to enhance the integrity of statistical inference for dd and id in an rsda fixed value tests and interval estimations of dd and id are presented in this paper with multinomial distribution as the carrier for statistical information in the databases the fixed value test of dd is successfully transformed into a restricted estimation of multinomial distribution and a goodness of fit test for distributions the fixed value test and interval estimation algorithms for dd and id are then presented in detail and illustrated with examples explicit expressions for the dd and id interval estimation dd confidence curves and the limit theory for dd and id are shown furthermore the effectiveness and discrimination of the proposed algorithms are validated using the car evaluation tic tac toe endgame and fisher s iris databases

nonlinear hyperspectral unmixing with robust nonnegative matrix factorization we introduce a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures the new model extends the commonly used linear mixing model by introducing an additional term accounting for possible nonlinear effects that are treated as sparsely distributed additive outliers with the standard nonnegativity and sum to one constraints inherent to spectral unmixing our model leads to a new form of robust nonnegative matrix factorization with a group sparse outlier term the factorization is posed as an optimization problem which is addressed with a block coordinate descent algorithm involving majorization minimization updates simulation results obtained on synthetic and real data show that the proposed strategy competes with the state of the art linear and nonlinear unmixing methods

attribute reduction and optimal decision rules acquisition for continuous valued information systems for continuous valued information systems the attribute values of objects for the same attribute represent not only their ordinal relationship but also their relative distances therefore the classical rough set model is not suitable for deducing attribute reductions and optimal decision rules for continuous valued information systems though some discretization methods are proposed to transform the continuous valued information systems into discrete ones but those methods are too categorical and may lead to loss of information in some cases to solve such information loss problem we propose a tolerance rough set model in this paper with a given level the proposed model can divide a universe into some maximal tolerance classes also two types of lower and upper approximations are defined accordingly then the reductions of the maximal tolerance class and optimal decision rules based on the proposed attribute descriptors are defined and the approximate discernibility function for the maximal tolerance class is constructed and used to compute all the corresponding optimal decision rules via using boolean reasoning techniques finally the general reductions and consistent reductions for continuous valued information systems are discussed

uncertainly measures of rough set prediction abstract the main statistics used in rough set data analysis the approximation quality is of limited value when there is a choice of competing models for predicting a decision variable in keeping within the rough set philosophy of non invasive data analysis we present three model selection criteria using information theoretic entropy in the spirit of the minimum description length principle our main procedure is based on the principle of indifference combined with the maximum entropy principle thus keeping external model assumptions to a minimum the applicability of the proposed method is demonstrated by a comparison of its error rates with results of c4 5 using 14 published data sets

generating probabilistic boolean networks from a prescribed stationary distribution modeling gene regulation is an important problem in genomic research boolean networks bn and its generalization probabilistic boolean networks pbns have been proposed to model genetic regulatory interactions bn is a deterministic model while pbn is a stochastic model in a pbn on one hand its stationary distribution gives important information about the long run behavior of the network on the other hand one may be interested in system synthesis which requires the construction of networks from the observed stationary distribution this results in an inverse problem which is ill posed and challenging because there may be many networks or no network having the given properties and the size of the inverse problem is huge in this paper we consider the problem of constructing pbns from a given stationary distribution and a set of given boolean networks bns we first formulate the inverse problem as a constrained least squares problem we then propose a heuristic method based on conjugate gradient cg algorithm an iterative method to solve the resulting least squares problem we also introduce an estimation method for the parameters of the pbns numerical examples are then given to demonstrate the effectiveness of the proposed methods

two dimensional solidification in a corner analytical and numerical techniques are used to study the solidification of 1 2 and 3 2 wedges of liquid which are initially at their fusion temperature an enthalpy method is used to obtain numerical solutions to these problems and the results are compared with asymptotic solutions for large and small stefan numbers the stefan number being defined as the ratio of latent to sensible heats the new solutions for small stefan number are shown to provide surprisingly good approximations especially for the 3 2 wedge new results for heat transfer in a wedge in the absence of a change of phase are derived and applied in the asymptotic analysis as are new conservation laws for the stefan problem

analytical and numerical solutions to two dimensional moving interface problems with applications to the solidification of killed steel ingots this paper is concerned with the development of methods for investigating moving interface problems that involve more than one space variable the work was motivated by problems arising from the british steel corporation scunthorpe concerning the solidification of killed steel ingots first we investigate certain two dimensional analytical solutions which simulate particular aspects of ingot solidification these relate to the inward solidification of a liquid half space either when the wall temperature varies with position along the wall or when newton cooling takes place at the wall with the local heat transfer coefficient a function of wall position other approximate analytical approaches with use of the heat balance integral method and formulation in terms of an integro differential equation are discussed briefly and their limited application to two dimensional problems noted a computer procedure is then developed for solving these half space problems and this yields results in exact agreement with the analytical solutions in the work special attention is given to obtaining reliable information for small stefan number beta l c p t f t 0 since this relates to values found in the steel making process in the major part of the paper a two dimensional mathematical model of ingot solidification is developed numerical solutions are given for an ingot when the mould surface varies in geometry and in composition good agreement is obtained with radio isotope tracer tests performed at the british steel corporation scunthorpe

quadratic nonnegative matrix factorization in nonnegative matrix factorization nmf a nonnegative matrix is approximated by a product of lower rank factorizing matrices most nmf methods assume that each factorizing matrix appears only once in the approximation thus the approximation is linear in the factorizing matrices we present a new class of approximative nmf methods called quadratic nonnegative matrix factorization qnmf where some factorizing matrices occur twice in the approximation we demonstrate qnmf solutions to four potential pattern recognition problems in graph partitioning two way clustering estimating hidden markov chains and graph matching we derive multiplicative algorithms that monotonically decrease the approximation error under a variety of measures we also present extensions in which one of the factorizing matrices is constrained to be orthogonal or stochastic empirical studies show that for certain application scenarios qnmf is more advantageous than other existing nonnegative matrix factorization methods

dynamic maintenance of approximations in set valued ordered decision systems under the attribute generalization set valued information systems are important type of data tables and generalized models of single valued information systems approximations are the focal point of approaches to knowledge discovery based on rough set theory which can be used to extract and represent the hidden knowledge in the form of decision rules attribute generalization refers to dynamic change of the attribute set in an information system with respect to the requirements of real life applications in this paper we focus on maintaining approximations dynamically in set valued ordered decision systems under the attribute generalization firstly a matrix based approach for computing approximations of upward and downward unions of decision classes is constructed by introducing the dominant and dominated matrices with respect to the dominance relation then incremental approaches for updating approximations are proposed which involves several modifications to relevant matrices without having to retrain from the start on all accumulated training data finally comparative experiments on data sets from uci as well as synthetic data sets show the proposed incremental updating methods are efficient and effective for dynamic attribute generalization

local attribute reductions for decision tables abstract attribute reduction is among the most important areas of research in rough sets this paper investigates the types of local attribute reduction for decision tables we propose the concepts of lth decision class lower approximation reduction lth decision class reduction and lth decision class reduction for decision tables and provide their corresponding reduction algorithms via discernibility matrices we also establish the relationship between positive region reduction and the lth decision class reduction and report a case study using the university of california irvine dataset to verify the theoretical results

nonnegative matrix factorization with the itakura saito divergence with application to music analysis this letter presents theoretical algorithmic and experimental results about nonnegative matrix factorization nmf with the itakura saito is divergence we describe how is nmf is underlaid by a well defined statistical model of superimposed gaussian components and is equivalent to maximum likelihood estimation of variance parameters this setting can accommodate regularization constraints on the factors through bayesian priors in particular inverse gamma and gamma markov chain priors are considered in this work estimation can be carried out using a space alternating generalized expectation maximization sage algorithm this leads to a novel type of nmf algorithm whose convergence to a stationary point of the is cost function is guaranteed we also discuss the links between the is divergence and other cost functions used in nmf in particular the euclidean distance and the generalized kullback leibler kl divergence as such we describe how is nmf can also be performed using a gradient multiplicative algorithm a standard algorithm structure in nmf whose convergence is observed in practice though not proven finally we report a furnished experimental comparative study of euclidean nmf kl nmf and is nmf algorithms applied to the power spectrogram of a short piano sequence recorded in real conditions with various initializations and model orders then we show how is nmf can successfully be employed for denoising and upmix mono to stereo conversion of an original piece of early jazz music these experiments indicate that is nmf correctly captures the semantics of audio and is better suited to the representation of music signals than nmf with the usual euclidean and kl costs

an incremental attribute reduction approach based on knowledge granularity with a multi granulation view dynamic updating of attribute reduction is a key factor for the success of rough set theory since many real data vary dynamically with time though many incremental methods for updating reduct have been proposed to deal with a dynamically varying data set and has attracted much attention however it is hard to update reduct when the large scale data vary dynamically to overcome this deficiency in this paper we develop an attribute reduction algorithm with a multi granulation view to discover reduct of large scale data sets then incremental mechanisms for knowledge granularity are introduced and two corresponding incremental approaches for updating reduct are developed when many objects are varied in a large scale decision table with a multi granulation view finally experiments have been run on six data sets from uci and the experimental results show that the proposed incremental algorithm with a multi granulation view can achieve better performance for large scale data sets

multistability of α divergence based nmf algorithms in this paper the multistability of a class of amari s a divergence based nonnegative matrix factorization learning algorithms is analyzed the analysis results show that invariant sets for the update algorithms can be constructed in these invariant sets the non convergence of the discussed algorithms can be guaranteed based on lyapunov s stability theorem the local convergence of this class of learning algorithms is proved in the domain of their update rules in the simulation the analysis results are applied to image representation experiment results demonstrate that selecting suitable initial data for different applications of these nonnegative matrix factorization algorithms is very important

uncertainty measures for general fuzzy relations abstract relation is one of the important concepts in rough set models some uncertainty measures for relations were proposed in recent years by generalizing information entropy however the existing theories considered only special relations and do not address mixed type data well they always transformed each attribute into a binary relation with the same structure regardless of attribute types as a result the structure information can be lost for other types of attributes in this paper a new theory about uncertainty measures for general fuzzy relations is proposed the proposed theory can overcome the weakness of the existing theories we first introduce a novel entropy to compute the uncertainty information of fuzzy binary relations and then present the concepts of joint fuzzy entropy conditional fuzzy entropy and fuzzy mutual information the basic properties of these uncertainty measures are studied finally we apply the proposed theory to perform attribute reduction of heterogeneous data sets the experimental results show that our proposed method is feasible and effective in some cases the proposed theory can provide a fundamental framework that integrates all kinds of methods for the uncertainty information of special relations

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

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

the superiority of three way decisions in probabilistic rough set models three way decisions provide a means for trading off different types of classification error in order to obtain a minimum cost ternary classifier this paper compares probabilistic three way decisions probabilistic two way decisions and qualitative three way decisions of the standard rough set model it is shown that under certain conditions when considering the costs of different types of miss classifications probabilistic three way decisions are superior to the other two

algorithms for nonnegative matrix factorization with the β divergence this letter describes algorithms for nonnegative matrix factorization nmf with the divergence nmf the divergence is a family of cost functions parameterized by a single shape parameter that takes the euclidean distance the kullback leibler divergence and the itakura saito divergence as special cases 2 1 0 respectively the proposed algorithms are based on a surrogate auxiliary function a local majorization of the criterion function we first describe a majorization minimization algorithm that leads to multiplicative updates which differ from standard heuristic multiplicative updates by a dependent power exponent the monotonicity of the heuristic algorithm can however be proven for 0 1 using the proposed auxiliary function then we introduce the concept of the majorization equalization me algorithm which produces updates that move along constant level sets of the auxiliary function and lead to larger steps than mm simulations on synthetic and real data illustrate the faster convergence of the me approach the letter also describes how the proposed algorithms can be adapted to two common variants of nmf penalized nmf when a penalty function of the factors is added to the criterion function and convex nmf when the dictionary is assumed to belong to a known subspace

extinction behaviour for two dimensional inward solidification problems the problem of the inward solidification of a two dimensional region of fluid is considered it being assumed that the liquid is initially at its fusion temperature and that heat flows by conduction only the resulting one phase stefan problem is reformulated using the baiocchi transform and is examined using matched asymptotic expansions under the assumption that the stefan number is large analysis on the first time scale reveals that the liquid solid free boundary becomes elliptic in shape at times just before complete freezing however as with the radially symmetric case considered previously this analysis leads to an unphysical singularity in the final temperature distribution a second time scale therefore needs to be considered and it is shown that the free boundary retains its shape until another non uniformity is formed finally a third exponentially short time scale which also describes the generic extinction behaviour for all stefan numbers is needed to resolve the non uniformity by matching between the last two time scales we are able to determine a uniformly valid description of the temperature field and the location of the free boundary at times just before extinction recipes for computing the time it takes to completely freeze the body and the location at which the final freezing occurs are also derived

a logic for rough sets abstract the collection of all subsets of a set forms a boolean algebra under the usual set theoretic operations while the collection of rough sets of an approximation space is a regular double stone algebra pomykala and pomykala 1988 the appropriate class of algebras for classical propositional logic are boolean algebras and it is reasonable to assume that regular double stone algebras are a class of algebras appropriate for a logic of rough sets using the representation theorem for these algebras by katrinak 1974 we present such a logic for rough sets and its algebraic semantics in the spirit of andreka and nemeti 1994

the numerical solution of two generalizations of the neumann moving interface problem into two dimensions we present numerical solutions for the following stefan problems the half space z 0 is initially filled with liquid at its fusion temperature the boundary z 0 taken to be the x axis is maintained at a constant temperature less than the fusion temperature for x 0 the first problem considers the case of an insulated boundary and the second problem considers the case of the boundary maintained at the fusion temperature this gives rise to a solid liquid interface curved in the x z plane

on nonnegative matrix factorization algorithms for signal dependent noise with application to electromyography data nonnegative matrix factorization nmf by the multiplicative updates algorithm is a powerful machine learning method for decomposing a high dimensional nonnegative matrix v into two nonnegative matrices w and h where it has been successfully applied in the analysis and interpretation of large scale data arising in neuroscience computational biology and natural language processing among other areas a distinctive feature of nmf is its nonnegativity constraints that allow only additive linear combinations of the data thus enabling it to learn parts that have distinct physical representations in reality in this letter we describe an information theoretic approach to nmf for signal dependent noise based on the generalized inverse gaussian model specifically we propose three novel algorithms in this setting each based on multiplicative updates and prove monotonicity of updates using the em algorithm in addition we develop algorithm specific measures to evaluate their goodness of fit on data our methods are demonstrated using experimental data from electromyography studies as well as simulated data in the extraction of muscle synergies and compared with existing algorithms for signal dependent noise

attribute selection with fuzzy decision reducts rough set theory provides a methodology for data analysis based on the approximation of concepts in information systems it revolves around the notion of discernibility the ability to distinguish between objects based on their attribute values it allows to infer data dependencies that are useful in the fields of feature selection and decision model construction in many cases however it is more natural and more effective to consider a gradual notion of discernibility therefore within the context of fuzzy rough set theory we present a generalization of the classical rough set framework for data based attribute selection and reduction using fuzzy tolerance relations the paper unifies existing work in this direction and introduces the concept of fuzzy decision reducts dependent on an increasing attribute subset measure experimental results demonstrate the potential of fuzzy decision reducts to discover shorter attribute subsets leading to decision models with a better coverage and with comparable or even higher accuracy