fast dimension reduction for document classification based on imprecise spectrum analysis latent semantic indexing lsi with singular value decomposition svd is an effective dimension reduction method for document classification and other information analysis tasks the computational overhead of svd is known to be a bottleneck in dealing with large data sets and faster dimension reduction with competitive accuracy is desired in such a setting this paper presents imprecise spectrum analysis isa to carry out fast dimension reduction for document classification isa follows the one sided jacobi method for computing svd and simplifies its intensive orthogonality computation it uses a representative matrix composed of top k column vectors derived from the original feature vector space and reduces the dimension of a feature vector by computing its product with this representative matrix the paper provides an analysis to show the approximation error and the rationale behind such a dimension reduction method to further improve classification accuracy this paper also presents a feature selection method in building the initial feature matrix and augments the representative matrix by including centroid vectors our extensive experimental results show that isa is fast in handling large term document feature matrices while delivering better or competitive classification accuracy for the tested benchmarks compared to lsi with svd

on photon correlation measurements of colloidal size distributions using bayesian strategies in this paper the evaluation of particle size distribution using photon correlation spectroscopy according to the method of regularization of first kind integral equation including laplace transform by means of bayesian strategy is presented we shall convert the laplace transform to first kind integral equation of convolution type which is an ill posed problem then we use the bayesian regularization method to solve it this type of problem plays an important role in the field of photon correlation spectroscopy fluorescent decay sedimentation equilibrium system theory and in other areas of physics and applied mathematics the method is applied to test problems taken from the literature and it gives a good approximation to the true solution

constructing a fuzzy controller from data abstract fuzzy control at the executive level can be interpreted as an approximation technique for a control function based on typical imprecisely specified input output tuples that are represented by fuzzy sets the imprecision is characterized by similarity relations that are induced by transformations of the canonical distance function between real numbers taking this interpretation of fuzzy controllers into account in order to derive a fuzzy controller from observed data typical input output tuples have to be identified in addition a concept of similarity based on a transformations of the canonical distance is needed in order to characterize the typical input output tuples by suitable fuzzy sets a variety of fuzzy clustering algorithms that are exactly working in this spirit exists they identify prototypes and assign fuzzy sets to the prototypes on the basis of a suitable transformed distance in this paper we discuss how such fuzzy clustering techniques can be applied to construct a fuzzy controller from data and introduce special clustering algorithms that are tailored for this problem

set approximations in fuzzy formal concept analysis formal concept analysis and rough set theory are two important tools in knowledge representation and knowledge discovery in relational information systems the purpose of this paper is to study rough set approximations within formal concept analysis in fuzzy environment properties of existent fuzzy concept lattices derived from an adjoint pair of operations are first reviewed and examined based on both lattice theoretic and fuzzy set theoretic operators two new pairs of rough fuzzy set approximations within fuzzy formal contexts are then defined finally properties of the rough fuzzy set approximation operators are presented in detail

fuzzy sets and vague environments abstract in this paper we propose a natural approach to handle imprecise numbers as they arise for example from measurements fuzzy sets turn out to be a canonical representation for such imprecise numbers that are induced by taking different tolerance or error bounds into account fuzzy sets are induced by scaling factors that describe the magnitude of the imprecision on the other the scaling factors can be derived from given fuzzy sets so that we have a correspondence between scaling factors and fuzzy sets when these concepts are applied to control problems the max min rule is rediscovered as an interpolation technique viewing fuzzy control as an interpolation technique in vague environments enables us to validate various concepts for the design and tuning of fuzzy controllers and also suggests new methods based on clear semantics

granular variable precision l fuzzy rough sets based on residuated lattices abstract firstly as for the beginning of this paper we introduce the granular variable precision l fuzzy rough sets based on residuated lattices with arbitrary l fuzzy relations and then the equivalent expressions for the lower and upper approximation operators are given with l fuzzy implications and l fuzzy coimplications on arbitrary l fuzzy relations which can calculate the lower and upper approximation operators efficiently finally some basic properties of the granular variable precision l fuzzy rough sets on residuated lattices are investigated and the conclusions on the granular variable precision fuzzy rough sets are generalized into the situations of the truth values set becoming residuated lattices

alternating cluster estimation a new tool for clustering and function approximation many clustering models define good clusters as extrema of objective functions optimization of these models is often done using an alternating optimization ao algorithm driven by necessary conditions for local extrema we abandon the objective function model in favor of a generalized model called alternating cluster estimation ace ace uses an alternating iteration architecture but membership and prototype functions are selected directly by the user virtually every clustering model can be realized as an instance of ace out of a large variety of possible instances of non ao models we present two examples 1 an algorithm with a dynamically changing prototype function that extracts representative data and 2 a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions we illustrate these non ao instances on three problems a simple clustering of plane data where we show that creating an unmatched ace algorithm overcomes some problems of fuzzy c means fcm ao and possibilistic c means pcm ao b functional approximation by clustering on a simple artificial data set and c functional approximation on a 12 input 1 output real world data set ace models work pretty well in all three cases

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

a contribution to convergence theory of fuzzy c means and derivatives in this paper we revisit the convergence and optimization properties of fuzzy clustering algorithms in general and the fuzzy c means fcm algorithm in particular our investigation includes probabilistic and a slightly modified implementation of possibilistic memberships which will be discussed under a unified view we give a convergence proof for the axis parallel variant of the algorithm by gustafson and kessel that can be generalized to other algorithms more easily than in the usual approach using reformulated fuzzy clustering algorithms we apply banach s classical contraction principle and establish a relationship between saddle points and attractive fixed points for the special case of fcm we derive a sufficient condition for fixed points to be attractive allowing identification of them as local minima of the objective function excluding the possibility of a saddle point

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

about the use of fuzzy clustering techniques for fuzzy model identification abstract in this work we present an alternative approach to generate fuzzy rules with a functional consequent associated to the tsk fuzzy model in our case using fuzzy clustering algorithms that look for linear behaviours in the product space of the input output data we analyse different methods to generate the associated fuzzy rules using in some cases multidimensional reference fuzzy sets in the product space of the input variables and in other cases fuzzy sets in each of the different dimensions in any case the rules being generated correspond to a tsk fuzzy model

rough set theory for the interval valued fuzzy information systems the notion of a rough set was originally proposed by pawlak z pawlak rough sets international journal of computer and information sciences 11 5 1982 341 356 later on dubois and prade d dubois h prade rough fuzzy sets and fuzzy rough sets international journal of general system 17 2 3 1990 191 209 introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough sets this paper deals with an interval valued fuzzy information system by means of integrating the classical pawlak rough set theory with the interval valued fuzzy set theory and discusses the basic rough set theory for the interval valued fuzzy information systems in this paper we firstly define the rough approximation of an interval valued fuzzy set on the universe u in the classical pawlak approximation space and the generalized approximation space respectively i e the space on which the interval valued rough fuzzy set model is built secondly several interesting properties of the approximation operators are examined and the interrelationships of the interval valued rough fuzzy set models in the classical pawlak approximation space and the generalized approximation space are investigated thirdly we discuss the attribute reduction of the interval valued fuzzy information systems finally the methods of the knowledge discovery for the interval valued fuzzy information systems are presented with an example

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

svd representation of unitarily invariant matrices it often happens that a signal processing application will involve a matrix operator that is invariant under specific preunitary and postunitary matrix multiplications this invariance feature may be exploited to establish algebraic invariance properties possessed by the singular vectors associated with that matrice s svd representation this characterization can be of considerable theoretical as well as computational value to illustrate the utility of this approach the new class of bisymmetric matrices will be examined in detail interest in bisymmetric matrices arises from their frequent appearance in signal processing applications for instance it is shown that the forward backward data matrix arising in linear prediction is bisymmetric the more general class of exponential bisymmetric matrices which includes among its members the discrete fourier transform is also briefly examined

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

towards the theory of m approximate systems fundamentals and examples the concept of an m approximate system is introduced basic properties of the category of m approximate systems and in a natural way defined morphisms between them are studied it is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of m approximate systems

a class of rough multiple objective programming and its application to solid transportation problem this paper establishes a rough multiple objective programming model for a solid transportation problem furthermore a general model for rough multiple objective programming problem is presented properties of the feasible and efficient solutions of rough multiple objective programming problems are investigated in addition compromise solutions are obtained by using the interactive fuzzy satisfying method to solve the rough multiple objective solid transportation problem the rough simulation based genetic algorithm is proposed in which the rough simulation is embedded into the genetic algorithm finally an application of the solid transportation problem at xiluodu hydropower station is provided as an illustration

tasc two attribute set clustering through decision tree construction clustering is the process of grouping a set of objects into classes of similar objects in the past clustering algorithms had a common problem that they use only one set of attributes for both partitioning the data space and measuring the similarity between objects this problem has limited the use of the existing algorithms on some practical situation hence this paper introduces a new clustering algorithm which partitions data space by constructing a decision tree using one attribute set and measures the degree of similarity using another three different partitioning methods are presented the algorithm is explained with illustration the performance and accuracy of the four partitioning methods are evaluated and compared

a hierarchical fuzzy clustering approach to fuzzy modeling abstract this paper introduces a new method for fuzzy modeling based on a hierarchical fuzzy clustering scheme the method consists of a sequence of steps aiming towards developing a takagi sugeno ts fuzzy model of optimal structure where the fuzzy sets in the premise part are of gaussian type starting from an initial ordinary fuzzy partition of the input space the algorithm performs a nearest neighbor search and groups the original input training data into a number of clusters the centers of these clusters are further processed using an optimal fuzzy clustering technique which is based on the weighted fuzzy c means algorithm the resulted optimal fuzzy partition defines the number of fuzzy rules and provides an initial estimation for the system parameters which in a next step are fine tuned using the well known gradient descend algorithm the proposed method is successfully applied to three test examples where the produced fuzzy models prove to be very accurate as well as compact in size

robust tsk fuzzy modeling for function approximation with outliers the takagi sugeno kang tsk type of fuzzy models has attracted a great attention of the fuzzy modeling community due to their good performance in various applications most approaches for modeling tsk fuzzy rules define their fuzzy subspaces based on the idea of training data being close enough instead of having similar functions besides training data sets algorithms often contain outliers which seriously affect least square error minimization clustering and learning algorithms a robust tsk fuzzy modeling approach is presented in the approach a clustering algorithm termed as robust fuzzy regression agglomeration rfra is proposed to define fuzzy subspaces in a fuzzy regression manner with robust capability against outliers to obtain a more precision model a robust fine tuning algorithm is then employed various examples are used to verify the effectiveness of the proposed approach from the simulation results the proposed robust tsk fuzzy modeling indeed showed superior performance over other approaches

on relationship between modified sets topological spaces and rough sets abstract in this paper we define modifiers by relations especially weakening and substantiating modifiers are defined by a so called accessibility relation which is a reflexive relation on a non empty set x after presenting some main results we prove that this type of modifiers will satisfy the kuratowski closure axioms this means that modifiers in fact induce topological spaces also rough sets are considered to be a special case of modified sets

granular variable precision fuzzy rough sets with general fuzzy relations the variable precision fuzzy rough sets were proposed to remedy the defects of preexisting fuzzy rough set models however the variable precision fuzzy rough sets were only defined and investigated on fuzzy similarity relations in this paper the granular variable precision fuzzy rough sets with general fuzzy relations are proposed on arbitrary fuzzy relations the equivalent expressions of the approximation operators are given with fuzzy co implications on arbitrary fuzzy relations which can calculate efficiently the approximation operators the granular variable precision fuzzy rough sets are characterized from the constructive approach which are investigated on different fuzzy relations the conclusions on the variable precision fuzzy rough sets are generalized into the granular variable precision fuzzy rough sets

a spectral order method for inverting sectorial laplace transforms laplace transforms which admit a holomorphic extension to some sector strictly containing the right half plane and exhibiting a potential behavior are considered a spectral order parallelizable method for their numerical inversion is proposed the method takes into account the available information about the errors arising in the evaluations several numerical illustrations are provided

design of a near optimal wide range fuzzy logic controller the paper describes a novel method for the design of a fuzzy logic controller with near optimal performance in the wide range of operating conditions the approach is based on the analysis of the system behaviour in the error state space the final control structure in a form of a dual fuzzy logic controller is arrived at in two stages the first stage encompasses design and tuning of the pi like fuzzy controller the second stage consists of placing an additional fuzzy controller of a structure similar to that of the first one in parallel with the pi like fuzzy controller designed in the first stage the final structure of the dual fuzzy controller is obtained by synthesis and tuning of those segments of the second controller that are different the resulting dual controller is characterised with high performance in the wide range of operating conditions and with small number of parameters that can be adjusted using simple optimisation methods the controller is developed and tested for a plant comprising a variable speed dc motor drive

estimating the concentration of optically active constituents of sea water by takagi sugeno models with quadratic rule consequents determining the concentrations of chlorophyll suspended particulate matter and coloured dissolved organic matter in the sea water is basic to support the monitoring of upwelling phenomena algae blooms and changes in the marine ecosystem since these concentrations affect the spectral distribution of the solar light back scattered by the water body their estimation can be computed by using a set of remotely sensed multispectral measurements of the reflected sunlight in this paper the relation between the concentrations of interest and the average subsurface reflectances is modelled by means of a set of second order takagi sugeno ts fuzzy rules unlike first order ts rules which adopt linear functions as consequent second order ts rules exploit quadratic functions thus improving the modelling capability of the rule in the subspace determined by the antecedent first we show how we can build a second order ts model through a simple transformation which allows estimating the consequent parameters using standard linear least squares algorithms and by adopting one of the most used methods proposed in the literature to generate first order ts models then we compare first order and second order ts models against mean square error and interpretability of rules we highlight how second order ts models allow us to achieve better approximation than first order ts models though maintaining interpretability of the rules finally we show how second order ts models perform considerably better the mean square error is lower by two orders of magnitude than the specific implementations of radial basis function networks and multi layer perceptron networks used in previous papers for the same application domain

comparison of the probabilistic approximate classification and the fuzzy set model abstract it is shown that the generalized notion probabilistic approximate classification of rough sets can be conveniently described by the concept of fuzzy sets a discussion of the proper choice of the definition for the membership function of the intersection union of fuzzy sets is also presented however from the point of view of the probabilistic approximation space it is argued that there does not exist a universal definition for the fuzzy intersection union operation

an iterative method for the numerical inversion of laplace transforms we present an algorithm for the numerical inversion of laplace transforms that is a particular case of the iterated regularization method proposed by vainikko in 1982 to construct the finite dimensional space we use laguerre polynomials error bounds for the approximations are derived

a study about dimensional change of industrial parts using fuzzy rules abstract this work presents the development of a fuzzy model aimed to predict the dimensional changes of actual industrial parts made in a new emerging material called austempered ductile iron adi the dimensional change is an important factor that must be taken into account to improve the fabrication process of any actual part of adi this change is produced during a heat treatment cycle and in the factory practice its prediction is difficult due to the high number of variables affecting it in the present case it was considered that the dimensional change is strongly influenced by 11 operative variables of the fabrication process associated to the chemical composition and heat treatment temperatures and holding times the data employed to build the model corresponds to measurements done by experts on different actual industrial parts the knowledge acquisition about the origin of the data was necessary to understand the uncertainty factors and to adjust the parameters for obtaining a proper model the model was developed with a takagi sugeno type structure and its parameters adjusted with the anfis learning algorithm and introduced into an expert system previously developed it allows the accurate prediction of dimensional changes and helps in the efficient design of new industrial adi parts

brouwer zadeh posets and three valued ł ukasiewicz posets abstract this paper is a study of the structure of brouwer zadeh or bz poset i e a poset endowed with two non usual orthocomplementations these two orthocomplementations allow definition of two unary operators which can be considered as algebraic counterparts of the necessity and possibility operators of modal logic a construction of how to induce a three valued bz poset from a bz poset is given the examples of the bz lattice of all generalized characteristic functionals on a reference space and of the bz poset of all generalized orthogonal projections on a hilbert space are dealt with

rough sets and fuzzy sets some remarks on interrelations abstract this short paper refers to two remarks given in 3 and disputes them any rough set can be expressed by means of a membership function u 0 0 5 1 we show that this representation can be extended to union and intersection

physical interpretation of signal reconstruction from reduced rank matrices an enhanced version of a signal is obtained after subtraction of a linear combination of rank one matrices from the signal observation matrix this operation results in a nontoeplitz observation matrix by averaging the elements of this matrix a new toeplitz matrix is produced and a reconstructed signal is generated this averaging operation is examined and physical interpretations are given

kernel based fuzzy clustering and fuzzy clustering a comparative experimental study in this study we present a comprehensive comparative analysis of kernel based fuzzy clustering and fuzzy clustering kernel based clustering has emerged as an interesting and quite visible alternative in fuzzy clustering however the effectiveness of this extension vis a vis some generic methods of fuzzy clustering has neither been discussed in a complete manner nor the performance of clustering quantified through a convincing comparative analysis our focal objective is to understand the performance gains and the importance of parameter selection for kernelized fuzzy clustering generic fuzzy c means fcm and gustafson kessel gk fcm are compared with two typical generalizations of kernel based fuzzy clustering one with prototypes located in the feature space kfcm f and the other where the prototypes are distributed in the kernel space kfcm k both generalizations are studied when dealing with the gaussian kernel while kfcm k is also studied with the polynomial kernel two criteria are used in evaluating the performance of the clustering method and the resulting clusters namely classification rate and reconstruction error through carefully selected experiments involving synthetic and machine learning repository http archive ics uci edu beta data sets we demonstrate that the kernel based fcm algorithms produce a marginal improvement over standard fcm and gk for most of the analyzed data sets it has been observed that the kernel based fcm algorithms are in a number of cases highly sensitive to the selection of specific values of the kernel parameters

optimal design of radial basis function neural networks for fuzzy rule extraction in high dimensional data abstract the design of an optimal radial basis function neural network rbfnf is not a straightforward procedure in this paper we take advantage of the functional equivalence between rbfn and fuzzy inference systems to propose a novel efficient approach to rbfn design for fuzzy rule extraction the method is based on advanced fuzzy clustering techniques solutions to practical problems are proposed by combining these different solutions a general methodology is derived the efficiency of our method is demonstrated on challenging synthetic and real world data sets

svd analysis by synthesis of harmonic signals an analysis by synthesis procedure based on the singular value decomposition svd methodology is proposed using this procedure a criterion for detecting the number of sinusoidal signals in the presence of noise is defined consecutive reconstructions are performed and the resulting error power is compared to the noise variance in order to get the best approximation of the original noncorrupted signal the number of the singular values corresponding to a reconstruction error power as close as possible to the noise variance gives the parsimonious order the existence of such a criterion is important for both high quality reconstruction and spectral analysis various spectral estimation techniques used on a reconstructed signal make it possible to retrieve harmonics in a highly noisy environment with very short data lengths

statistical analysis of effective singular values in matrix rank determination a major problem in using svd singular value decomposition as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end conference regions are derived for the perturbed singular values of matrices with noisy observation data the analysis is based on the theories of perturbations of singular values and statistical significance test threshold bounds for perturbation due to finite precision and i i d random models are evaluated in random models the threshold bounds depend on the dimension of the matrix the noisy variance and predefined statistical level of significance results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given

exclusive disjunctive soft sets soft sets theory initiated by molodtsov is an emerging tool to deal with uncertain problems and has been studied by scholars in both theory and practice this paper proposes the notion of exclusive disjunctive soft sets and studies some of its operations such as restricted relaxed and operations dependency between exclusive disjunctive soft sets and bijective soft sets exclusive disjunctive soft decision systems reduction of exclusive disjunctive soft decision systems core of exclusive disjunctive soft decision systems decision rules in exclusive disjunctive decision soft sets moreover this study gives an application of exclusive disjunctive soft sets which shows that it can be applied to attribute reduction of incomplete information system

on a ktb modal fuzzy logic abstract an extension of the classical ktb modal logic to the fuzzy case is considered a new notion of similarity is introduced and a fuzzy logic based on this relation is proposed also the validity of formulas is defined by introducing a notion of logical consequence then the decision procedure of this logic is described in the tableau method

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

fuzzy reasoning based on a new fuzzy rough set and its application to scheduling problems in this paper we study the fuzzy reasoning based on a new fuzzy rough set first we define a broad family of new lower and upper approximation operators of fuzzy sets between different universes using a set of axioms then based on the approximation operators above we propose the fuzzy reasoning based on the new fuzzy rough set by means of the above fuzzy reasoning based on the new fuzzy rough set for a given premise we can obtain the fuzzy reasoning consequence expressed by the fuzzy interval constructed by the above two approximations of fuzzy sets furthermore through the defuzzification of the lower and upper approximations we can get the corresponding two values constructing the interval used as the fuzzy reasoning consequence after defuzzification then from the above interval a suitable value can be selected as the final reasoning consequence so that some special constraints are satisfied as possibly at last we apply the fuzzy reasoning based on the new fuzzy rough set to the scheduling problems and numerical computational results show that the fuzzy reasoning based on the new fuzzy rough set is more suitable for the scheduling problems compared with the fuzzy reasoning based on the cri method and the iii method

numerical inversion of the laplace transform from the real axis a numerical method for inversion of the laplace transform f p given for p 0 only is proposed recommendations for the choice of the abscissa of convergence and parameters of numerical integration are given the results of the numerical tests are discussed

on the eigenvectors of symmetric toeplitz matrices this paper presents a number of results concerning the eigenvectors of a symmetric toeplitz matrix and the location of the zeros of the filters eigenfilters whose coefficients are the elements of the eigenvectors one of the results is that the eigenfilters corresponding to the maximum and minimum eigenvalues if distinct have their zeros on the unit circle while the zeros of the other eigenfilters may or may not have their zeros on the unit circle even if the zeros of the eigenfilters of a matrix are all on the unit circle the matrix need not be toeplitz examples are given to illustrate the different properties

fuzzy rough set theory for the interval valued fuzzy information systems the concept of the rough set was originally proposed by pawlak as a formal tool for modelling and processing incomplete information in information systems then in 1990 dubois and prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets the aim of this paper is to present a new extension of the rough set theory by means of integrating the classical pawlak rough set theory with the interval valued fuzzy set theory i e the interval valued fuzzy rough set model is presented based on the interval valued fuzzy information systems which is defined in this paper by a binary interval valued fuzzy relations r f i uxu on the universe u several properties of the rough set model are given and the relationships of this model and the others rough set models are also examined furthermore we also discuss the knowledge reduction of the classical pawlak information systems and the interval valued fuzzy information systems respectively finally the knowledge reduction theorems of the interval valued fuzzy information systems are built

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

fuzzy rough attribute reduction via mutual information with an application to cancer classification establishing a classification model for cancer recognition based on dna microarrays is useful for cancer diagnosis feature selection is a key step to perform cancer classification with dna microarrays for there is a large number of genes from which to predict classes and a relatively small number of samples automatic methods must be developed for extracting relevant genes which are essential for classification this paper proposes a novel approach for reducing data redundancy based on fuzzy rough set theory and information theory a mutual information based algorithm for attribute reduction is suggested the method is applied to the problem of gene selection for cancer classification experimental results show that the algorithm is more effective than conventional rough sets based approaches

rough set approach to incomplete numerical data rough set theory has been applied successfully in many fields however classical rough set model can only deal with complete and symbolic data sets some researchers have proposed extended rough set models to handle incomplete data while others proposed extensions of classical rough set models to deal with numerical data however there exist many data which contain numerical attributes and missing values simultaneously we propose in this paper an extended rough set model i e tolerance fuzzy rough set model to deal with this type of data characterized with numerical attributes and missing values that is incomplete numerical data discernibility matrices and discernibility functions for incomplete numerical information systems and incomplete numerical decision systems are defined to compute reducts or relative reducts meanwhile the relationship between the proposed tolerance fuzzy rough set model and the tolerance rough set model is also examined it is shown that the tolerance fuzzy rough set model is an extension of the tolerance rough set model finally uncertainty measurement is also investigated it is suggested that the proposed tolerance fuzzy rough set model provide an optional approach to incomplete numerical data

further remarks on the relation between rough and fuzzy sets abstract based on results of pawlak and wygralak some remarks on the relation between rough sets and fuzzy sets are given an improved definition of rough set is also proposed

equality relations as a basis for fuzzy control abstract the aim of this paper is to introduce a fuzzy control model with well founded semantics in order to explain the concepts applied in fuzzy control assuming that the domains of the input and output variables for the process are endowed with equality relations that reflect the indistinguishability of values lying closely together the use of triangular and trapezoidal membership functions can be justified and max inference where is a t norm turns out to be a consequence of our model distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like mom or coa are appropriate or lead to undesired results

on constructing new expansions of functions using linear operators let t u be two linear operators mapped onto the function f such that u t f f but t u f f in this paper we first obtain the expansion of functions t u f and u t f in a general case then we introduce four special examples of the derived expansions first example is a combination of the fourier trigonometric expansion with the taylor expansion and the second example is a mixed combination of orthogonal polynomial expansions with respect to the defined linear operators t and u in the third example we apply the basic expansion u t f f x to explicitly compute some inverse integral transforms particularly the inverse laplace transform and in the last example a mixed combination of taylor expansions is presented a separate section is also allocated to discuss the convergence of the basic expansions t u f and u t f

concept analysis via rough set and afs algebra formal concept analysis fca was originally proposed by wille 1982 which is an important theory for data analysis and knowledge discovery afs axiomatic fuzzy set algebra was proposed by liu x liu the fuzzy theory based on afs algebras and afs structure journal of mathematical analysis and applications 217 1998 459 478 x liu the topology on afs algebra and afs structure journal of mathematical analysis and applications 217 1998 479 489 which is a semantic methodology relating to the fuzzy theory combining above two theories we propose afs formal concept which can be viewed as the generalization and development of monotone concept proposed by deogun and saquer 2003 moreover we show that the set of all afs formal concepts forms a complete lattice afs formal concept can be applied to represent the logic operations of queries in information retrieval furthermore we give an approach to find the afs formal concepts whose intents extents approximate any element of afs algebra by virtue of rough set theory

a neuro fuzzy method to learn fuzzy classification rules from data abstract neuro fuzzy systems have recently gained a lot of interest in research and application neuro fuzzy models as we understand them are fuzzy systems that use local learning strategies to learn fuzzy sets and fuzzy rules neuro fuzzy techniques have been developed to support the development of e g fuzzy controllers and fuzzy classifiers in this paper we discuss a learning method for fuzzy classification rules the learning algorithm is a simple heuristics that is able to derive fuzzy rules from a set of training data very quickly and tunes them by modifying parameters of membership functions our approach is based on nefclass a neuro fuzzy model for pattern classification we also discuss some results obtained by our software implementation of nefclass which is freely available on the internet

a roughness measure for fuzzy sets recently an attempt of integration between the theories of fuzzy sets and rough sets has resulted in providing a roughness measure for fuzzy sets m banerjee s k pal roughness of a fuzzy set information sciences 93 1996 235 246 essentially banerjee and pal s roughness measure depends on parameters that are designed as thresholds of definiteness and possibility in membership of the objects to a fuzzy set in this paper we first remark that this measure of roughness has several undesirable properties and then propose a parameter free roughness measure for fuzzy sets based on the notion of the mass assignment of a fuzzy set several interesting properties of this new measure are examined furthermore we also discuss how the proposed approach is used to describe the rough approximation quality of a fuzzy classification

further comments on on the eigenvectors of symmetric toeplitz matrices attention is drawn to some previous work on the matrices discussed in the comments of datta and morgera on the above paper