from a discrete to a continuous model of biological cell movement the process by which one may take a discrete model of a biophysical process and construct a continuous model based upon it is of mathematical interest as well as being of practical use in this work we take the extended potts model applied to biological cell movement to its continuous limit beginning with a single cell moving in one dimension on a lattice and obeying potts model rules of movement we develop an expression for the diffusion coefficient of a collection of noninteracting cells which depends explicitly on the potts model parameters we show how this coefficient varies when the potts parameters for cell membrane elasticity and cell medium adhesion are varied and perform computer simulations which support our theoretical result we explain the relationship between the probability of occupancy of lattice points and the density profile in the continuous limit and extend our analysis by including interactions between the cells in so doing we are able to develop a set of coupled ordinary differential equations showing the evolution of a density profile in the presence of significant cell cell adhesion and show how increases in the strength of this adhesion modulates diffusion in so doing we develop some insights into how continuous models of physical systems can be based upon discrete models which describe the same system

aggregation blowup and collapse the abc s of taxis in reinforced random walks in many biological systems movement of an organism occurs in response to a diffusible or otherwise transported signal and in its simplest form this can be modeled by diffusion equations with advection terms of the form first derived by patlak bull of math biophys 15 1953 pp 311 338 however other systems are more accurately modeled by random walkers that deposit a nondiffusible signal that modifies the local environment for succeeding passages in these systems one example of which is the myxobacteria the question arises as to whether aggregation is possible under suitable hypotheses on the transition rules and the production of a control species that modulates the transition rates davis probab theory related fields 84 1990 pp 203 229 has studied this question for a certain class of random walks and here we extend this analysis to the continuum limit of such walks we first derive several general classes of partial differential equations that depend on how the movement rules are

a hierarchical coevolutionary mapreduce based knowledge reduction algorithm with robust ensemble pareto equilibrium with the rapid development of electronic engineering information and network technologies large scale data mining and knowledge discovery have become a new challenge in this paper a hierarchical coevolutionary mapreduce based knowledge reduction algorithm hcmrkr with robust ensemble pareto dominance is proposed for big data analysis firstly a novel hierarchical co evolutionary mapreduce framework with niche neighborhood radius is designed to divide the entire population into n subpopulations the layered niche neighborhood radius is constructed so that subpopulations can be self adaptively decomposed into the attribute approximate space with uncovering the underlying interaction structure of decision attributes the reduction performances of elitist leaders are surely guaranteed to be the same with those using the whole independent dataset secondly a robust ensemble strategy of reduction pareto equilibrium is adopted to help elitist leaders from the pareto front region to conduct the ensemble game of reduction subsets in different niche conic subspaces thus most reduction solutions will be enhanced to be more robust within the stable elitists region thirdly various elitist leaders will use the parallel mapreduce mechanism to determine the best strategy to extract their knowledge reduction set and the adaptive reduction evolution with incremental learning can be implemented well experimental results illustrate that the proposed hcmrkr algorithm can effectively and efficiently handle the knowledge reduction problem in the big data sets as well as keeping more robust and stable performances compared with existing state of the art algorithms furthermore the validation performed on two kinds of neonatal brain mris further demonstrates the hcmrkr s promising advantage for the real world applications

discernibility matrix simplification for constructing attribute reducts this paper proposes a reduct construction method based on discernibility matrix simplification the method works in a similar way to the classical gaussian elimination method for solving a system of linear equations elementary matrix simplification operations are introduced each operation transforms a matrix into a simpler form by applying these operations a finite number of times one can transform a discernibility matrix into one of its minimum i e the simplest forms elements of a minimum discernibility matrix are either the empty set or singleton subsets in which the union derives a reduct with respect to an ordering of attributes which is either computed based on a certain measure of attributes or directly given by a user two heuristic reduct construction algorithms are presented one algorithm attempts to exclude unimportant attributes from a reduct and the other attempts to include important attributes in a reduct

extended rough set based attribute reduction in inconsistent incomplete decision systems a systematic study of attribute reduction in inconsistent incomplete decision systems iidss has not yet been performed and no complete methodology of attribute reduction has been developed for iidss to date in an iids there are various ways to handle missing values in this paper a missing attribute value may be replaced with any known value of a corresponding attribute such a missing attribute value is called a do not care condition in this way this paper establishes reduction concepts specifically for iidss mainly by extending related reduction concepts from other types of decision systems into iidss and then derives their relationships and properties with these derived properties the extended reducts are divided into two distinct types heritable reducts and nonheritable reducts and algorithms for computing them are presented using the relationships derived here the eight types of extended reducts established for iidss can be converted to five equivalent types then five discernibility function based approaches are proposed each for a particular kind of reduct each approach can find all reducts of its associated type the theoretical analysis of the proposed approaches is described in detail finally numerical experiments have shown that the proposed approaches are effective and suitable for handling both numerical and categorical attributes but that they have different application conditions the proposed approaches can provide a solution to the reduction problem for iidss

from a discrete to a continuum model of cell dynamics in one dimension multiscale modeling is emerging as one of the key challenges in mathematical biology however the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions for example at the cellular scale how can the appropriate discrete cell level model be identified in a given context additionally how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior in order to begin to address such questions we consider a discrete one dimensional cell based model in which cells are assumed to interact via linear springs from the discrete equations of motion the continuous rouse p e rouse j chem phys 21 1272 1953 model is obtained this formalism readily allows the definition of a cell number density for which a nonlinear fast diffusion equation is derived excellent agreement is demonstrated between the continuum and discrete models subsequently via the incorporation of cell division we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail in the limit of stiff springs where cells can be considered to be incompressible we show that cell velocity can be directly related to cell production this assumption is frequently made in the literature but our derivation places limits on its validity finally the model is compared with a model of a similar form recently derived for a different discrete cell based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models

ergodic directional switching in mobile insect groups we obtain a fokker planck equation describing experimental data on the collective motion of locusts the noise is of internal origin and due to the discrete character and finite number of constituents of the swarm the stationary probability distribution shows a rich phenomenology including nonmonotonic behavior of several order and disorder transition indicators in noise intensity this complex behavior arises naturally as a result of the randomness in the system its counterintuitive character challenges standard interpretations of noise induced transitions and calls for an extension of this theory in order to capture the behavior of certain classes of biologically motivated models our results suggest that the collective switches of the group s direction of motion might be due to a random ergodic effect and as such they are inherent to group formation

a new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets traditional rough set theory is mainly used to extract rules from and reduce attributes in databases in which attributes are characterized by partitions while the covering rough set theory a generalization of traditional rough set theory does the same yet characterizes attributes by covers in this paper we propose a way to reduce the attributes of covering decision systems which are databases characterized by covers first we define consistent and inconsistent covering decision systems and their attribute reductions then we state the sufficient and the necessary conditions for reduction finally we use a discernibility matrix to design algorithms that compute all the reducts of consistent and inconsistent covering decision systems numerical tests on four public data sets show that the proposed attribute reductions of covering decision systems accomplish better classification performance than those of traditional rough sets

rfrr robust fuzzy rough reduction this paper proposes a robust method of dimension reduction using fuzzy rough sets in which the reduction results can reflect the reducts obtained on all of the possible parameters here the reducts being obtained on all of the possible parameters mean that all of the reducts are obtained on different degrees of robustness to handle noise this method is completely different from the existing methods of fuzzy rough reduction the differences are shown in three aspects the concept the tool and the algorithm first the key concept of attribute reduction is redefined in a new way that is the robust fuzzy rough reduct which is shortened to a robust reduct is proposed to reflect the classical reducts obtained on all of the possible parameters the new robust reduct is not a crisp subset of condition attributes rather it is a fuzzy subset whose most interesting property is that any cut set of the robust reduct is a classical reduct on a certain parameter second the tool used to measure the discernibility power is different from the existing discernibility measures in this paper the robustness of each attribute to handle misclassification and perturbation is considered by considering both the robustness and the discernibility a robust fuzzy discernibility matrix is designed finally the algorithms used to find the robust reducts are designed based upon the robust fuzzy discernibility matrix which is completely different from the existing algorithms used to find the classical reducts

the relationship between attribute reducts in rough sets and minimal vertex covers of graphs the problems to find attribute reduction in rough sets and to obtain the minimal vertex cover for graphs are both np hard problems this paper studies the relationship between the two problems the vertex cover problem for graphs from the perspective of rough sets is first investigated the attribute reduction of an information system is then studied in the framework of graph theory the results in this paper show that finding the minimal vertex cover of a graph is equivalent to finding the attribute reduction of an information system induced from the graph conversely the attribute reduction computation can be translated into the calculation of the minimal vertex cover of a derivative graph finally a new algorithm for the vertex cover problem based on rough sets is presented furthermore experiments are conducted to verify the effectiveness of the proposed method

simulation of stochastic reaction diffusion processes on unstructured meshes we model stochastic chemical systems with diffusion by a reaction diffusion master equation on a macroscopic level the governing equation is a reaction diffusion equation for the averages of the chemical species on a mesoscopic level the master equation for a well stirred chemical system is combined with a discretized brownian motion in space to obtain the reaction diffusion master equation the space is covered in our method by an unstructured mesh and the diffusion coefficients on the mesoscale are obtained from a finite element discretization of the laplace operator on the macroscale the resulting method is a flexible hybrid algorithm in that the diffusion can be handled either on the meso or on the macroscale level the accuracy and the efficiency of the method are illustrated in three numerical examples inspired by molecular biology

an efficient local search framework for the minimum weighted vertex cover problem the minimum weighted vertex cover mwvc problem an extension of the classical minimum vertex cover mvc problem is an important np complete combinatorial optimization problem with a wide range of applications the objective of this paper is to design an efficient local search algorithm to solve the mwvc problem first the weighted edge strategy is proposed to define the dynamic scoring strategy so that our algorithm can find different possible optimal solutions second the weighted configuration checking wcc strategy is proposed to overcome the cycling problem in local search by combining the wcc strategy with the scoring strategy we design the vertex selection strategy to determine the vertex to be selected as a candidate solution component based on these strategies a novel local search framework namely diversion local search based on weighted configuration checking dlswcc is presented dlswcc is evaluated against several state of the art algorithms on various benchmark instances experimental results show that dlswcc outperforms its competitors in terms of both solution quality and computational efficiency in most classical instances specifically dlswcc can obtain 22 new upper bounds of 71 moderate scale problem instances 5 new upper bounds of 15 large scale problem instances and 56 new upper bounds of 56 massive graph instances

reduction target structure based hierarchical attribute reduction for two category decision theoretic rough sets abstract attribute reduction is an essential subject in rough set theory but because of quantitative extension it becomes a problem when considering probabilistic rough set prs approaches the decision theoretic rough set dtrs has a threshold semantics and decision feature and thus becomes a typical and fundamental prs based on reduction target structures this paper investigates hierarchical attribute reduction for a two category dtrs and is divided into five parts 1 the knowledge preservation property and reduct are explored by knowledge coarsening 2 the consistency preservation principle and reduct are constructed by a consistency mechanism 3 region preservation is analyzed and the separability between consistency preservation and region preservation is concluded thus the double preservation principle and reduct are studied 4 structure targets are proposed by knowledge structures and an attribute reduction is further described and simulated thus general reducts are defined to preserve the structure targets or optimal measures 5 the hierarchical relationships of the relevant four targets and reducts are analyzed and a decision table example is provided for illustration this study offers promotion rationality structure hierarchy and generalization and it establishes a fundamental reduction framework for two category dtrs the relevant results also provide some new insights into the attribute reduction problem for prs

quick attribute reduction in inconsistent decision tables this paper focuses on three types of attribute reducts in inconsistent decision tables assignment reduct distribution reduct and maximum distribution reduct it is quite inconvenient to judge these three types of reduct directly according to their definitions this paper proposes judgment theorems for the assignment reduct the distribution reduct and the maximum distribution reduct which are expected to greatly simplify the judging of these three types of reducts on this basis we derive three new types of attribute significance measures and construct the q ara quick assignment reduction algorithm the q dra quick distribution reduction algorithm and the q mdra quick maximum distribution reduction algorithm these three algorithms correspond to the three types of reducts we conduct a series of comparative experiments with twelve uci machine learning data repository university of california at irvine data sets including consistent and inconsistent decision tables to evaluate the performance of the three reduction algorithms proposed with the relevant algorithm quickreduct 9 34 the experimental results show that quickreduct possesses weak robustness because it cannot find the reduct even for consistent data sets whereas our proposed three algorithms show strong robustness because they can find the reduct for each data set in addition we compare the q dra quick distribution reduction algorithm with the cebarknc conditional entropy based algorithm for reduction of knowledge without a computing core 43 because both find the distribution reduct by using a heuristic search the experimental results demonstrate that q dra runs faster than cebarknc does because the distribution function of q dra has a lower calculation cost instructive conclusions for these reduction algorithms are drawn from the perspective of classification performance for the c4 5 and rbf svm classifiers last we make a comparison between discernibility matrix based methods and our algorithms the experimental results indicate that our algorithms are efficient and feasible

relative reducts in consistent and inconsistent decision tables of the pawlak rough set model a relative reduct can be considered as a minimum set of attributes that preserves a certain classification property this paper investigates three different classification properties and suggests three distinct definitions accordingly in the pawlak rough set model while the three definitions yield the same set of relative reducts in consistent decision tables they may result in different sets in inconsistent tables relative reduct construction can be carried out based on a discernibility matrix the study explicitly stresses a fact that the definition of a discernibility matrix should be tied to a certain property regarding the three classification properties we can define three distinct definitions accordingly based on the common structure of the specific definitions of relative reducts and discernibility matrices general definitions of relative reducts and discernibility matrices are suggested

power spectra methods for a stochastic description of diffusion on deterministically growing domains a central challenge in developmental biology is understanding the creation of robust spatiotemporal heterogeneity generally the mathematical treatments of biological systems have used continuum mean field hypotheses for their constituent parts which ignores any sources of intrinsic stochastic effects in this paper we consider a stochastic space jump process as a description of diffusion i e particles are able to undergo a random walk on a discretized domain by developing analytical fourier methods we are able to probe this probabilistic framework which gives us insight into the patterning potential of diffusive systems further an alternative description of domain growth is introduced with which we are able to rigorously link the mean field and stochastic descriptions finally through combining these ideas it is shown that such stochastic descriptions of diffusion on a deterministically growing domain are able to support the nucleation of states that are far removed from the deterministic mean field steady state

kernel density estimation for length biased data a new kernel density estimator for length biased data which derives from smoothing the nonparametric maximum likelihood estimator is proposed and investigated it has various advantages over an alternative method suggested by bhattacharyya franklin richardson 1988 it is necessarily a probability density it is particularly better behaved near zero it has better asymptotic mean integrated squared error properties and it is more readily extendable to related problems such as density derivative estimation

multi species simple exclusion processes abstract a motility mechanism based on a simple exclusion process where the movement of discrete agents on a lattice is either unbiased symmetric or biased asymmetric is considered estimates of diffusivities from tracking data do not describe the population level response of the system this mismatch between the individual level and population level behaviour can be resolved by averaging the individual level mechanism in terms of an expected site occupancy new insight into simple exclusion processes is obtained by representing the system as a series of interacting subpopulations this formalism leads to a system of nonlinear advection diffusion equations which can be interpreted in terms of the agent fluxes these interactions have consequences for both agent based modelling and continuum modelling in cell biology such as tracking subpopulations of cells within a total cell population

pessimistic rough set based decisions a multigranulation fusion strategy abstract multigranulation rough sets mgrs is one of desirable directions in rough set theory in which lower upper approximations are approximated by granular structures induced by multiple binary relations it provides a new perspective for decision making analysis based on rough set theory in decision making analysis people often adopt the decision strategy seeking common ground while eliminating differences sced this strategy implies that one reserves common decisions while deleting inconsistent decisions from this point of view the objective of this study is to develop a new multigranulation rough set based decision model based on sced strategy called pessimistic multigranulation rough sets we study this model from three aspects which are lower upper approximation and their properties decision rules and attribute reduction in this paper

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

decision region distribution preservation reduction in decision theoretic rough set model abstract in the pawlak rough set model the positive region the boundary region and the non negative region are monotonic with respect to the set inclusion of attributes however the monotonicity property of the decision regions positive region boundary region or non negative region with respect to the set inclusion of attributes does not hold in the decision theoretic rough set model therefore the decision regions may be changed after attribute reduction based on quantitative preservation or qualitative preservation of decision regions this effect is observed partly because three decision regions are defined by introducing the probabilistic threshold values in addition heuristic reduction algorithms based on decision regions may find super reducts because of the non monotonicity of decision regions to address the above issues this paper proposes solutions to the attribute reduction problem based on decision region preservation in the decision theoretic rough set model first the positive region distribution preservation reduct the boundary region distribution preservation reduct and the negative region distribution preservation reduct are introduced into the decision theoretic rough set model second three new monotonic measures are constructed by considering variants of the conditional information entropy from which we can obtain the heuristic reduction algorithms the results of the experimental analysis validate the monotonicity of new measures and verify the effectiveness of decision region distribution preservation reducts

choice based samples a non parametric approach abstract in this paper we discuss a non parametric approach to choice based grouping specifically we derive the non parametric maximum likelihood estimate for f x z the joint distribution of x z choice attributes from choice based samples this estimate can be thought of as the bias corrected empirical distribution of choice attributes derived from our biased data having f at hand we investigate two alternative approaches for estimating the conditional probability p choice attributes the first is based on smoothing a non parametric estimate derived from f x z in the second we fit a parametric family f x z to the bias corrected empirical distribution function the asymptotic behavior of this semi parametric estimate as well as numerical examples that demonstrate both methods are given

going from microscopic to macroscopic on nonuniform growing domains throughout development chemical cues are employed to guide the functional specification of underlying tissues while the spatiotemporal distributions of such chemicals can be influenced by the growth of the tissue itself these chemicals termed morphogens are often modeled using partial differential equations pdes the connection between discrete stochastic and deterministic continuum models of particle migration on growing domains was elucidated by baker yates and erban bull math biol 72 719 2010 in which the migration of individual particles was modeled as an on lattice position jump process we build on this work by incorporating a more physically reasonable description of domain growth instead of allowing underlying lattice elements to instantaneously double in size and divide we allow incremental element growth and splitting upon reaching a predefined threshold size such a description of domain growth necessitates a nonuniform partition of the domain we first demonstrate that an individual based stochastic model for particle diffusion on such a nonuniform domain partition is equivalent to a pde model of the same phenomenon on a nongrowing domain providing the transition rates which we derive are chosen correctly and we partition the domain in the correct manner we extend this analysis to the case where the domain is allowed to change in size altering the transition rates as necessary through application of the master equation formalism we derive a pde for particle density on this growing domain and corroborate our findings with numerical simulations

generalized fractional diffusion equations for subdiffusion in arbitrarily growing domains the ubiquity of subdiffusive transport in physical and biological systems has led to intensive efforts to provide robust theoretical models for this phenomena these models often involve fractional derivatives the important physical extension of this work to processes occurring in growing materials has proven highly nontrivial here we derive evolution equations for modeling subdiffusive transport in a growing medium the derivation is based on a continuous time random walk the concise formulation of these evolution equations requires the introduction of a new comoving fractional derivative the implementation of the evolution equation is illustrated with a simple model of subdiffusing proteins in a growing membrane

the diffusion limit of transport equations ii chemotaxis equations in this paper we use the diffusion limit expansion of transport equations developed earlier t hillen and h g othmer siam j appl math 61 2000 pp 751 775 to study the limiting equation under a variety of external biases imposed on the motion when applied to chemotaxis or chemokinesis these biases produce modification of the turning rate the movement speed or the preferred direction of movement depending on the strength of the bias it leads to anisotropic diffusion to a drift term in the flux or to both in the parabolic limit we show that the classical chemotaxis equation which we call the patlak keller segel alt pksa equation arises only when the bias is sufficiently small using this general framework we derive phenomenological models for chemotaxis of flagellated bacteria of slime molds and of myxobacteria we also show that certain results derived earlier for one dimensional motion can easily be generalized to two or three dimensional motion as well

the diffusion limit of transport equations derived from velocity jump processes in this paper we study the diffusion approximation to a transport equation that describes the motion of individuals whose velocity changes are governed by a poisson process we show that under an appropriate scaling of space and time the asymptotic behavior of solutions of such equations can be approximated by the solution of a diffusion equation obtained via a regular perturbation expansion in general the resulting diffusion tensor is anisotropic and we give necessary and sufficient conditions under which it is isotropic we also give a method to construct approximations of arbitrary high order for large times in a second paper part ii we use this approach to systematically derive the limiting equation under a variety of external biases imposed on the motion depending on the strength of the bias it may lead to an anisotropic diffusion equation to a drift term in the flux or to both our analysis generalizes and simplifies previous derivations that lead to the classical patlak keller segel alt

approximation algorithms for the set covering and vertex cover problems we propose a heuristic that delivers in o n 3 steps a solution for the set covering problem the value of which does not exceed the maximum number of sets covering an element times the optimal value

a novel method for attribute reduction of covering decision systems attribute reduction has become an important step in pattern recognition and machine learning tasks covering rough sets as a generalization of classical rough sets have attracted wide attention in both theory and application this paper provides a novel method for attribute reduction based on covering rough sets we review the concepts of consistent and inconsistent covering decision systems and their reducts and we develop a judgment theorem and a discernibility matrix for each type of covering decision system furthermore we present some basic structural properties of attribute reduction with covering rough sets based on a discernibility matrix we develop a heuristic algorithm to find a subset of attributes that approximate a minimal reduct finally the experimental results for uci data sets show that the proposed reduction approach is an effective technique for addressing numerical and categorical data and is more efficient than the method presented in the paper d g chen c z wang q h hu a new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets information sciences 177 17 2007 3500 3518

hybrid attribute reduction based on a novel fuzzy rough model and information granulation feature subset selection has become an important challenge in areas of pattern recognition machine learning and data mining as different semantics are hidden in numerical and categorical features there are two strategies for selecting hybrid attributes discretizing numerical variables or numericalize categorical features in this paper we introduce a simple and efficient hybrid attribute reduction algorithm based on a generalized fuzzy rough model a theoretic framework of fuzzy rough model based on fuzzy relations is presented which underlies a foundation for algorithm construction we derive several attribute significance measures based on the proposed fuzzy rough model and construct a forward greedy algorithm for hybrid attribute reduction the experiments show that the technique of variable precision fuzzy inclusion in computing decision positive region can get the optimal classification performance number of the selected features is the least but accuracy is the best

neighbor inconsistent pair selection for attribute reduction by rough set approach rough set theory as one of the most useful soft computing methods dealing with vague and uncertain information has been successfully applied to many fields and one of its main applications is to perform attribute reduction although many heuristic attribute reduction algorithms have been proposed within the framework of the rough set theory these methods are still computationally time consuming in order to overcome this deficit we propose in this paper two quick feature selection algorithms based on the neighbor inconsistent pair which can reduce the time consumed in finding a reduct at first we propose several concepts regarding simplified decision table u prime and neighbor inconsistent pairs based on neighbor inconsistent pairs we constructed two new attribute significance measures furthermore we put forward two new attribute reduction algorithms based on quick neighbor inconsistent pairs the key characteristic of the presented algorithms is that they only need to calculate u prime r once under the process of selecting the best attribute from attribute sets c r while most existing algorithms need to calculate partition of u prime for c r times in addition the proposed algorithms need only to deal with the equivalent classes in u prime r that contain at least one neighbor inconsistent pair while most existing algorithms need to consider all objects in u prime the experimental results show that the proposed algorithms are feasible and efficient

fuzzy preference based rough sets preference analysis is an important task in multi criteria decision making the rough set theory has been successfully extended to deal with preference analysis by replacing equivalence relations with dominance relations the existing studies involving preference relations cannot capture the uncertainty presented in numerical and fuzzy criteria in this paper we introduce a method to extract fuzzy preference relations from samples characterized by numerical criteria fuzzy preference relations are incorporated into a fuzzy rough set model which leads to a fuzzy preference based rough set model the measure of attribute dependency of the pawlak s rough set model is generalized to compute the relevance between criteria and decisions the definitions of upward dependency downward dependency and global dependency are introduced algorithms for computing attribute dependency and reducts are proposed and experimentally evaluated by using two publicly available data sets

identifying the minimal transversals of a hypergraph and related problems the paper considers two decision problems on hypergraphs hypergraph saturation and recognition of the transversal hypergraph and discusses their significance for several search problems in applied computer science hypergraph saturation i e given a hypergraph cal h decide if every subset of vertices is contained in or contains some edge of cal h is shown to be co np complete a certain subproblem of hypergraph saturation the saturation of simple hypergraphs i e sperner families is shown to be under polynomial transformation equivalent to transversal hypergraph recognition i e given two hypergraphs cal h 1 cal h 2 decide if the sets in cal h 2 are all the minimal transversals of cal h 1 the complexity of the search problem related to the recognition of the transversal hypergraph the computation of the transversal hypergraph is an open problem this task needs time exponential in the input size it is unknown whether an output polynomial algorithm exists for several important subcases for instance if an upper or lower bound is imposed on the edge size or for acyclic hypergraphs output polynomial algorithms are presented computing or recognizing the minimal transversals of a hypergraph is a frequent problem in practice which is pointed out by identifying important applications in database theory boolean switching theory logic and artificial intelligence ai particularly in model based diagnosis

quantitative information architecture granular computing and rough set models in the double quantitative approximation space of precision and grade because precision and grade act as fundamental quantitative information in approximation space they are used in relative and absolute quantifications respectively at present the double quantification regarding precision and grade is a novel and valuable subject but quantitative information fusion has become a key problem thus this paper constructs the double quantitative approximation space of precision and grade pg approx space and tackles the fusion problem using normal logical operations it further conducts double quantification studies on granular computing and rough set models 1 first for quantitative information organization and storage we construct space and plane forms of pg approx space using the cartesian product and for quantitative information extraction and fusion we establish semantics construction and semantics granules of pg approx space 2 second by granular computing we investigate three primary granular issues quantitative semantics complete system and optimal calculation accordingly six types of fundamental granules are proposed based on the semantic microscopic and macroscopic descriptions their semantics forms structures calculations and relationships are studied and the granular hierarchical structure is achieved 3 finally we investigate rough set models in pg approx space accordingly model regions are proposed by developing the classical regions model expansion is systematically analyzed some models are constructed as their structures are obtained and a concrete model is provided based on the quantitative information architecture this paper systematically conducts and investigates double quantification and establishes a fundamental and general exploration framework

decision theoretic rough fuzzy set model and application this article investigates the rough approximation of a fuzzy concept on a probabilistic approximation space we propose the probabilistic rough fuzzy set by defining the conditional probability of a fuzzy event then we establish the model of probabilistic rough fuzzy set and discuss several properties in detail furthermore three generalizations of probabilistic rough fuzzy set namely 0 5 probabilistic rough fuzzy set variable precision probabilistic rough fuzzy set and bayesian rough fuzzy set are reported in order to give a systematic method of selecting parameters for the probabilistic rough fuzzy set we propose a decision theoretic rough fuzzy set that is we formulate a non parametric definition of the probabilistic rough fuzzy set moreover we illustrate the motivation and verify the validity of the decision theoretic rough fuzzy set by using a credit card applicant decision making problem furthermore the interrelationship between the decision theoretic rough fuzzy set and the probabilistic rough fuzzy set is explained the main contribution of this paper is twofold one is to extend the probabilistic rough set to fuzzy environment i e the probabilistic rough fuzzy set model another is to present an approach to select parameters needed in probabilistic rough fuzzy set modeling by using the process of decision making under conditions of risk

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

knowledge reduction in random information systems via dempster shafer theory of evidence knowledge reduction is one of the main problems in the study of rough set theory this paper deals with knowledge reduction in random information systems based on dempster shafer theory of evidence the concepts of belief and plausibility reducts in random information systems are first introduced it is proved that both of belief reduct and plausibility reduct are equivalent to classical reduct in random information systems the relative belief and plausibility reducts in consistent and inconsistent random decision systems are then proposed and compared to the relative reduct and relationships between the new reducts and some existing ones are examined

rough set based 1 v 1 and 1 v r approaches to support vector machine multi classification support vector machines svms are essentially binary classifiers to improve their applicability several methods have been suggested for extending svms for multi classification including one versus one 1 v 1 one versus rest 1 v r and dagsvm in this paper we first describe how binary classification with svms can be interpreted using rough sets a rough set approach to svm classification removes the necessity of exact classification and is especially useful when dealing with noisy data next by utilizing the boundary region in rough sets we suggest two new approaches extensions of 1 v r and 1 v 1 to svm multi classification that allow for an error rate we explicitly demonstrate how our extended 1 v r may shorten the training time of the conventional 1 v r approach in addition we show that our 1 v 1 approach may have reduced storage requirements compared to the conventional 1 v 1 and dagsvm techniques our techniques also provide better semantic interpretations of the classification process the theoretical conclusions are supported by experimental findings involving a synthetic dataset

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

the reaction diffusion master equation as an asymptotic approximation of diffusion to a small target the reaction diffusion master equation rdme has recently been used as a model for biological systems in which both noise in the chemical reaction process and diffusion in space of the reacting molecules is important in the rdme space is partitioned by a mesh into a collection of voxels there is an unanswered question as to how solutions depend on the mesh spacing to have confidence in using the rdme to draw conclusions about biological systems we would like to know that it approximates a reasonable physical model for appropriately chosen mesh spacings this issue is investigated by studying the dependence on mesh spacing of solutions to the rdme in mathbb r 3 for the bimolecular reaction mathrm a mathrm b to varnothing with one molecule of species mathrm a and one molecule of species mathrm b present initially we prove that in the continuum limit the molecules never react and simply diffuse relative to each other nevertheless we show that the rdme with nonzero lattice spacin

positive approximation an accelerator for attribute reduction in rough set theory feature selection is a challenging problem in areas such as pattern recognition machine learning and data mining considering a consistency measure introduced in rough set theory the problem of feature selection also called attribute reduction aims to retain the discriminatory power of original features many heuristic attribute reduction algorithms have been proposed however quite often these methods are computationally time consuming to overcome this shortcoming we introduce a theoretic framework based on rough set theory called positive approximation which can be used to accelerate a heuristic process of attribute reduction based on the proposed accelerator a general attribute reduction algorithm is designed through the use of the accelerator several representative heuristic attribute reduction algorithms in rough set theory have been enhanced note that each of the modified algorithms can choose the same attribute reduct as its original version and hence possesses the same classification accuracy experiments show that these modified algorithms outperform their original counterparts it is worth noting that the performance of the modified algorithms becomes more visible when dealing with larger data sets

modeling and solving the crew rostering problem the crew rostering problem crp aims at determining an optimal sequencing of a given set of duties into rosters satisfying operational constraints deriving from union contract and company regulations previous work on crp addresses mainly urban mass transit systems in which the minimum number of crews to perform the duties can easily be determined and the objective is to evenly distribute the workload among the crews in typical railway applications however the roster construction has to take into account more involved sequencing rules and the main objective is the minimization of the number of crews needed to perform the duties in this paper we propose a basic model for crp and describe a lagrangian lower bound based on the solution of an assignment problem on a suitably defined graph the information obtained through the lower bound computation is used to drive an effective algorithm for finding a tight approximate solution to the problem computational results for real world instances from railway applications involving up to 1 000 duties are presented showing that the proposed approach yields within short computing time lower and upper bound values that are typically very close the code based on the approach we propose won the faro competition organized by the italian railway company ferrovie dello stato spa in 1995