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Showing papers on "Rough set published in 2011"


Book
01 Jan 2011
TL;DR: This book effectively constitutes a detailed annotated bibliography in quasitextbook style of the some thousand contributions deemed by Messrs. Dubois and Prade to belong to the area of fuzzy set theory and its applications or interactions in a wide spectrum of scientific disciplines.
Abstract: (1982). Fuzzy Sets and Systems — Theory and Applications. Journal of the Operational Research Society: Vol. 33, No. 2, pp. 198-198.

5,861 citations


Journal ArticleDOI
Yiyu Yao1
TL;DR: It is shown that, under certain conditions when considering the costs of different types of miss-classifications, probabilistic three-way decisions are superior to the other two.

569 citations


Journal ArticleDOI
TL;DR: It is shown that Pawlak's rough set model can be viewed as a special case of the soft rough sets, and these two notions will coincide provided that the underlying soft set in the soft approximation space is a partition soft set.

494 citations


25 Jun 2011
TL;DR: 14th International Conference, RSFDGrC 2013, Halifax, NS, Canada, October 11-14, 2013.

304 citations


Journal ArticleDOI
01 Jun 2011
TL;DR: For any subset X of the universe U, there is a fuzzy subset of U associated with each parameter of the soft set and each soft set over a set U, gives rise to a fuzzysoft set over P(U) and induces a soft equivalence relation over P (U).
Abstract: Concept of an approximation space associated with each parameter in a soft set is discussed and an approximation space associated with the soft set is defined. For any subset X of the universe U, there is a fuzzy subset of U associated with each parameter of the soft set, also there is a fuzzy subset associated with the soft set. Furthermore each soft set over a set U, gives rise to a fuzzy soft set over P(U) and induces a soft equivalence relation over P(U).

259 citations


Journal ArticleDOI
TL;DR: This work presents a general rule induction algorithm based on sequential covering, suitable for variable consistency rough set approaches, and shows how to improve rule induction efficiency due to application of consistency measures with desirable monotonicity properties.

217 citations


Journal ArticleDOI
TL;DR: This article investigates the Game-theoretic Rough Set model and its capability of analyzing a major decision problem evident in existing probabilistic rough set models and formulate a learning method using the GTRS model that repeatedly analyzes payoff tables created from approximation measures and modified conditional risk strategies to calculate parameter values.
Abstract: This article investigates the Game-theoretic Rough Set (GTRS) model and its capability of analyzing a major decision problem evident in existing probabilistic rough set models. A major challenge in the application of probabilistic rough set models is their inability to formulate a method of decreasing the size of the boundary region through further explorations of the data. To decrease the size of this region, objects must be moved to either the positive or negative regions. Game theory allows a solution to this decision problem by having the regions compete or cooperate with each other in order to find which is best fit to be selected for the move. There are two approaches discussed in this article. First, the region parameters that define the minimum conditional probabilities for region inclusion can either compete or cooperate in order to increase their size. The second approach is formulated by having classification approximation measures compete against each other. We formulate a learning method using the GTRS model that repeatedly analyzes payoff tables created from approximation measures and modified conditional risk strategies to calculate parameter values.

205 citations


Journal ArticleDOI
TL;DR: A formal approach to granular computing with multi-scale data measured at different levels of granulations is proposed in this paper and the unravelling of decision rules at different scales in multi- scale decision tables is discussed.

202 citations


Journal ArticleDOI
TL;DR: A theoretic framework based on rough set theory, which is called positive approximation and can be used to accelerate a heuristic process for feature selection from incomplete data is introduced and several modified representative heuristic feature selection algorithms in roughSet theory are obtained.

172 citations


Journal ArticleDOI
TL;DR: This study integrates kernel functions with fuzzy rough set models and proposes two types of kernelized fuzzy rough sets, and extends the measures existing in classical rough sets to evaluate the approximation quality and approximation abilities of the attributes.
Abstract: Kernel machines and rough sets are two classes of commonly exploited learning techniques. Kernel machines enhance traditional learning algorithms by bringing opportunities to deal with nonlinear classification problems, rough sets introduce a human-focused way to deal with uncertainty in learning problems. Granulation and approximation play a pivotal role in rough sets-based learning and reasoning. However, a way how to effectively generate fuzzy granules from data has not been fully studied so far. In this study, we integrate kernel functions with fuzzy rough set models and propose two types of kernelized fuzzy rough sets. Kernel functions are employed to compute the fuzzy T-equivalence relations between samples, thus generating fuzzy information granules in the approximation space. Subsequently fuzzy granules are used to approximate the classification based on the concepts of fuzzy lower and upper approximations. Based on the models of kernelized fuzzy rough sets, we extend the measures existing in classical rough sets to evaluate the approximation quality and approximation abilities of the attributes. We discuss the relationship between these measures and feature evaluation function ReliefF, and augment the ReliefF algorithm to enhance the robustness of these proposed measures. Finally, we apply these measures to evaluate and select features for classification problems. The experimental results help quantify the performance of the KFRS.

153 citations


Journal ArticleDOI
TL;DR: In this paper, a conceptual performance measurement framework that takes into account company-level factors is presented for a real world application problem and an integrated approach of analytic hierarchy process improved by rough sets theory and fuzzy TOPSIS method is proposed to obtain final ranking.
Abstract: In today's organizations, performance measurement comes more to the foreground with the advancement in the high technology. So as to manage this power, which is an important element of the organizations, it is needed to have a performance measurement system. Increased level of competition in the business environment and higher customer requirements forced industry to establish a new philosophy to measure its performance beyond the existing financial and non-financial based performance indicators. In this paper, a conceptual performance measurement framework that takes into account company-level factors is presented for a real world application problem. In order to use the conceptual framework for measuring performance, a methodology that takes into account both quantitative and qualitative factors and the interrelations between them should be utilized. For this reason, an integrated approach of analytic hierarchy process (AHP) improved by rough sets theory (Rough-AHP) and fuzzy TOPSIS method is proposed to obtain final ranking.

01 Jan 2011
TL;DR: This paper presents a new feature selection approach that combines the RST with nature inspired ‘firefly’ algorithm that simulates the attraction system of real fireflies that guides the feature selection procedure.
Abstract: Irrelevant, noisy and high dimensional data, containing large number of features, degrades the performance of data mining and machine learning tasks. One of the methods used in data mining to reduce the dimensionality of data is feature selection. Feature selection methods select a subset of features that represents original features in problem domain with high accuracy. Various methods have been proposed that utilize heuristic or nature inspired strategies along with Rough Set Theory (RST) to find these subsets. However these methods either consume more time to find subset or compromise with optimality. The paper presents a new feature selection approach that combines the RST with nature inspired ‘firefly’ algorithm. The algorithm simulates the attraction system of real fireflies that guides the feature selection procedure. The experimental result proves that the proposed algorithm scores over other feature selection method in terms of time and optimality.

Journal ArticleDOI
TL;DR: A new feature selection algorithm is presented based on rough set theory that selects a set of genes from microarray data by maximizing the relevance and significance of the selected genes.

Journal ArticleDOI
TL;DR: A new soft rough set model is proposed and its properties are derived and a more general model called soft fuzzy rough set is established.
Abstract: Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed.

Journal ArticleDOI
TL;DR: In this paper, the authors further investigate the covering rough sets based on neighborhoods by approximation operations and show that the upper approximation based on neighborhood can be defined equivalently without using neighborhoods.

Journal ArticleDOI
TL;DR: It is proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology.

Journal ArticleDOI
TL;DR: This paper proposes an NN algorithm that uses the lower and upper approximations from fuzzy-rough set theory in order to classify test objects, or predict their decision value, and shows that it outperforms other NN approaches and is competitive with leading classification and prediction methods.

Journal ArticleDOI
TL;DR: This work extends Pawlak's rough set theory to numerical feature spaces by replacing partition of universe with neighborhood covering and derive a neighborhood covering reduction based approach to extracting rules from numerical data.

Journal ArticleDOI
TL;DR: It is shown that in the incomplete information system, the smaller upper approximations can be obtained by neighborhood system based rough sets than by the methods in [Y.Y. Leung], and a new knowledge operation is discussed in the neighborhood system, from which more knowledge can be derived from the initial neighborhood system.
Abstract: Neighborhood system formalized the ancient intuition, infinitesimals, which led to the invention of calculus, topology and non-standard analysis. In this paper, the neighborhood system is researched from the view point of knowledge engineering and then each neighborhood is considered as a basic unit with knowledge. By using these knowledge in neighborhood system, the rough approximations and the corresponding properties are discussed. It is shown that in the incomplete information system, the smaller upper approximations can be obtained by neighborhood system based rough sets than by the methods in [Y. Leung, D.Y. Li, Maximal consistent block technique for rule acquisition in incomplete information systems, Information Sciences 115 (2003) 85-106] and [Y. Leung, W.Z. Wu, W.X. Zhang, Knowledge acquisition in incomplete information systems: a rough set approach, European Journal of Operational Research 168 (2006) 164-180]. Furthermore, a new knowledge operation is discussed in the neighborhood system, from which more knowledge can be derived from the initial neighborhood system. By such operations, the regions of lower and upper approximations are further expanded and narrowed, respectively. Some numerical examples are employed to substantiate the conceptual arguments.

Journal ArticleDOI
TL;DR: The optimistic and pessimistic multi-granulation fuzzy rough sets models in a fuzzy tolerance approximation space with the point view of granular computing are proposed.
Abstract: Based on the analysis of the rough set model on a tolerance relation and the fuzzy rough set, two types of fuzzy rough sets models on tolerance relations are constructed and researched. Then we propose the optimistic and pessimistic multi-granulation fuzzy rough sets models in a fuzzy tolerance approximation space with the point view of granular computing. In these models, the fuzzy lower and upper approximations of a fuzzy set are defined on multiple fuzzy tolerance relations. It follows the research on the properties of the fuzzy lower and upper approximations of the new models. The fuzzy rough set model, rough set model on a tolerance relation and multi-granulation rough sets models are special cases of the new ones from the perspective of the considered concepts, related relations and granular computing. The new models are meaningful generalizations of the classical rough sets.

Journal ArticleDOI
Yiyu Yao1
TL;DR: This paper examines two fundamental semantics-related questions: the interpretation and determination of the required parameters, i.e., thresholds on probabilities, for defining the probabilistic lower and upper approximations and the interpretation of rules derived from the Probabilistic positive, boundary and negative regions.
Abstract: Probabilistic rough set models are quantitative generalizations of the classical and qualitative Pawlak model by considering degrees of overlap between equivalence classes and a set to be approximated. The extensive studies, however, have not sufficiently addressed some semantic issues in a probabilistic rough set model. This paper examines two fundamental semantics-related questions. One is the interpretation and determination of the required parameters, i.e., thresholds on probabilities, for defining the probabilistic lower and upper approximations. The other is the interpretation of rules derived from the probabilistic positive, boundary and negative regions. We show that the two questions can be answered within the framework of a decision-theoretic rough set model. Parameters for defining probabilistic rough sets are interpreted and determined in terms of loss functions based on the well established Bayesian decision procedure. Rules constructed from the three regions are associated with different actions and decisions, which immediately leads to the notion of three-way decision rules. A positive rule makes a decision of acceptance, a negative rule makes a decision of rejection, and a boundary rules makes a decision of deferment. The three-way decisions are, again, interpreted based on the loss functions. (This work is partially supported by a Discovery Grant from NSERC Canada. The author thanks the reviewers for their constructive comments.)

Journal ArticleDOI
TL;DR: This paper presents the lattice-theoretical background and the learning algorithms for morphological perceptrons with competitive learning which arise by incorporating a winner-take-all output layer into the original Morphological perceptron model.

Proceedings ArticleDOI
08 Sep 2011
TL;DR: This framework is further extended into sequential three-way decision-making, in which the cost of obtaining required evidence or information is also considered.
Abstract: When approximating a concept, probabilistic rough set models use probabilistic positive, boundary and negative regions. Rules obtained from the three regions are recently interpreted as making three-way decisions, consisting of acceptance, deferment, and rejection. A particular decision is made by minimizing the cost of correct and incorrect classifications. This framework is further extended into sequential three-way decision-making, in which the cost of obtaining required evidence or information is also considered.

Journal ArticleDOI
TL;DR: This paper defines a structure called power set tree (PS-tree), which is an order tree representing the power set, and each possible reduct is mapped to a node of the tree.
Abstract: Feature selection is viewed as an important preprocessing step for pattern recognition, machine learning and data mining Traditional hill-climbing search approaches to feature selection have difficulties to find optimal reducts And the current stochastic search strategies, such as GA, ACO and PSO, provide a more robust solution but at the expense of increased computational effort It is necessary to investigate fast and effective search algorithms Rough set theory provides a mathematical tool to discover data dependencies and reduce the number of features contained in a dataset by purely structural methods In this paper, we define a structure called power set tree (PS-tree), which is an order tree representing the power set, and each possible reduct is mapped to a node of the tree Then, we present a rough set approach to feature selection based on PS-tree Two kinds of pruning rules for PS-tree are given And two novel feature selection algorithms based on PS-tree are also given Experiment results demonstrate that our algorithms are effective and efficient

Journal ArticleDOI
TL;DR: A heuristic algorithm is designed to compute reducts with Gaussian kernel fuzzy rough sets and parameterized attribute reduction with the derived model of fuzzy Rough sets is introduced.

Journal ArticleDOI
01 Jan 2011
TL;DR: This paper proposed and proved two incremental methods for fast computing the rough fuzzy approximations, one starts from the boundary set, the other is based on the cut sets of a fuzzy set.
Abstract: The lower and upper approximations are basic concepts in rough fuzzy set theory. The effective computation of approximations is very important for improving the performance of related algorithms. This paper proposed and proved two incremental methods for fast computing the rough fuzzy approximations, one starts from the boundary set, the other is based on the cut sets of a fuzzy set. Then some illustrative examples are conducted. Consequently, two algorithms corresponding to the two incremental methods are put forward respectively. In order to test the efficiency of algorithms, some experiments are made on a large soybean data set from UCI. The experimental results show that the two incremental methods effectively reduce the computing time in comparison with the traditional non-incremental method [1].

Journal ArticleDOI
TL;DR: The proposed method can deal with decision systems with numerical conditional attribute values and fuzzy decision attributes rather than crisp ones and Experimental results imply that the algorithm of attribute reduction with general fuzzy rough sets is feasible and valid.
Abstract: Fuzzy rough set is a generalization of crisp rough set to deal with data sets with real value attributes. A primary use of fuzzy rough set theory is to perform attribute reduction for decision systems with numerical conditional attribute values and crisp (symbolic) decision attributes. In this paper we define inconsistent fuzzy decision system and their reductions, and develop discernibility matrix-based algorithms to find reducts. Finally, two heuristic algorithms are developed and comparison study is provided with the existing algorithms of attribute reduction with fuzzy rough sets. The proposed method in this paper can deal with decision systems with numerical conditional attribute values and fuzzy decision attributes rather than crisp ones. Experimental results imply that our algorithm of attribute reduction with general fuzzy rough sets is feasible and valid.

Journal ArticleDOI
TL;DR: In this article, the rank function of the matroid induced by a relation is used to construct a pair of approximation operators, namely, matroid approximation operators and an approach to induce a relation from a matroid.
Abstract: Rough set theory is a useful tool for dealing with the vagueness, granularity and uncertainty in information systems. This paper connects generalized rough sets based on relations with matroid theory. We define the upper approximation number to induce a matroid from a relation. Therefore, many matroidal approaches can be used to study generalized rough sets based on relations. Specifically, with the rank function of the matroid induced by a relation, we construct a pair of approximation operators, namely, matroid approximation operators. The matroid approximation operators present some unique properties which do not exist in the existing approximation operators. On the other hand, we present an approach to induce a relation from a matroid. Moreover, the relationship between two inductions is studied.

Journal ArticleDOI
TL;DR: The precise role of covering-based approximations of sets that extend the standard rough sets in the presence of incomplete information about attribute values is described, and the notion of measure of accuracy is extended to the incomplete information setting, and this construct to fuzzy attribute mappings is outlined.
Abstract: Rough sets are often induced by descriptions of objects based on the precise observations of an insufficient number of attributes. In this paper, we study generalizations of rough sets to incomplete information systems, involving imprecise observations of attributes. The precise role of covering-based approximations of sets that extend the standard rough sets in the presence of incomplete information about attribute values is described. In this setting, a covering encodes a set of possible partitions of the set of objects. A natural semantics of two possible generalisations of rough sets to the case of a covering (or a non transitive tolerance relation) is laid bare. It is shown that uncertainty due to granularity of the description of sets by attributes and uncertainty due to incomplete information are superposed, whereby upper and lower approximations themselves (in Pawlak's sense) become ill-known, each being bracketed by two nested sets. The notion of measure of accuracy is extended to the incomplete information setting, and the generalization of this construct to fuzzy attribute mappings is outlined.

Journal ArticleDOI
TL;DR: A technique of an automatic selection of a threshold parameter, which determines approximation regions in rough set-based clustering, is developed, which exploits a concept of shadowed sets and leads to an efficient description of information granules obtained through the process of clustering.