Classical Rough Set Research Articles

General vague rough approximation: an extended method of fuzzy knowledge representation

The classical rough set theory has been extended to fuzzy data environments by many authors, resulting in the development of the fuzzy rough set. Recently, vague set is treated as an extension of fuzzy set, but the existing theories and approaches of fuzzy rough set could not be applied directly to data set represented by vague set. In this article, we attempt to establish a theoretical model for vague data by combing both rough set and vague set. We first introduced the basic notions of vague t-norms and t-conorms. Next, we developed a general vague rough approximation set for generalizing to fuzzy rough set. Then, to overcome the inconvenience of dealing vague data, we also introduced a model for transforming a vague set into a fuzzy set to take the place of an interval vague set. Moreover, we also give some perspectives for future research.

Multi-granulation rough sets based on tolerance relations

The original rough set model is primarily concerned with the approximations of sets described by a single equivalence relation on the universe. Some further investigations generalize the classical rough set model to rough set model based on a tolerance relation. From the granular computing point of view, the classical rough set theory is based on a single granulation. For some complicated issues, the classical rough set model was extended to multi-granulation rough set model (MGRS). This paper extends the single-granulation tolerance rough set model (SGTRS) to two types of multi-granulation tolerance rough set models (MGTRS). Some important properties of the two types of MGTRS are investigated. From the properties, it can be found that rough set model based on a single tolerance relation is a special instance of MGTRS. Moreover, the relationship and difference among SGTRS, the first type of MGTRS and the second type of MGTRS are discussed. Furthermore, several important measures are presented in two types of MGTRS, such as rough measure and quality of approximation. Several examples are considered to illustrate the two types of multi-granulation tolerance rough set models. The results from this research are both theoretically and practically meaningful for data reduction.

Two Database Related Interpretations of Rough Approximations: Data Organization and Query Execution

We present analytic data processing technology derived from the principles of rough sets and granular computing. We show how the idea of approximate computations on granulated data has evolved toward complete product supporting standard analytic database operations and their extensions. We refer to our previous works where our query execution algorithms were described in terms of iteratively computed rough approximations. We explain how to interpret our data organization methods in terms of classical rough set notions such as reducts and generalized decisions.

Covering-Based Rough Sets on Eulerian Matroids

Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Covering-based rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively from linear algebra and graph theory. In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids. First, we explore the circuits of an Eulerian matroid from the perspective of coverings. Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids. Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented. Finally, a matroidal structure of covering-based rough sets is constructed. These results show many potential connections between covering-based rough sets and matroids.

Properties of two types of covering-based rough sets

Rough set theory is a tool to deal with the vagueness and granularity in information systems. The core concepts of classical rough sets are lower and upper approximations based on equivalence relations, or partitions. Recently, some sufficient and necessary conditions were given in Zhu (Proceedings of the first international workshop granular computing and brain informatics (Gr BI’06), IEEE international conference on web intelligence (WI 06), pp. 494–497, 2006), Zhu and Wang (Proceedings of the IEEE international conference on data mining (ICDM’06) workshop foundation of data mining and novel techniques in high dimensional structural and unstructured data, pp. 407–411, 2006), (IEEE Trans Knowl Data Eng, 19, pp 1131–1144, 2007, Proceedings of the sixth international conference on machine learning and cybernetics, 33), under which a lower approximation operator and an upper approximation operator satisfy certain classical properties. In this paper, we give a counterexample to show that the condition given in Theorem 13 in (Proceedings of the first international workshop granular computing and brain informatics (Gr BI’06), IEEE international conference on web intelligence (WI 06), pp. 494–497, 2006) is not necessary. The correct formulation is stated. We also give other conditions for a covering, under which certain classical properties hold for the second and third types of covering-based lower and upper approximation operators.

Review of the Extraction Methods of DNA Microarray Features Based on Central Decision Class Separation vs Rough Set Classifier

AbstractThe study of DNA microarray gene extraction methods is an important and current area of research. Many researchers study gene ontological character, which contain significant information about symptoms of illnesses in tissues, types of organisms, and the distinguishing of some organisms’ features. DNA microarray gene extraction methods allow us to choose the most significant genes for a given problem and some ways of their extraction. In this article, we aim to compare three methods of gene extraction. The first and second types are based on, respectively, the modified Fisher and F statistics methods. The last one is based on the novel experimental statistics called A. A common element of those three methods is the way in which we choose genes after the calculation of decision classes’ separation ratio. Additionally, all three algorithms are based on the idea of central class separation from other decision concepts. We use our best 8v1.4 granular weighted voting classier as the basic element of comparison of our gene selection methods. The results of the research show that A statistics are better than other methods in all cases. In this article the best one is the SAM10 method, which works well for a small number of genes - less than one hundred. For a higher number of separated genes the SAM5 method is better - its effectiveness has been proven in recent published works.

Incremental updating approximations in dominance-based rough sets approach under the variation of the attribute set

Dominance-based Rough Sets Approach (DRSA) is a generalized model of the classical Rough Sets Theory (RST) which may handle information with preference-ordered attribute domain. The attribute set in the information system may evolve over time. Approximations of DRSA used to induce decision rules need updating for knowledge discovery and other related tasks. We firstly introduce a kind of dominance matrix to calculate P-dominating sets and P-dominated sets in DRSA. Then we discuss the principles of updating P-dominating sets and P-dominated sets when some attributes are added into or deleted from the attribute set P. Furthermore, we propose incremental approaches and algorithms for updating approximations in DRSA. The proposed incremental approaches effectively reduce the computational time in comparison with the non-incremental approach are validated by experimental evaluations on different data sets from UCI.

Hybrid models based on rough set classifiers for setting credit rating decision rules in the global banking industry

Banks are important to national, and even global, economic stability. Banking panics that follow bank insolvency or bankruptcy, especially of large banks, can severely jeopardize economic stability. Therefore, issuers and investors urgently need a credit rating indicator to help identify the financial status and operational competence of banks. A credit rating provides financial entities with an assessment of credit worthiness, investment risk, and default probability. Although numerous models have been proposed to solve credit rating problems, they have the following drawbacks: (1) lack of explanatory power; (2) reliance on the restrictive assumptions of statistical techniques; and (3) numerous variables, which result in multiple dimensions and complex data. To overcome these shortcomings, this work applies two hybrid models that solve the practical problems in credit rating classification. For model verification, this work uses an experimental dataset collected from the Bankscope database for the period 1998–2007. Experimental results demonstrate that the proposed hybrid models for credit rating classification outperform the listing models in this work. A set of decision rules for classifying credit ratings is extracted. Finally, study findings and managerial implications are provided for academics and practitioners.

Assessing mathematics learning achievement using hybrid rough set classifiers and multiple regression analysis

Education is recognized as the key to individual success. Particularly, elementary education is vital for providing students with basic literacy and numeracy, as well as establishing foundations in mathematics, language, science, geography, history, and other social sciences. Mathematics is fundamental to numerous fields with real life applications, including natural science, engineering, medicine, and social sciences; therefore, student mathematics-learning achievement (MLA) in elementary school is valuable. This study aims to eliminate wastage of educational resources and seek suitable hybrid models for application to education. This study proposes an integrated hybrid model based on rough set classifiers and multiple regression analysis and provides a new trial of such a hybrid model to process MLA problems for elementary schools and their teachers. The proposed model is illustrated by examining a dataset from an elementary school in Taiwan. The experimental results reveal that the proposed model outperforms the listing methods in both classification accuracy and standard deviation. The rough set LEM2 (Learning from Examples Module, version 2) algorithm generates a set of comprehensible decision rules that can be applied in a knowledge-based education system designed for interested parties. Consequently, the analytical results have important implications for strategies related to mathematics teaching/learning and support to achieve teaching goals related to mathematics education.

Application of Data Mining in Protein Sequence Classification

Protein sequence classification involves feature selection for accurate classification. Popular protein sequence classification techniques involve extraction of specific features from the sequences. Researchers apply some well-known classification techniques like neural networks, Genetic algorithm, Fuzzy ARTMAP,Rough Set Classifier etc for accurate classification. This paper presents a review is with three different classification models such as neural network model, fuzzy ARTMAP model and Rough set classifier model. This is followed by a new technique for classifying protein sequences. The proposed model is typically implemented with an own designed tool and tries to reduce the computational overheads encountered by earlier approaches and increase the accuracy of classification

Relationships between covering-based rough sets and relation-based rough sets

Rough set theory is an important technique to deal with vagueness and granularity in information systems. In rough set theory, relation-based rough sets and covering-based rough sets are two important extensions of the classical rough sets. This paper investigates relationships between relation-based rough sets and covering-based rough sets. Firstly, we unify five types of covering-based rough sets under a framework of a type of relation-based rough sets, and establish the equivalences between four types of covering-based rough sets and the type of relation-based rough sets, respectively. Then, within the proposed framework, conditions required for two different coverings to generate the same approximation operators are investigated. We also present some sufficient and necessary conditions for different types of covering-based rough sets to be equal. Furthermore, two examples are taken to illustrate applications of the discussion about relationships between covering-based rough sets and relation-based rough sets.

A Comparative Analysis of Multigranular Approaches and on Topoligical Properties of Incomplete Pessimistic Multigranular Rough Fuzzy Sets

Rough sets, introduced by Pawlak as a model to capture impreciseness in data have been a very useful tool in several applications. These basic rough sets are defined by taking equivalence relations over a universe. In order to enhance the modeling powers of rough sets, several extensions to the basic definition has been introduced over the past few years. Extending the single granular structure of research in classical rough set theory two notions of Multigranular approaches; Optimistic Multigranulation and Pessimistic Multigranulation have been introduced so far. Topological properties of rough sets along with accuracy measures are two important features of rough sets from the application point of view. Topological properties of Optimistic Multigranular rough sets Optimistic Multigranular rough fuzzy sets and Pessimistic Multigranular rough sets have been studied. Incomplete information systems take care of missing values for items in data tables. Optimistic and pessimistic MGRS have also been extended to such type of incomplete information systems. In this paper we provide a comparative study of the two types of Multigranular approaches along with other related notions. Also, we extend the study to topological properties of incomplete pessimistic MGRFS. These results hold both for complete and incomplete information systems.

Rough set analysis of relational structures

In classical rough set theory, objects are partitioned into equivalence classes based on their attribute values, which essentially represent the functional information associated with the objects. Therefore, rough set theory can be viewed as a theory of functional granulation. In contrast, relational information systems (RISs) specify the relationships between objects, instead of their properties. This study presents a rough set analysis of relational structures, which are more general than functional information systems (FISs) and RISs. Unlike classical rough set theory, in which the attribute values of objects fully determine the indiscernibility relation, the rough set analysis of relational structures must account for the relationships between objects. This study considers three important concepts of indiscernibility with respect to relational structures: congruence, bisimulation, and exact equivalence. Using these indiscernibility relations, we investigate rough approximations and knowledge reduction. This study extends the application scope of rough set analysis from table-style information systems to relational structures. This extension is important because relational structures play a crucial role in the processing of complex data, such as graph mining or social network analysis.

On fuzzy-rough attribute selection: Criteria of Max-Dependency, Max-Relevance, Min-Redundancy, and Max-Significance

Attribute selection is one of the important problems encountered in pattern recognition, machine learning, data mining, and bioinformatics. It refers to the problem of selecting those input attributes or features that are most effective to predict the sample categories. In this regard, rough set theory has been shown to be successful for selecting relevant and nonredundant attributes from a given data set. However, the classical rough sets are unable to handle real valued noisy features. This problem can be addressed by the fuzzy-rough sets, which are the generalization of classical rough sets. A feature selection method is presented here based on fuzzy-rough sets by maximizing both relevance and significance of the selected features. This paper also presents different feature evaluation criteria such as dependency, relevance, redundancy, and significance for attribute selection task using fuzzy-rough sets. The performance of different rough set models is compared with that of some existing feature evaluation indices based on the predictive accuracy of nearest neighbor rule, support vector machine, and decision tree. The effectiveness of the fuzzy-rough set based attribute selection method, along with a comparison with existing feature evaluation indices and different rough set models, is demonstrated on a set of benchmark and microarray gene expression data sets.

Using a rough set model to extract rules in dominance-based interval-valued intuitionistic fuzzy information systems

Interval-valued intuitionistic fuzzy information systems are generalizations of conventional fuzzy-valued information systems. We introduce a dominance relation in the framework of interval-valued intuitionistic fuzzy information systems to come up with the concept we call a dominance-based interval-valued intuitionistic fuzzy information system (DIIFIS). This system is used to establish a dominance-based rough set model, which is grounded primarily on the substitution of the indiscernibility relation in the classic rough set theory with the aforementioned dominance-based relation. This relation is defined by the score and accuracy of interval-valued intuitionistic fuzzy value. To simplify knowledge representation and extract useful and simple dominance-based interval-valued intuitionistic fuzzy rules, we present two attribute reduction approaches to eliminating redundant information. To demonstrate the potential of these approaches, we apply them to computer auditing risk assessment, decision-making problems in wealth management, and pattern classification. Our findings confirm that the proposed rough set model is an effective means of extracting knowledge from dominance-based interval-valued intuitionistic fuzzy information systems.

Attribute Reduction Algorithm for Fuzzy Decision Table with Membership Degrees and Weights

The classical rough set can not show the fuzziness and the importance of objects in decision procedure because it uses definite form to express each object. In order to solve this problem, this paper firstly introduces a special decision table in which each object has a membership degree to show its fuzziness and has been assigned a weight to show its importance in decision procedure. And then, the special decision table is studied and the relevant rough set model is provided. In the meantime, relevant definitions and theorems are proposed. On the above basis, an attribute reduction algorithm is presented. Finally, feasibility of the relevant rough set model and the presented attribute reduction algorithm are verified by an example.

Quantitative analysis for covering-based rough sets through the upper approximation number

Coverings are a useful form of data, while covering-based rough sets provide an effective tool for dealing with this data. Covering-based rough sets have been widely used in attribute reduction and rule extraction. However, few quantitative analyses for covering-based rough sets have been conducted, while many advances for classical rough sets have been obtained through quantitative tools. In this paper, the upper approximation number is defined as a measurement to quantify covering-based rough sets, and a pair of upper and lower approximation operators are constructed using the approximation number. The operators not only inherit some important properties of existing approximation operators, but also exhibit some new quantitative characteristics. It is interesting to note that the upper approximation number of a covering approximation space is similar to the dimension of a vector space or the rank of a matrix.

Minimum cost attribute reduction in decision-theoretic rough set models

In classical rough set models, attribute reduction generally keeps the positive or non-negative regions unchanged, as these regions do not decrease with the addition of attributes. However, the monotonicity property in decision-theoretic rough set models does not hold. This is partly due to the fact that all regions are determined according to the Bayesian decision procedure. Consequently, it is difficult to evaluate and interpret region-preservation attribute reduction in decision-theoretic rough set models. This paper provides a new definition of attribute reduct for decision-theoretic rough set models. The new attribute reduction is formulated as an optimization problem. The objective is to minimize the cost of decisions. Theoretical analysis shows the meaning of the optimization problem. Both the problem definition and the objective function have good interpretation. A heuristic approach, a genetic approach and a simulated annealing approach to the new problem are proposed. Experimental results on several data sets indicate the efficiency of these approaches.

On Some Topological Properties of Pessimistic Multigranular Rough Sets

Rough set theory was introduced by Pawlak as a model to capture impreciseness in data and since then it has been established to be a very efficient tool for this purpose. The definition of basic rough sets depends upon a single equivalence relation defined on the universe or several equivalence relations taken one each at a time. There have been several extensions to the basic rough sets introduced since then in the literature. From the granular computing point of view, research in classical rough set theory is done by taking a single granulation. It has been extended to multigranular rough set (MGRS) model, where the set approximations are defined by taking multiple equivalence relations on the universe simultaneously. Multigranular rough sets are of two types; namely optimistic MGRS and pessimistic MGRS. Topological properties of rough sets introduced by Pawlak in terms of their types were studied by Tripathy and Mitra to find the types of the union, intersection and complement of such sets. Tripathy and Raghavan have extended the topological properties of basic single granular rough sets to the optimistic MGRS context. Incomplete information systems take care of missing values for items in data tables. MGRS has also been extended to such type of incomplete information systems. In this paper we have carried out the study of topological properties of pessimistic MGRS by finding out the types of the union, intersection and complement of such sets. Also, we have provided proofs and examples to illustrate that the multiple entries in the table can actually occur in practice. Our results hold for both complete and incomplete information systems. The multiple entries in the tables occur due to impreciseness and ambiguity in the information. This is very common in many of the real life situations and needed to be addressed to handle such situations in efficient manner.

Multiple granulation rough set approach to ordered information systems

With granular computing point of view, the classical dominance-based rough set model is based on a single granulation. For an ordered information system, this paper proposes two new types of multiple granulation rough set (MGRS) models, where a target concept is approximated from different kinds of views by using dominant classes induced by multiple granulations. And a number of important properties of the two types of MGRS are investigated in an ordered information system. From the properties, it can be found that Greco's rough set model is a special instance compared to our MGRS model. Moreover, the relationships and differences are discussed carefully among Greco's rough set and two new types of MGRS. Furthermore, several important measures are presented in two types of MGRS models, such as rough measure, quality of approximation in an ordered information system. In order to illustrate our MGRS models in an ordered information system, a real life example is considered, which is helpful for applying this theory in practical issues. One can see get that the research is meaningful in applications for the issue of knowledge reduction in complex ordered information systems.