A neighborhood rough setsbased attribute reduction method. Combining the concept of attribute dependence and attribute similarity in rough sets, the pruning ideas in the attribute reduction was proposed, the estimate method and fitness function in the processing of reduction was designed, and a new reduction algorithm based on pruning rules was developed, the complexity was analyzed, furthermore, many examples was given. To compute the optimal attribute reduction is nphard. Attribute reduction in rough set theory offers a systematic theoretic framework for consistencybased feature selection, which does not attempt to maximize the class separability but rather attempts to retain the discerning ability of original features for the objects from the universe. The purpose of attribute reduction is to find a minimal attribute subset that satisfies some specific criteria, while the minimal attribute subset is called attribute reduct. In this paper, a new coding method about the subset of attribute sets is proposed. Several strategies for the minimal attribute reduction with polynomial time complexity on k have been developed in rough set theory. Pdf an incremental approach to attribute reduction from. In the standard version of rough set theory pawlak 1991, the lower and. Attribute reduction based on rough set theory is proposed in many researches 3031 32 to solve the indiscernibility and fuzziness in given information system or dynamic database. Attribute reduction is one of the most important problems in rough set theory. Pawlak, is a formal approximation of a crisp set i. Rough set theory is similar to fuzzy set theory, however the uncertain and imprecision in this approach is expressed by a boundary region of a set, and not by a partial membership as in fuzzy set theory. Significant application of fuzzy rough set is attribute reduction for crisp and real valued attribute data sets.
Many heuristic attribute reduction algorithms with polynomialtime complexity have been proposed. In realworld applications, the domain of a few or all attributes of the data set may be continuous. These continuous attributes need to be discretized as a preprocessing step to attribute reduction. Keywords rough set theory, reducts, attribute reduction, metaheuristics 1. An efficient accelerator for attribute reduction from. Many heuristic attribute reduction algorithms have been proposed however, quite often. 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.
Attribute reduction is one of the most important topics in rough set theory, which is a useful mathematical tool for data analysis and has been widely used in many fields. Based on approach attributes reduction methods of traditional rough set theory 1, 6, this paper improves, analyzes. Pdf variable neighborhood search for attribute reduction. In rough set theory, the information granulation is of extensive concern 4549, and the granulation monotonicity plays an important role in attribute reduction 12,50 51 52. Pdf variable neighborhood search for attribute reduction in. At the heart of the rsar approach is the concept of indiscernibility 24. Attribute reduction of an information system is a key problem in rough set theory and its applications. In this paper, a multiobjective attribute reduction moar is modeled by designing a new effective cost function to optimize the minimum number of attributes with the maximum dependency coefficient of the rst. Matroidal structure of rough sets and its characterization.
Attribute reduction on continuous data in rough set theory. Genetic algorithm selection strategies based rough set for. Reducing the unnecessary redundant attributes becomes very necessary for data mining 1. Attribute reduction is an important preprocessing step in data mining and knowledge discovery. A complete attribute reduction algorithm in rough set theory bing wang, shanben chen school of materials science and engineering shanghai jiao tong university 1954 hua shan road, shanghai china abstract. By using the covering rough set, the process of continuous attribute discretization can be avoided. Examples e1 and e2 are characterized by the same values of both attributes. Pdf the main objective of the attribute reduction problem in rough set theory is to find and retain the set of attributes whose values vary. As an important processing step for rough set theory, attribute reduction aims at eliminating data redundancy and drawing useful information. However, most of them are incomplete for the definition of attribute reduction given by z. Decisiontheoretic rough set model dtrsm is one of the probabilistic approaches to rough set model. There are two different types of classification rules, positive and. The starting point of rough set theory the is the concept of indiscernibility.
In classical set theory, either an element belongs to a set or it does not. Algorithms for attribute reduction in rough sets based on concept of knowledge entropy was given, and an example analysis was done in this paper. The typical high dimensionality of datasets precludes the use of greedy methods to find reducts. Reducing attributes in rough set theory with the viewpoint of.
Experimental results are given in section 5, while section 6 concludesthe paper. Equivalence relations are the mathematical basis for the rough set theory. Based on the proposed accelerator, a general attribute reduction algorithm is. What is known about rs in computer science, a rough set, first described by a polish computer scientist zdzislaw pawlak, is a formal approximation of a crisp set i. Pdf reducing attributes in rough set theory with the viewpoint. Tabu search for attribute reduction in rough set theory. An innovative approach for attribute reduction using rough. Stable attribute reduction for neighborhood rough set. This paper addresses attribute reduction in decisiontheoretic rough set models regarding different classification properties, such. Research article multigranulations rough set method of. Attribute reduction based on consistent covering rough set and. An improved approach to attribute reduction with covering. Pawlaks rough set model can only deal with data containing nominal values. Abstract rough set theory is a relatively new intelligent technique used in the discovery of data dependencies.
Experts need efficient data mining methods to extract useful information and to perform the analysis of the data. An innovative approach for attribute reduction in rough. Our fsa algorithm based on rough sets for attribute reduction flrsar is then presented in section 4. Attribute reduction for massive data based on rough set theory. Attribute reduction is one of the most important and hot research topics in rough set theory as a basis of rule generation by rough set theory and there have been many proposals of heuristic algorithms to compute some candidates of relative reducts for example, see 3, 5, 7, 10, 11, 22, 24. On the reduction of covering generalized rough sets arxiv. Reduct is a minimal attribute subset of the original data which is independent and has the same discernibility power as all of the attributes in rough set framework. Through preprocessing of original data, one can use the classical rough set theory to select a subset of features that is the most suitable for agivenrecognitionproblem.
Attribute reduction problems for rough set theory literature. Rough set theory in this section, we present some of the necessary fundamentals for rough set rs theory and rsbased feature selection. Pdf design and algorithms realization of rough set. Stimulated by fuzzy rough set theory, which allows different fuzzy relations to measure the similarity between samples under different labels. The parallel programming mode of mapreduce is introduced and combined with the attribute reduction algorithm of rough set theory, a parallel attribute. Enhanced cultural algorithm to solve multiobjective. Rough set theory, reducts, attribute reduction, metaheuristics 1. Request pdf attribute reduction in decisiontheoretic rough set models rough set theory can be applied to rule induction. Rough set approach for attribute reduction and rule.
The set of attributes can be translated as an assignment of variables. The corresponding membership function is the characteristic function for the set, i. On quick attribute reduction in decisiontheoretic rough. This paper deals with reduction of unimportant attribute s for classification and decision making, using fuzzyrough set. This paper proposes an attribute reduction algorithm in dtrsm, through region preservation. Attribute reduction can be defined as a process of selecting a minimal subset of attributes based on a rough set theory as a mathematical tool from an original set with least lose of information. The values of attributes are true, when they areincluded in the reduction. Rough set concept can be defined quite generally by means of interior and closure topological operations know approximations pawlak, 1982. Feature selection is a challenging problem in areas such as pattern recognition, machine learning and data mining. Since satis fiability problem is classical and sophisticated, it is a smart idea to find solutions of attribute reduction by methods of.
Characterization of a set of objects in terms of attribute values. Di erent from the works mentioned above, in rough set theory, attribute reduction is an important concept. In computer science, a rough set, first described by polish computer scientist zdzislaw i. Pdf tabu search for attribute reduction in rough set theory. Rough set theory has proved to be a powerful tool for uncertainty and has been applied to data reduction, rule extraction, data mining and granularity computation. In the standard version of rough set theory pawlak 1991, the lower and upper. Attribute reduction ar in the rough set theory rst removes redundant or. An innovative approach for attribute reduction in rough set. By transforming discernibility matrix into a simplest equivalent matrix, valuable attributes have been. I u, a, va v where u is a nonempty set of finite objects, a is a. Index termsgenetic algorithm, the rough set, the rough approximation precision, attribute reduction. Attribute reduction has a significant role in different branches of artificial intelligence like machine learning, pattern recognition, data mining from databases etc. Rough set theory fundamental concepts, principals, data.
According to researches, the attribute reduction in the rough set theory can be regarded as a combination optimization process, so the genetic algorithm can be introduced into attribute reduction. A novel strategy for minimum attribute reduction based on. Each attribute set induces an indiscernibility equivalence class structure, the equivalence classes induced by given by. Quantization of rough set based attribute reduction. Attribute reduction as an important preprocessing step for data mining, and has become a hot research topic in rough set theory. Attribute set is reduced by generating redacts using the indiscernibility relation of. An attribute reduction method using neighborhood entropy. Attribute reduction techniques based on pawlak rough set theory work only on data sets with discrete attributes.
The socalled attribute reduction is to delete the irrelevant or unimportant attributes under the condition of keeping the classification and the decisionmaking capacity of the knowledge unchanged 4. Attribute reduction is a challenging problem in rough set theory, which has been applied in many research fields, including knowledge representation, machine learning, and artificial intelligence. The proposed method, called tabu search attribute reduction tsar, shows promising and competitive performance compared with some other ci tools in terms of solution qualities. It can be used for feature selection, feature extraction, data reduction, decision. Fuzzy rough set is emerging tool frequently used in pattern recognition and machine learning.
Attribute reduction is the process of identifying and removing redundant and irrelevant attributes from huge data sets, reducing its volume. In order to simplify the calculation of fitness function under the condition of keeping the algorithm correct, the relative importance of. The effective computation of an attribute reduct has a direct bearing on the efficiency of knowledge acquisition and various related tasks. Research article costsensitive attribute reduction in. Entropy based attribute reduction algorithms for rough sets. Moreover, classical rough sets and their extensions canbeusedin con ict analysis, a. Moreover, classical rough sets and their extensions canbeusedin con ict analysis, a eld related to decision making and game theory. However, little work has been done on applying rough set theory to attribute reduction in multilabel classification. Considering a consistency measure introduced in rough set theory, the.
Rough set theory is an extension of set theory for study of the intelligent. The main concept of rough set attribute reduction rsar 7 is indiscernibility relation. An attribute reduction algorithm based on rough set theory and an improved genetic algorithm is proposed in this paper. Attribute reduction based on minimizing both missed information and selected subset attributes is logical solution for the challenge. Let us take two disjoint sets of attributes, set and set, and inquire what degree of dependency obtains between them. Attribute reduction is a combinational optimization problem in data mining domain that aims to find a minimal subset from a large set of attributes. Attribute reduction is one of the most important research issues in the rough set theory. Neighborhood rough set theory can overcome the shortcoming that classical rough set theory may lose some useful information in the process of discretization for continuousvalued data sets. It is very important to compute the attribute reduction in real applications of rough set theory. In this paper, we define a similaritybased attribute reduct based on a clustering perspective.
We demonstrate rough set based attribute reduction is a subproblem of propositional satisfiability problem. As an important concept of rough set theory, an attribute reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property of the given information table. Rough set theory has been widely used for attribute reduction with much success. In this paper, a novel attribute reduction method based on rough set theory is proposed for multilabel data. Attribute reduction in rough set theory has been recognized as an important feature selection method 2. However, from the granular computing point of view, the classical rough set theory is based on a single granulation. On the basis of algorithm 1 and the concept of attribute significance degree by definition 6, a quick attribute reduction algorithm based on approximation dependency degree is. Rough set theory is a mathematical approach to analyse the vagueness and uncertaintyin data. This paper presents the implementation of the genetic algorithm on attribute reductionan based rough set. On attribute reduction of rough set based on pruning rules. Genetic algorithm refers to a global search algorithm, and is featured by good stability and parallel execution ability. In realworld applications, the domain of a few or all attributes of the data set.
In rough set theory, the notion of dependency is defined very simply. In section 4, we conclude the paper with a summary. Reducing attributes in rough set theory with the viewpoint. Attribute reduction for multilabel learning with fuzzy rough set. Some notions related to covering rough sets attribute reduction is an important application field of rough set theory. Similaritybased attribute reduction in rough set theory. Attribute reduction based on consistent covering rough set. While investigating the attribute reduction strategy based on the discernibility matrix dm, a counterexample is constructed theoretically, which demonstrates that these strategies are all incomplete with respect to the minimal reduction. Grzymalabusselersa system for learning from examples based on rough sets. Therefore, the key issue for attribute reduction in multilabel data is to measure the quality of each attribute with respect to a set of labels. The purpose of attribute reduction is to find a minimal attribute subset that satisfies some specific.
Rough sets theory is an effective mathematical tool dealing with vagueness and uncertainty. Matroidal structure of rough sets and its characterization to. Analysis on attribute reduction strategies of rough set. Using computational intelligence ci tools to solve such problems has recently fascinated. Pdf tabu search for attribute reduction in rough set. Rough sets can be also defined by using, instead of approximations, a rough membership function. An attribute reduction algorithm based on rough set theory. It has been applied in a variety of fields such as data mining, pattern recognition or process control. For the example, the calculation result is coincident with the result calculated by using the traditional method of attribute reduction in rough set theory. Similar to other generalized rough sets, attribute reduction 2, 10, 19, 23 plays a fundamental role in neighborhood rough set.
Generalized attribute reduct in rough set theory request pdf. However, many important problems including attribute reduction in rough sets are nphard. Design and algorithms realization of rough set simulation tool box. Introduction attribute reduction is one of the main research direction of rough set theory.
A novel strategy for minimum attribute reduction based on rough. An extensive experimental analysis is described in x5. Attributes that are irrelevant to recognition tasks can be omitted, which will not seriously impact. Due to the combinatorial explosion problem of attributes, obtaining a minimum attribute reduction set is an nphard problem. Introduction attribute reduction ar is considered as a nphard problem 1 and could be described as a process of discovering the most predictable input features of a given result in various fields as signal processing, data mining, pattern recognition and machine. The theory provides powerful and useful tools required for data analysis as well.
Attribute reduction in decisiontheoretic rough set models. Information attribute reduction based on the rough set theory. Based on rough set theory, application research mainly focuses on attribute reduction, rule acquisition, intelligent algorithm, etc. An improved attribute reduction algorithm based on mutual. In application, rough set theory has been widely used in attribute reduction 2,20,25,38 and rule extraction 4,23,29. Gene expression data analysis using heuristic attribute. A complete attribute reduction algorithm in rough set theory. Rough set theory rst is an information recognition technique in uncertain data that it shows the value missed information for the selected attributes.
In rough set theory, the definition and interpretation of attribute reduction are mainly dependent on construction methods of the lower and upper approximations. Hence those algorithms for them are almost greedy ones 79,20, especially heuristic ones 10,19, 21,30. Attribute reduction ar in the rough set theory rst removes redundant or insignificant knowledge with keeping the classification ability of the information system the same as before. A neighborhood rough setsbased attribute reduction. Recently, a great number of evaluation criteria such that neighborhood decision. This paper addresses attribute reduction in decisiontheoretic rough set models regarding different classification properties, such as. Fuzzy rough set theory has been analyzed further 39 in terms of property and axioms. Attribute reduction, water cycle algorithm, rough set theory. Goals of rough set theory the main goal of the rough set analysis is the induction of learning approximations of concepts. Feature selection in rough set theory is called attribute reduction, which is a common problem in pattern recognition, data mining and machine learning. Now, rst is widely used in many fields such as machine learning, data mining, and knowledge discovery 36. Introduction large amounts of data are generated everyday and the ability to analyze them is normally a challenge.
A novel attribute reduction approach for multilabel data. Pdf modified great deluge for attribute reduction in. Experts need efficient data mining methods to extract useful. Attribute reduction approaches based on rough set theory. Covering rough set, as a generalization of classical rough set theory, has attracted wide attention on both theory and application.