Similarity-based attribute reduction in rough set theory: a clustering perspective

Tri-level attribute reduction in rough set theory

Attribute reduction plays an important role in rough set theory. It is an important application in data mining. In this paper, we focus on discussing the relation between set covering and attribute reduction in rough set theory. Based on the equivalence between minimal set covering and minimal attribute reduction sets, attribute reduction graph (ARG) is constructed. A novel algorithm to find the minimal attribute reduction sets, which is based on combination of binary discernibility matrix and graph theory is proposed in this paper. This algorithm demonstrates its efficiency and feasibility by an example.

The variable precision rough set (VPRS) model generalizes the Pawlak rough set model with variable parameters. The Bayesian rough set (BRS) model improves the VPRS model with non-parametric modification by using the prior probability as a reference. This paper presents two research results related to rough set model and rough vague sets. One is a modification to the Bayesian rough set model and the other is a modification to rough vague sets. First, the Bayesian rough set model is analyzed and discussed. Second, a modification to this model is proposed and verified. Finally, a modification to rough vague sets is presented and its related properties are discussed..

Distance metric learning-based multi-granularity neighborhood rough sets for attribute reduction

Attribute reduction for hierarchical classification based on improved fuzzy rough set

Rough sets theory for multicriteria decision analysis

Bayesian Decision theoretic rough set has been invented by the author. In this paper the attribute reduction by the aid of Bayesian decision theoretic rough set has been studied. Lot of other methods are there for attribute reduction such as Variable precision method, probabilistic approach, Bayesian method, Pawlaks rough set method using Boolean function. But with the help of some example it is shown that Bayesian decision theoretic rough set model gives better result than other method. Lastly an example of HIV /AIDS is taken and attribute reduction is done by this new method and various other method. It is shown that this method gives better result than the previously defined methods. By this method the authors get only the reduced attribute age which is the best significant attribute. Though in Pawlak model age sex or age living status are the reduced attribute and variable precision method fails to work here. In this paper attribute reduction is done by the help of discernibility matrix after determining the positive, boundary and negative region. This model is a hybrid model of Bayesian rough set model and decision theory. So this technique gives better result than Bayesian method and decision theoretic rough set method.

Attribute reduction is a basic issue in knowledge representation and data mining. It simplifies an information system by discarding some redundant attributes. In this paper, we present a hybrid approach that combines the nature of variable neighbourhood search in the first phase with an iterated local search in the second phase that always accepts best solutions. The approach is tested over 13 well-known established datasets. The results demonstrate that the variable neighbourhood search approach is able to produce solutions that are competitive with those state-of-the-art techniques from the literature in terms of minimal reducts.

An incremental approach to attribute reduction from dynamic incomplete decision systems in rough set theory

Rough set theory has been proposed by Pawlak in the early 80s to deal with inconsistency problems following from information granulation. It operates on an information table composed of a set U of objects described by a set Q of condition and decision attributes. Decision attributes make a partition of U into decision classes. Basic concepts of rough set theory are: indiscernibility relation on U, lower and upper (rough) approximations of decision classes, dependence and reduction of attributes from Q, and decision rules induced from rough approximations of decision classes. The original rough set idea was failing, however, to handle preferential ordering of domains of attributes (scales of criteria), as well as preferential ordering of decision classes. In order to deal with multiple criteria decision problems a number of methodological changes to the original rough set theory were necessary. The main change is the substitution of the indiscernibility relation by a dominance relation, which permits approximation of ordered sets. In multiple criteria decision context, the information table is composed of decision examples given by a decision maker. The Dominance-based Rough Set Approach (DRSA) applied to this information table results with a set of decision rules, being a preference model of the decision maker. It is more general than the classical multiple attribute utility model or outranking model, and it is more understandable because of its natural syntax. In this chapter, after recalling the classical rough set approach and DRSA, we review their fuzzy set extensions. Moreover, we characterize the dominance-based rough approximation of a fuzzy set, and we show that the classical rough approximation of a crisp set is its particular case. In this sense, DRSA is also relevant in the case where preferences are not considered, but just a kind of monotonicity relating values of different attributes is meaningful for the analysis of data at hand. In general terms, monotonicity concerns relationship between different aspects of a phenomenon described by data: for example, “the larger the house, the higher its price” or “the closer the house to the city centre, the higher its price”. In this perspective, DRSA gives a very general framework for reasoning about data using only monotonicity relationships.

In real-life applications, partial order may exist in the domain of attributes and different data types often coexist in an decision system. Dominance-based rough set approach has been used widely in multi-attribute and multi-criteria decision by using the dominating relation. Neighborhood rough set aims to deal with hybrid data types. But the preference relation in the context of neighborhood rough set has not been taken into consideration. In this paper, a novel rough set model, Dominance-based Neighborhood Rough Sets (DNRS), is proposed which aims to process a decision system with hybrid data types where the partial order between objects is taken into consideration. The properties of DNRS are studied. Attribute reduction under DNRS is investigated.

An improved attribute reduction scheme with covering based rough sets

Dominance-based rough set approach (DRSA) has attracted much attention in multi-criteria decision-making problems for data with preference-ordered relations since its inception. However, in the real world, there is often the challenge of incomplete information. This paper addresses approaches to attribute reduction in an incomplete ordered decision system (IODS). Attribute evaluation is crucial in the attribute reduction process. Traditional evaluation functions primarily depend on the relationships between features, neglecting their impact on classification, and incur high computational costs when calculating lower and upper approximations. To address these issues, this paper proposes whole inter-class non-dominance as the criterion for attribute importance. First, we define the concepts of inter-class proximity and inter-class non-dominance in an IODS, with whole inter-class non-dominance serving as the evaluation index for attribute importance. Next, we propose a method for calculating inter-class non-dominance based on the expanded dominance matrix. Finally, combined with the heuristic search strategy, an attribute reduction algorithm based on inter-class non-dominance (HANDR) was designed, and experiments on various datasets from the University of California at Irvine (UCI) demonstrate that the proposed algorithm significantly improves running time and classification accuracy.

In the face of the explosive growth in data volume, current technologies have encountered many difficulties in both storage and knowledge discovery processes. Moreover, the quality of data has also deteriorated due to excessive noisy information, which reduces the effectiveness of machine learning models. Therefore, many solutions have been proposed, in which attribute reduction has emerged as an important research direction. Currently, research on attribute reduction has become very active and is primarily focused on the processing of decision tables. In this area, research on attribute reduction based on rough set theory and its extensions is considered a promising direction, which has been yielding many impressive results. To gain a clearer understanding of the attribute reduction research direction, this study will provide an overview of the methods of attribute reduction from their inception to the methods proposed in recent times.

Rough set theory is emerging as a powerful toll for reasoning about data. Attribute reduction is one of important topics in the research on the rough set theory. Heuristic, discernibility matrix and matrix method are three usually methods for designing attribute reduction algorithm in attribute reduction based on rough set. Some researchers use matrix method to design attribute reduction algorithm. The time complexity of the algorithm is O(|C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> |U| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), and the computation of the algorithm is time consuming. To lower the time complexity, it was first proposed a new matrix, and provided an attribute reduction definition based on the new matrix. Then it was proved that the new attribute reduction definition is the same as the old reduction. At last, we used the matrix of attribute to define the significance of attribute, and designed a new attribute reduction algorithm, which time complexity is cut to O(|C||U|)+O(|C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> |U/C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). At the same time, an example was used to illustrate the new algorithm.