Attribute reduction in interval-valued information systems based on information entropies

2021

IEEE Access

An incomplete interval-valued decision information system (IIVDIS) is a significant type of data decision table, which is ubiquitous in real life. Interval value is a form of knowledge representation, and it seems to be an embodiment of the uncertainty of research objects. In this paper, we focus on attribute reduction on the basis of a parameterized tolerance-based rough set model in an IIVDIS. Firstly, we give the similarity degree between information values on each attribute in an IIVDIS by considering incomplete information. Then, we present tolerance relations on the object set of an IIVDIS based on this similarity degree. Next, we define the rough approximations by means of the presented tolerance relation. Based on Kryszkiewicz's ideal, we introduce α-generalized decision and consider attribute reduction in an IIVDIS by means of this decision. Furthermore, we put forward the notions of α-information entropy, α-conditional information entropy and α-joint information entropy in an IIVDIS. And we prove that α-positive region reduction theorem, α-conditional entropy reduction theorem, α-dependency reduction theorem and α-generalized decision reduction theorem are equivalent to each other. Finally, we propose two attribute reduction methods in an IIVDIS by using entropy measurement and the rough approximations, and design the relevant algorithms. We carry out a series of numerical experiments to verify the effectiveness of the proposed algorithms. The experimental results show that proposed algorithms often choose fewer attributes and improve classification accuracies in most cases.

Section: Classification Resultsmentioning

confidence: 99%

Section: Introduction a Research Background And Related Workmentioning

confidence: 99%

Attribute Reduction in an Incomplete Interval-Valued Decision Information System

Chen

2021

IEEE Access

“…In studies of heuristic attribute reduction, the attribute similarity measure (heuristic information, dependency degree) is an important factor. Recently, to obtain the various reducts, different similarity measures have been proposed in rough set theory, such as the positive dependency degree [1], information entropy [35], conditional entropy [40], and maximum decision entropy [41]. However, there have been few studies on the similarity measure for generalized decision preservation.…”

Section: The Similarity Degree For Generalized Decision Preservationmentioning

confidence: 99%

“…Qian et al [34] closely focused on increasing the efficiencies of heuristic reduction algorithms, and adopted a positive approximation strategy to accelerate heuristic reduction algorithms. Dai et al [35] used a variant form of conditional entropy to design an attribute reduction algorithm for an interval-valued decision system. Many attribute reduction algorithms based on metaheuristic methods [24][25][26][27][28][29][30]36,37] have been developed recently.…”

Section: Introductionmentioning

confidence: 99%

Heuristic Approaches to Attribute Reduction for Generalized Decision Preservation

Gao

2019

Applied Sciences

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 main objective of attribute reduction is to obtain a minimal attribute subset that can retain the same classification or discernibility properties as the original information system. Recently, many attribute reduction algorithms, such as positive region preservation, generalized decision preservation, and distribution preservation, have been proposed. The existing attribute reduction algorithms for generalized decision preservation are mainly based on the discernibility matrix and are, thus, computationally very expensive and hard to use in large-scale and high-dimensional data sets. To overcome this problem, we introduce the similarity degree for generalized decision preservation. On this basis, the inner and outer significance measures are proposed. By using heuristic strategies, we develop two quick reduction algorithms for generalized decision preservation. Finally, theoretical and experimental results show that the proposed heuristic reduction algorithms are effective and efficient.

“…Gao et al [ 13 ] developed a heuristic attribute reduction algorithm based on the maximum decision entropy in the decision-theoretic rough set model. Dai et al [ 14 ] proposed a framework for attribute reduction in interval-valued data from the information view. It is known that there is a strong complementarity between the algebra view and the information view of attribute importance, and the two views can be combined to produce a more comprehensive measurement mechanism [ 15 ].…”

Section: Introductionmentioning

confidence: 99%

An Attribute Reduction Method Using Neighborhood Entropy Measures in Neighborhood Rough Sets

Sun

et al. 2019

Entropy

Attribute reduction as an important preprocessing step for data mining, and has become a hot research topic in 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 continuous-valued data sets. In this paper, to improve the classification performance of complex data, a novel attribute reduction method using neighborhood entropy measures, combining algebra view with information view, in neighborhood rough sets is proposed, which has the ability of dealing with continuous data whilst maintaining the classification information of original attributes. First, to efficiently analyze the uncertainty of knowledge in neighborhood rough sets, by combining neighborhood approximate precision with neighborhood entropy, a new average neighborhood entropy, based on the strong complementarity between the algebra definition of attribute significance and the definition of information view, is presented. Then, a concept of decision neighborhood entropy is investigated for handling the uncertainty and noisiness of neighborhood decision systems, which integrates the credibility degree with the coverage degree of neighborhood decision systems to fully reflect the decision ability of attributes. Moreover, some of their properties are derived and the relationships among these measures are established, which helps to understand the essence of knowledge content and the uncertainty of neighborhood decision systems. Finally, a heuristic attribute reduction algorithm is proposed to improve the classification performance of complex data sets. The experimental results under an instance and several public data sets demonstrate that the proposed method is very effective for selecting the most relevant attributes with great classification performance.