Attribute Reduction in an Incomplete Interval-Valued Decision Information System
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...
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| Format: | Article |
| Language: | English |
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IEEE
2021-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9406010/ |
| _version_ | 1818479690771333120 |
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| author | Yiying Chen Zhaowen Li Gangqiang Zhang |
| author_facet | Yiying Chen Zhaowen Li Gangqiang Zhang |
| author_sort | Yiying Chen |
| collection | DOAJ |
| description | 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 <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-generalized decision and consider attribute reduction in an IIVDIS by means of this decision. Furthermore, we put forward the notions of <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-information entropy, <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-conditional information entropy and <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-joint information entropy in an IIVDIS. And we prove that <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-positive region reduction theorem, <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-conditional entropy reduction theorem, <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-dependency reduction theorem and <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-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. |
| first_indexed | 2024-12-10T11:14:06Z |
| format | Article |
| id | doaj.art-3457b4edd349469d987b0a105e5db086 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-10T11:14:06Z |
| publishDate | 2021-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-3457b4edd349469d987b0a105e5db0862022-12-22T01:51:18ZengIEEEIEEE Access2169-35362021-01-019645396455710.1109/ACCESS.2021.30737099406010Attribute Reduction in an Incomplete Interval-Valued Decision Information SystemYiying Chen0Zhaowen Li1https://orcid.org/0000-0002-4437-9214Gangqiang Zhang2https://orcid.org/0000-0001-5424-6389School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, ChinaDepartment of Guangxi Education, Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, ChinaSchool of Artificial Iintelligence, Guangxi University for Nationalities, Nanning, ChinaAn 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 <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-generalized decision and consider attribute reduction in an IIVDIS by means of this decision. Furthermore, we put forward the notions of <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-information entropy, <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-conditional information entropy and <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-joint information entropy in an IIVDIS. And we prove that <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-positive region reduction theorem, <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-conditional entropy reduction theorem, <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-dependency reduction theorem and <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-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.https://ieeexplore.ieee.org/document/9406010/Attribute reductionIIVDISsimilarity degreerough set theory<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">α</italic>-generalized decision<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">α</italic>-dependence |
| spellingShingle | Yiying Chen Zhaowen Li Gangqiang Zhang Attribute Reduction in an Incomplete Interval-Valued Decision Information System IEEE Access Attribute reduction IIVDIS similarity degree rough set theory <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">α</italic>-generalized decision <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">α</italic>-dependence |
| title | Attribute Reduction in an Incomplete Interval-Valued Decision Information System |
| title_full | Attribute Reduction in an Incomplete Interval-Valued Decision Information System |
| title_fullStr | Attribute Reduction in an Incomplete Interval-Valued Decision Information System |
| title_full_unstemmed | Attribute Reduction in an Incomplete Interval-Valued Decision Information System |
| title_short | Attribute Reduction in an Incomplete Interval-Valued Decision Information System |
| title_sort | attribute reduction in an incomplete interval valued decision information system |
| topic | Attribute reduction IIVDIS similarity degree rough set theory <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">α</italic>-generalized decision <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">α</italic>-dependence |
| url | https://ieeexplore.ieee.org/document/9406010/ |
| work_keys_str_mv | AT yiyingchen attributereductioninanincompleteintervalvalueddecisioninformationsystem AT zhaowenli attributereductioninanincompleteintervalvalueddecisioninformationsystem AT gangqiangzhang attributereductioninanincompleteintervalvalueddecisioninformationsystem |