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Soft Covering Entropy and Its Applications in Multi-attribute Group Decision-Making |
WU Jiaming1, HUANG Zhehuang1, LI Jinjin1,2, LIU Danyue1, WU Zhe1 |
1. School of Mathematical Sciences, Huaqiao University, Quan-zhou 362021 2. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000 |
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Abstract Information entropy and soft coverings are combined to propose soft covering information entropy. Soft covering information entropy, soft covering joint entropy and soft covering conditional entropy are defined. The relationships between these entropies and their important properties are studied. Two kinds of algorithms for multi-attribute group decision making based on soft covering conditional entropy are presented, and the consistency between the results of these two algorithms is illustrated by examples.
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Received: 03 February 2021
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Fund:National Natural Science Foundation of China(No.11871259), Natural Science Foundation of Fujian Province(No.2020J02043,2017J01114) |
Corresponding Authors:
HUANG Zhehuang, Ph.D., associate professor. His research interests include rough set and granular computing.
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About author:: WU Jiaming, master student. His research interests include rough set, uncertainty analysis and its application. LI Jinjin, Ph.D., professor.His research interests include topology, rough set and concept lattice. LIU Danyue, master student. Her research interests include rough set, uncertainty analysis and its application. WU Zhe, master, lecturer. Her research interests include image processing, machine vision and pattern recognition. |
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[1] PAWLAK Z. Rough Sets. International Journal of Computer and Information Sciences, 1982, 11(5): 341-356. [2] PAWLAK Z. Rough Sets and Intelligent Data Analysis. Information Sciences, 2002, 147(1/2/3/4): 1-12. [3] ALI M I. A Note on Soft Sets, Rough Soft Sets and Fuzzy Soft Sets. Applied Soft Computing, 2011, 11(4): 3329-3332. [4] 纪 霞,赵 鹏,姚 晟.加权多粒度直觉模糊信息系统的粗糙集模型及其决策.模式识别与人工智能, 2017, 30(11): 971-982. (JI X, ZHAO P, YAO S. Rough Set Model and Decision Research in Intuitionistic Fuzzy Information System Based on Weighted Multi-granulation. Pattern Recognition and Artificial Intelligence, 2017, 30(11): 971-982.) [5] FENG F, LIU X Y, LEOREANU-FOTEA V, et al. Soft Sets and Soft Rough Sets. Information Sciences, 2011, 181(6): 1125-1137. [6] 薛占熬,赵丽平,张 敏,等.多粒度支持直觉模糊粗糙集的多属性决策方法.模式识别与人工智能, 2019, 32(8): 677-690. (XUE Z A, ZHAO L P, ZHANG M, et al. Multi-attribute Decision-Making Method Based on Multi-granulation Support Intuitionistic Fuzzy Rough Sets. Pattern Recognition and Artificial Intelligence, 2019, 32(8): 677-690.) [7] ZHANG Q H, XIE Q, WANG G Y. A Survey on Rough Set Theory and Its Applications. CAAI Transactions on Intelligence Technology, 2016, 1(4): 323-333. [8] LUO S, MIAO D Q, ZHANG Z F, et al. A Neighborhood Rough Set Model with Nominal Metric Embedding. Information Sciences, 2020, 520: 373-388. [9] ZHANG L, ZHAN J M, XU Z S, et al. Covering-Based General Multigranulation Intuitionistic Fuzzy Rough Sets and Corresponding Applications to Multi-attribute Group Decision-Making. Information Sciences, 2019, 494: 114-140. [10] WANG Z H, ZHANG X P, DENG J P. The Uncertainty Measures for Covering Rough Set Models. Soft Computing, 2020, 24: 11909-11929. [11] ZHANG L, ZHAN J M, XU Z S. Covering-Based Generalized IF Rough Sets with Applications to Multi-attribute Decision-Making. Information Sciences, 2019, 478: 275-302. [12] 陈应生,李进金,林荣德,等.多尺度覆盖决策信息系统的布尔矩阵方法.模式识别与人工智能, 2020, 33(9): 776-785. (CHEN Y S, LI J J, LIN R D, et al. Boolean Matrix Approach for Multi-scale Covering Decision Information System. Pattern Recognition and Artificial Intelligence, 2020, 33(9): 776-785.) [13] MOLODTSOV D. Soft Set Theory-First Results. Computers and Mathematics with Applications, 1999, 37(4/5): 19-31. [14] LI Z W, XIE N X, WEN G Q. Soft Coverings and Their Parameter Reductions. Applied Soft Computing, 2015, 31: 48-60. [15] ZHAN J M, WANG Q M. Certain Types of Soft Coverings Based Rough Sets with Applications. International Journal of Machine Learning and Cybernetics, 2019, 10(5): 1065-1076. [16] ZHANG L, ZHAN J M. Fuzzy Soft β-Covering Based Fuzzy Rough Sets and Corresponding Decision-Making Applications. Internatio-nal Journal of Machine Learning and Cybernetics, 2019, 10(6): 1487-1502. [17] DENG Z X, ZHENG Z L, DENG D Y, et al. Feature Selection for Multi-label Learning Based on F-Neighborhood Rough Sets. IEEE Access, 2020, 8: 39678-39688. [18] WANG C Z, HUANG Y, SHAO M W, et al. Feature Selection Based on Neighborhood Self-Information. IEEE Transactions on Cybernetics, 2020, 50(9): 4031-4042. [19] WANG C Z, HE Q, SHAO M W, et al. A Unified Information Measure for General Binary Relations. Knowledge-Based Systems, 2017, 135: 18-28. [20] LEI D F, LIANG P, HU J H, et al. New Online Streaming Feature Selection Based on Neighborhood Rough Set for Medical Data. Symmetry, 2020, 12(10). DOI: 10.3390/sym12101635. [21] WANG C Z, HE Q, SHAO M W, et al. Feature Selection Based on Maximal Neighborhood Discernibility. International Journal of Machine Learning and Cybernetics, 2018, 9: 1929-1940. [22] REHMAN N, SHAH N, ALI M I, et al. Uncertainty Measurement for Neighborhood Based Soft Covering Rough Graphs with Applications. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019, 113: 2515-2535. [23] LIANG J Y, CHIN K S, DANG C Y, et al. A New Method for Measuring Uncertainty and Fuzziness in Rough Set Theory. International Journal of General Systems, 2002, 31(4): 331-342. [24] LIANG J Y, WANG F, DANG C Y, et al. A Group Incremental Approach to Feature Selection Applying Rough Set Technique. IEEE Transactions on Knowledge and Data Engineering, 2014, 26(2): 294-308. [25] 陈东晓,李进金,林荣德,等.基于信息熵的形式背景属性约简.模式识别与人工智能, 2020, 33(9): 786-798. (CHEN D X, LI J J, LIN R D, et al. Attribute Reductions of Formal Context Based on Information Entropy. Pattern Recognition and Artificial Intelligence, 2020, 33(9): 786-798.) [26] LEI B, FAN J L. Image Thresholding Segmentation Method Based on Minimum Square Rough Entropy. Applied Soft Computing, 2019, 84. DOI: 10.1016/j.asoc.2019.105687. [27] WANG C Z, HU Q H, WANG X Z, et al. Feature Selection Based on Neighborhood Discrimination Index. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(7): 2986-2999. [28] SUN L, WANG L Y, DING W P, et al. Feature Selection Using Fuzzy Neighborhood Entropy-Based Uncertainty Measures for Fuzzy Neighborhood Multigranulation Rough Sets. IEEE Transactions on Fuzzy Systems, 2021, 29(1): 19-33. [29] ZHANG X, MEI C L, CHEN D G, et al. Active Incremental Feature Selection Using a Fuzzy-Rough-Set-Based Information Entropy. IEEE Transactions on Fuzzy Systems, 2020, 28(5): 901-915. [30] YÜKSEL S, TOZLU N, DIZMAN T H. An Application of Multicriteria Group Decision Making by Soft Covering Based Rough Sets. Filomat, 2015, 29(1): 209-219. |
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