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| Two-Universe Multi-granularity Probability Rough Sets Based on Intuitionistic Fuzzy Relations |
| HUANG Xinhong1,2, ZHANG Xianyong1,2, YANG Jilin2,3 |
1. School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066;
2. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu 610066;
3. College of Computer Science, Sichuan Normal University, Chengdu 610066 |
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Abstract In the complex uncertainty environment, extension factors are introduced into rough sets to enhance model robustness. Based on intuitionistic fuzzy relations, multi-granularity probability rough sets are investigated in two universes in this paper. Firstly, the intuitionistic fuzzy relations and two-universe background are utilized to model multi-granularity probabilistic rough sets, and four models and their integrated algorithms are acquired, including positive optimism, positive pessimism, inverse optimism and inverse pessimism. Then, mathematical properties of model lower and upper approximations are studied from the perspectives of set operation relation, probability parameter limitation and precision size comparison. Finally, the effectiveness and property correctness of the model are verified by a medical example, and the corresponding three-way decision making is provided. Regarding multi-granularity two-universe intuitionistic-fuzzy probability rough sets, systematicness, extension and applicability of the obtained models, algorithms and properties are confirmed in depth.
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Received: 17 May 2021
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| Fund:National Natural Science Foundation of China(No.61673258,11671284), Sichuan Science and Technology Program of China(No.2021YJ0085,2019YJ0529) |
About author:: HUANG Xinhong, master student. Her research interests include rough sets and fuzzy sets.
ZHANG Xianyong, Ph.D., professor. His research interests include uncertainty analysis and intelligent decision.
YANG Jilin, Ph.D., associate professor. Her research interests include granular computing and data mining. |
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[1] 马建敏,景嫄,姚红娟.区间集概率粗糙集的单调性.模糊系统与数学, 2018, 32(4): 180-190.
(MA J M, JING Y, YAO H J. The Monotonicity of Interval-Set Probabilistic Rough Sets. Fuzzy Systems and Mathematics, 2018, 32(4): 180-190.)
[2] YAO Y Y, SHE Y H. Rough Set Models in Multigranulation Spaces. Information Sciences, 2016, 327: 40-56.
[3] 邓切,张贤勇,杨霁琳,等.基于双论域笛卡尔积的粗糙熵与知识粒度.模式识别与人工智能, 2019, 32(11): 975-986.
(DENG Q, ZHANG X Y, YANG J L, et al. Rough Entropy and Knowledge Granularity Based on Cartesian Product of Double Universes. Pattern Recognition and Artificial Intelligence, 2019, 32(11): 975-986.)
[4] YAN R X, ZHENG J G, LIU J L, et al. Research on the Model of Rough Set over Dual-Universes. Knowledge-Based Systems, 2010, 23(8): 817-822.
[5] 孙秉珍,胡晓元.双论域上量化粗糙集模型及应用.计算机工程与应用, 2017, 53(20): 50-55, 99.
(SUN B Z, HU X Y. Quantitative Rough Set Model over Two Universes and Its Application. Computer Engineering and Applications, 2017, 53(20): 50-55, 99.)
[6] LI X N, SUN Q Q, CHEN H M, et al. Three-Way Decision on Two Universes. Information Sciences, 2020, 515: 263-279.
[7] 王佳琪,苗夺谦,张红云.基于可变多粒度概率粗糙集的分类模型.模式识别与人工智能, 2017, 30(8): 710-717.
(WANG J Q, MIAO D Q, ZHANG H Y. Classification Model Based on Variable Multi-granularity Probability Rough Set. Pattern Recognition and Artificial Intelligence, 2017, 30(8): 710-717.)
[8] SUN B Z, ZHOU X M, LIN N N. Diversified Binary Relation-Based Fuzzy Multigranulation Rough Set over Two Universes and Application to Multiple Attribute Group Decision Making. Information Fusion, 2020, 55: 91-104.
[9] MA W M, SUN B Z. Probabilistic Rough Set over Two Universes and Rough Entropy. International Journal of Approximate Reaso-ning, 2012, 53(4): 608-619.
[10] MANDAL P, RANADIVE A S. Multi-granulation Bipolar-Valued Fuzzy Probabilistic Rough Sets and Their Corresponding Three-Way Decisions over Two Universes. Soft Computing, 2018, 22(24): 8207-8226.
[11] 李金海,王飞,吴伟志,等.基于粒计算的多粒度数据分析方法综述.数据采集与处理, 2021, 36(3): 418-435.
(LI J H, WANG F, WU W Z, et al. Review of Multi-granularity Data Analysis Methods Based on Granular Computation. Journal of Data Acquisition and Processing, 2021, 36(3): 418-435.)
[12] 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-granularity Support Intuitionis-tic Fuzzy Rough Sets. Pattern Recognition and Artificial Intelligence, 2019, 32(8): 677-690.)
[13] 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-granularity. Pattern Recognition and Artificial Intelligence, 2017, 30(11): 971-982.)
[14] 薛占熬,司小朦,朱泰隆,等.乐观和悲观多粒度覆盖粗糙直觉模糊集模型的研究.小型微型计算机系统, 2017, 38(6): 1334-1340.
(XUE Z A, SI X M, ZHU T L, et al. On the Model of Optimistic and Pessimistic Multi-granularity Covering-Based Rough Intuitionis-tic Fuzzy Sets. Journal of Chinese Computer Systems, 2017, 38(6): 1334-1340.)
[15] 高玲玲. 基于双论域的多粒度直觉模糊粗糙集模型研究.硕士学位论文.临汾:山西师范大学, 2018.
(GAO L L. A Study of Multi-granularity Intuitionistic Fuzzy Rough Set Model Based on Two Universes. Master Dissertation. Linfen, China: Shanxi Normal University, 2018.)
[16] 郭智莲,杨海龙,王珏.双论域上的直觉模糊概率粗糙集模型及其应用.系统工程理论与实践, 2014, 34(7): 1828-1834.
(GUO Z L, YANG H L, WANG J. Intuitionistic Fuzzy Probabilistic Rough Set Model on Two Universes and Its Applications. Systems Engineering-Theory & Practice, 2014, 34(7): 1828-1834.) |
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2022, Vol. 35 
