JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (1): 60-67.doi: 10.6040/j.issn.1671-9352.0.2020.205

Previous Articles    

Graph-based granularity reduction in pessimistic multi-granulation rough set

ZHANG Wen-juan1, LI Jin-jin1*, LIN Yi-dong1,2   

  1. 1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, Fujian, China;
    2. School of Mathematical Sciences, Xiamen University, Xiamen 361000, Fujian, China
  • Published:2021-01-05

Abstract: This paper combines the theory of the vertex cover of graph, and a new method of the granularity reduction of pessimistic multi-granulation rough set is discussed. Firstly, the concept of the graph induced from pessimistic multi-granulation rough set is presented, and the graph characteristic of its granularity reduction is given. On this basis, the significance of granularity is depicted by the method of graph, and then a algorithm about granularity reduction of pessimistic multi-granulation rough set based on graph is designed. Secondly, the concept of the graph induced from multi-granulation decision-theoretic rough set is defined, the graph characteristic of its granularity reduction and the significance of granularity are proposed at the same way, then a algorithm of granularity reduction of pessimistic multi-granulation decision-theoretic rough set based on graph is designed. Finally, it is rational to give an example to illustrate the pessimistic lower approximate multi-granulation rough set algorithm.

Key words: granularity reduction, graph theory, multi-granulation rough set, vertex cover

CLC Number: 

  • TP18
[1] PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Sciences, 1982, 11(5):341-356.
[2] QIAN Yuhua, LIANG Jiye, YAO Yiyu, et al. MGRS: a multi-granulation rough set[J]. Information Sciences, 2009, 180(6):949-970.
[3] LIN Guoping, QIAN Yuhua, LI Jinjin. MGRS: neighborhood-based multi-granulation rough sets[J]. International Journal of Approximate Reasoning, 2012, 53(7):1080-1093.
[4] 张明,唐振明,徐维艳,等. 可变多粒度粗糙集模型[J]. 模式识别与人工智能, 2012, 25(4):709-720. ZHANG Ming, TANG Zhenming, XU Weiyan, et al. Variable multigranulation rough set model[J]. Pattern Recognition and Artificial Intelligence, 2012, 25(4):709-720.
[5] 吴志远,钟培华,胡建根,等. 程度多粒度粗糙集[J]. 模糊系统与数学, 2014, 28(3):165-172. WU Zhiyuan, ZHONG Peihua, HU Jiangen, et al. Graded multi-granulation rough sets[J]. Fuzzy Systems and Mathematics, 2014, 28(3):165-172.
[6] 桑妍丽,钱宇华. 一种悲观多粒度粗糙集中的粒度约简算法[J]. 模式识别与人工智能, 2012, 25(3):361-366. SANG Yanli, QIAN Yuhua. A granular space reduction approach to pessimistic multi-granulation rough sets[J]. Pattern Recognition and Artificial Intelligence, 2012, 25(3):361-366.
[7] 孟慧丽,马媛媛,徐久成. 基于信息量的悲观多粒度粗糙集粒度约简[J].南京大学学报(自然科学版), 2015, 51(2):343-348. MENG Huili, MA Yuanyuan, XU Jiucheng. The granularity reduction of pessimistic multi-granulation rough set based on the information quantity[J]. Journal of Nanjing University(Natural Sciences Edition), 2015, 51(2):343-348.
[8] 胡善终,徐怡,何明慧,等. 多粒度粗糙集粒度约简的高效算法[J]. 计算机应用. 2017, 37(12):3391-3399. HU Shanzhong, XU Yi, HE Minghui, et al. Effective algorithm for granulation reduction of multigranulation rough set[J]. Journal of Computer Applications, 2017, 37(12):3391-3399.
[9] CHEN Jinkun, LIN Yaojin, LIN Guoping, et al. Attribute reduction of covering decision systems by hypergraph model[J]. Information Science, 2017, 118:93-104.
[10] 米据生,陈锦坤. 基于图的粗糙集属性约简方法[J]. 西北大学学报(自然科学版), 2019, 49(4):508-516. MI Jusheng, CHEN Jinkun. Graph-based approaches for attribute reduction in rough sets[J]. Journal of Northwest University(Natural Sciences Edition), 2019, 49(4):508-516.
[11] TAN Anhui, WU Weizhi, LI Jinjin, et al. Reduction foundation with multigranulation rough sets using discernibility[J]. Atificial Intelligence Review, 2019, 53(4):2425-2452.
[12] CHEN Jinkun, LIN Yaojin, LIN Guoping, et al. The relationship between attribute reducts in rough sets and minimal vertex covers of graphs[J]. Information Sciences, 2015, 325:87-97.
[13] CHEN Jinkun, LIN Yaojin, LI Jinjin, et al. A rough set method for the minimum vertex cover problem of graphs[J]. Applied Soft Computing, 2016, 42:360-367.
[14] BONDY J A, MURTY U S R. Graph therory with applications[M]. London: Macmillan, 1976.
[15] BONDY J A, MURTY U S R. Graph theory[M]. Beilin: Springer, 2008.
[1] ZHANG Hai-yang, MA Zhou-ming, YU Pei-qiu, LIN Meng-lei, LI Jin-jin. Incremental method for approximating sets of multi-granularity rough sets [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(1): 51-61.
[2] WANG Xiao-yan, SHEN Jia-lan, SHEN Yuan-xia. Graded multi-granulation rough set based on weighting granulations and dominance relation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(3): 97-104.
[3] WANG Qiang, WANG Yu-zhen*. Flocking control protocol design based on Hamiltonian framework [J]. J4, 2011, 46(7): 70-77.
[4] QI Zhong-bin,ZHANG He-ping . 1-resonance of a class of Fullerene graphs [J]. J4, 2008, 43(4): 67-72 .
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!