代数商空间粒度转换计算研究

doi:10.3778/j.issn.1673-9418.2103028

计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (12): 2870-2878.DOI: 10.3778/j.issn.1673-9418.2103028

代数商空间粒度转换计算研究

魏宗萱(), 王加阳

中南大学计算机学院，长沙 410083

收稿日期:2021-03-08 修回日期:2021-10-28 出版日期:2022-12-01 发布日期:2021-11-03
通讯作者: +E-mail: 2414011485@qq.com
作者简介:魏宗萱（1995—），女，河北保定人，硕士研究生，主要研究方向为粒度计算、智能信息处理等。
王加阳（1963—），男，湖南长沙人，博士，教授，博士生导师，CCF高级会员，主要研究方向为粒度计算、智能信息处理、决策支持等。
基金资助:
国家自然科学基金(61772031);湖南省自然科学基金(2020JJ4753)

Research on Granular Conversion Computing in Algebraic Quotient Space

WEI Zongxuan(), WANG Jiayang

School of Computer Science and Engineering, Central South University, Changsha 410083, China

Received:2021-03-08 Revised:2021-10-28 Online:2022-12-01 Published:2021-11-03
About author:WEI Zongxuan, born in 1995, M.S. candidate. Her research interests include granular computing, intelligent information processing, etc.
WANG Jiayang, born in 1963, Ph.D., professor, Ph.D. supervisor, senior member of CCF. His research interests include granular computing, intelligent information processing, decision sup-port, etc.
Supported by:
National Natural Science Foundation of China(61772031);Natural Science Foundation of Hunan Province(2020JJ4753)

摘要/Abstract

摘要：

粒度计算是一种基于多层次结构的问题处理范式，近年来受到国内外学者的广泛关注。粒度转换技术与问题求解是进行多粒度计算的关键，然而代数商空间却缺乏对这两个重要问题的讨论。为此，针对代数商空间模型，首先，根据商空间的构造方法定义三种完备的代数商空间簇，以论证代数粒度转换的封闭性。在上述工作基础上，针对不同的粒化准则与粒化方式，从多角度给出完整的代数粒度转换方法，并详细讨论了不同转换方法的异同以及粒度转换结果之间的关系。其次，为描述代数问题在粗细粒度转换中的求解结果，基于粒度转换方法与代数求解规则，提出求解一致性原理。通过理论分析证明了粒度转换方法与一致性原理的可靠性，以实例验证了所提方法的有效性，且实例结果与理论分析结论相符合，佐证了一致性原理的正确性；解决了使用代数商空间模型进行粒度计算的核心问题，为使用代数粒度计算求解大规模复杂问题提供了理论依据。

关键词: 粒度计算, 代数商空间, 多粒度, 粒度转换, 一致性

Abstract:

Granular computing is a problem processing paradigm based on multi-level structure, which has attracted extensive attention of domestic and foreign scholars in recent years. Granular transformation and problem solving are key issues of multi-granular computing. However, the algebraic quotient space model lacks discussion of these issues. In light of above problems, for the algebraic quotient space model, three complete clusters of algebraic quotient space are defined according to the algebraic quotient space construction methods, so as to analyze and demonstrate the closeness of granular conversion. Furthermore, for different granularity principles and modes, the complete algebraic granularity conversion methods are given from multiple angles. Next, the similarities and differences between different conversion methods and the relationship between granularity conversion results of the algebraic are discussed. In addition, in order to describe the solution results of algebraic problems after coarse grain and fine grain transformations, the consistency principle of solution results is proposed based on the granularity transformation method and algebraic solution rules. The reliability of the granularity conversion methods and the consistency principle is proven by theoretical analysis, and the effectiveness of the proposed methods is verified by an example. The example results are consistent with the theoretical analysis conclusions, which proves the correctness of the consistency principle. It solves the core problem of granular computing using algebraic quotient space model, and provides a theoretical basis for solving large-scale complex problems using algebraic granular computing.

Key words: granular computing, algebraic quotient space, multi-granularity, granularity conversion, consistency

中图分类号:

TP18

魏宗萱, 王加阳. 代数商空间粒度转换计算研究[J]. 计算机科学与探索, 2022, 16(12): 2870-2878.

WEI Zongxuan, WANG Jiayang. Research on Granular Conversion Computing in Algebraic Quotient Space[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(12): 2870-2878.

参考文献 21

[1]	YAO Y Y. Three perspectives of granular computing[J]. Journal of Nanchang Institute of Technology, 2006, 25(2): 16-21.
[2]	王国胤, 张清华, 胡军. 粒计算研究综述[J]. 智能系统学报, 2007, 2(6): 8-26.
	WANG G Y, ZHANG Q H, HU J. An overview of granular computing[J]. CAAI Transactions on Intelligent Systems, 2007, 2(6): 8-26.
[3]	苗夺谦, 张清华, 钱宇华, 等. 从人类智能到机器实现模型——粒计算理论与方法[J]. 智能系统学报, 2016, 11(6): 743-757.
	MIAO D Q, ZHANG Q H, QIAN Y H, et al. From human intelligence to machine implementation model: theories and applications based on granular computing[J]. CAAI Transactions on Intelligent Systems, 2016, 11(6): 743-757.
[4]	张铃, 张钹. 问题求解理论及应用: 商空间粒度计算理论及其应用[M]. 北京: 清华大学出版社, 2007: 4-106.
	ZHANG L, ZHANG B. Theory and applications of pro-blem solving: quotient space based granular computing[M]. Beijing: Tsinghua University Press, 2007: 4-106.
[5]	ORTHE Y A, ESCANDE A, YOSHIDA E. Quotient-space mo-tion planning[C]// Proceedings of the 2018 IEEE/RSJ Inter-national Conference on Intelligent Robots and Systems, Ma-drid, Oct 1-5, 2018. Piscataway: IEEE, 2018: 8089-8096.
[6]	刘利敏, 余洁, 李小娟, 等. 引入商空间粒度计算的全极化SAR影像分类[J]. 武汉大学学报(信息科学版), 2018, 43(1): 74-80.
	LIU L M, YU J, LI X J, et al. An improved full polarimetric SAR image classification method combining with granu-larity computing of quotient space theory[J]. Geomatics and Information Science of Wuhan University, 2018, 43(1): 74-80.
[7]	ZHAO T, WANG G Y, XIAO B. Image enhancement based on quotient space[C]// LNCS 8537: Proceedings of the 2nd International Conference on Rough Sets and Intelligent Sys-tems Paradigms, Granada and Madrid, Jul 9-13, 2014. Cham: Springer, 2014: 384-391.
[8]	XU G, WU R, WANG Q. Multi-granular angle description for plant leaf classification and retrieval based on quotient space[J]. Journal of Information Processing Systems, 2020, 16(3): 663-676.
[9]	ZHAO S H, SUN X, CHEN J, et al. Relational granulation me-thod based on quotient space theory for maximum flow pro-blem[J]. Information Sciences, 2020, 507: 472-484. DOI URL
[10]	LU J, QING J, HE H, et al. Classification algorithm of case retrieval based on granularity calculation of quotient space[J]. International Journal of Pattern Recognition and Artifi-cial Intelligence, 2020, 35(1): 2150003.
[11]	谢娟英, 鲁肖肖, 屈亚楠, 等. 粒计算优化初始聚类中心的K-medoids聚类算法[J]. 计算机科学与探索, 2015, 9(5): 611-620. DOI
	XIE J Y, LU X X, QU Y N, et al. K-medoids clustering al-gorithms with optimized initial seeds by granular compu-ting[J]. Journal of Frontiers of Computer Science and Tech-nology, 2015, 9(5): 611-620.
[12]	魏华珍, 赵姝, 陈洁, 等. 基于标签传播的大规模网络最大流求解方法[J]. 计算机科学与探索, 2017, 11(10): 1609-1620. DOI URL
	WEI H Z, ZHAO S, CHEN J, et al. Method of solving ma-ximum flow problem in large-scale network based on label propagation[J]. Journal of Frontiers of Computer Science and Technology, 2017, 11(10): 1609-1620.
[13]	陶永芹, 崔杜武. 基于动态模糊粒神经网络算法的负荷辨识[J]. 控制与决策, 2011, 26(4): 519-523.
	TAO Y Q, CUI D W. Load identification of algorithm based on dynamic fuzzy granular neural network[J]. Control and Decision, 2011, 26(4): 519-523.
[14]	张金凤, 李雪, 杨蕊, 等. 基于商空间和支持向量机的滚动轴承故障智能诊断[J]. 计量学报, 2020, 41(7): 835-841.
	ZHANG J F, LI X, YANG R, et al. Intelligent diagnosis for rolling bearing fault based on quotient space and support vector machine[J]. Acta Metrologica Sinica, 2020, 41(7): 835-841.
[15]	CZAJA L, WOLSKI M, GOMOLI A, et al. An incidence algebra approach to knowledge granulation in Pawlak infor-mation systems[J]. Fundamenta Informaticae, 2013, 128(1/2): 223-238. DOI URL
[16]	陈林书, 王加阳, 杨正华, 等. 基于代数结构的商空间模型研究[J]. 电子学报, 2016, 44(4): 952-958. DOI
	CHEN L S, WANG J Y, YANG Z H, et al. A study for quotient space model based on algebraic structure[J]. Acta Electronica Sinica, 2016, 44(4): 952-958.
[17]	王加阳, 杨正华. 两种结构的商空间模型比较研究[J]. 电子学报, 2013, 41(11): 2262-2269.
	WANG J Y, YANG Z H. A comparative study of quotient space model with two structures[J]. Acta Electronica Sinica, 2013, 41(11): 2262-2269.
[18]	CHEN L S, WANG J Y, LI L. The models of granular sys-tem and algebraic quotient space in granular computing[J]. Chinese Journal of Electronics, 2016, 25(6): 1109-1113. DOI URL
[19]	CHEN L S, WANG J Y. The rough representation and mea-surement of quotient structure in algebraic quotient space model[J]. High Technology Letters, 2017, 23(3): 293-297.
[20]	孙野, 王加阳, 张思同. 代数商空间的同余结构研究[J]. 电子学报, 2017, 45(10): 2434-2438. DOI
	SUN Y, WANG J Y, ZHANG S T. A study of congruence structurein algebraic quotient space[J]. Acta Electronica Sinica, 2017, 45(10): 2434-2438. DOI
[21]	CHEN L S, WANG J Y, WANG W C, et al. A new granular computing model based on algebraic structure[J]. Chinese Journal of Electronics, 2019, 28(1): 136-142. DOI

代数商空间粒度转换计算研究

Research on Granular Conversion Computing in Algebraic Quotient Space

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献 21

相关文章 15

编辑推荐

Metrics

[1]	李勇, 高灿, 刘子荣, 罗金涛. 动态一致自信的深度半监督学习[J]. 计算机科学与探索, 2022, 16(11): 2557-2564.
[2]	刘宇, 孟敏, 武继刚. 一致性约束的半监督多视图分类[J]. 计算机科学与探索, 2022, 16(1): 242-252.
[3]	吴将, 宋晶晶, 程富豪, 王平心, 杨习贝. 面向连续参数的多粒度属性约简方法研究[J]. 计算机科学与探索, 2021, 15(8): 1555-1562.
[4]	吕昊远, 俞璐, 周星宇, 邓祥. 半监督深度学习图像分类方法研究综述[J]. 计算机科学与探索, 2021, 15(6): 1038-1048.
[5]	陈洁, 刘洋, 赵姝, 张燕平. 利用多粒度属性网络表示学习进行引文推荐[J]. 计算机科学与探索, 2021, 15(6): 1103-1113.
[6]	辛利柯, 杨琬琪, 杨明. 基于判别稀疏性表示的不完整多视图分类[J]. 计算机科学与探索, 2021, 15(10): 1938-1948.
[7]	杨涵，秦克云. 面向属性（对象）多粒度概念格之间的关系[J]. 计算机科学与探索, 2020, 14(3): 527-533.
[8]	冯雅妮，蒋林，山蕊，刘阳，张园. 改进的阵列处理器数据Cache实时动态迁移机制[J]. 计算机科学与探索, 2020, 14(12): 2028-2038.
[9]	李彬，姜建国. 少数决：更安全的分布式一致性算法选举机制[J]. 计算机科学与探索, 2020, 14(10): 1693-1701.
[10]	孙文鑫，刘玉锋，卓春英. 程度多粒度软粗糙集模型[J]. 计算机科学与探索, 2019, 13(10): 1793-1800.
[11]	韩玮，孙永河. 多粒度拓展语言层级群组DEMATEL改进方法[J]. 计算机科学与探索, 2019, 13(1): 169-180.
[12]	郑海军，吴建国，刘政怡. 相似矩阵和聚类一致性的协同显著检测[J]. 计算机科学与探索, 2018, 12(9): 1454-1464.
[13]	陈家俊，徐华丽，魏赟. 多重代价多粒度决策粗糙集模型研究[J]. 计算机科学与探索, 2018, 12(5): 839-850.
[14]	张双越，蔡剑平，田丰，吴振强. 差分隐私下满足一致性的轨迹流量发布方法[J]. 计算机科学与探索, 2018, 12(12): 1903-1913.
[15]	佟威，和箫，卢英. 引入视觉显著性的多特征融合跟踪[J]. 计算机科学与探索, 2017, 11(3): 438-449.