多尺度形式背景及其粗糙近似

doi:10.6040/j.issn.1671-9352.c.2020.001

摘要/Abstract

摘要： 首先提出一种新的多尺度形式背景的概念。在该背景中,随着尺度的变化,每一个属性所拥有对象呈现单调性的变化。其次,引入形式背景的粗糙近似概念,并讨论在多尺度形式背景下,不同尺度下近似集的关系。最后,在多尺度形式背景和决策多尺度形式背景下,通过借助信任函数和似然函数,研究它们在不同尺度下的关系,给出上、下近似协调集的定义。

关键词: 多尺度形式背景, 近似概念, 证据理论, 上、下近似

Abstract: Firstly, a kind of multi-scale formal context is proposed in this paper. In this context, with the change of scale, the objects owned by each attribute change monotonously. Furthermore, the concept of rough approximation in multi-scale formal context is introduced, and the relationship between approximation sets in different scales is discussed. Finally, the belief and plausibility functions from the evidence theory are employed to introduce the definitions of upper and lower approximate consistent sets in multi-scale formal context and multi-scale formal decision context.

Key words: multi-scale formal context, approximate concept, evidence theory, upper and lower approximation

中图分类号:

TP18

陈东晓,李进金,林荣德,陈应生. 多尺度形式背景及其粗糙近似[J]. 《山东大学学报(理学版)》, 2020, 55(5): 22-31.

CHEN Dong-xiao, LI Jin-jin, LIN Rong-de, CHEN Ying-sheng. Rough approximation in multi-scale formal context[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 22-31.

参考文献

[1] WILLE R. Restructuring lattice theory: an approach based on hierarchies of concepts[C] //Ordered Sets. Berlin: Springer, 1982: 445-470.
[2] 魏玲,祁建军,张文修. 决策形式背景的概念格属性约简[J].中国科学E辑:信息科学,2008, 38(2):195-208. WEI Ling, QI Jianjun, ZHANG Wenxiu. Attribute reduction theory of concept lattice based on decision formal contexts[J]. Science in China Series E: Information Science, 2008, 38(2):195-208.
[3] PAWLAK Z. Rough sets[J]. International Journal of Computer & Information Sciences, 1982, 11(5):341-356.
[4] YAO Yiyu. Concept lattices in rough set theory[C] //Proceedings of 2004 Annual Meeting of the North American Fuzzy Information Processing Society. Washington: IEEE, 2004: 796-801.
[5] DUNTSCH N, GEDIGA G. Modal-style operators in qualitative data analysis[C] //Proceedings of the 2002 IEEE International Conference on Data Mining. Washington: IEEE, 2002: 155-162.
[6] YAO Yiyu. Rough-set concept analysis: interpreting RS-definable concepts based on ideas from formal concept analysis[J]. Information Sciences, 2016, 346/347:442-462.
[7] QIAN Yuhua, LIANG Jiye, YAO Yiyu, et al. MGRS: a multi-granulation rough set[J]. Information Sciences, 2010, 180(6):949-970.
[8] WU Weizhi, LEUNG Yee. Theory and applications of granular labelled partitions in multi-scale decision tables[J]. Information Sciences, 2011, 181(18):3878-3897.
[9] WU Weizhi, LEUNG Yee. Optimal scale selection for multi-scale decision tables[J]. International Journal of Approximate Reasoning, 2013, 54(8):1107-1129.
[10] 吴伟志.多粒度粗糙集数据分析研究的回顾与展望[J].西北大学学报(自然科学版),2018, 48(4):501-512. WU Weizhi. Reviews and prospects on the study of multi-granularityrough set data analysis[J]. Journal of Northwest University(Natural Science Edition), 2018, 48(4):501-512.
[11] 吴伟志,高仓健,李同军.序粒度标记结构及其粗糙近似[J].计算机研究与发展,2014, 51(12):2623-2632. WU Weizhi, GAO Cangjian, LI Tongjun. Ordered granular labeled structures and rough approximations[J]. Journal of Computer Research and Development, 2014, 51(12):2623-2632.
[12] 吴伟志,杨丽,谭安辉,等. 广义不完备多粒度标记决策系统的粒度选择[J].计算机研究与发展,2018,55(6):149-158. WU Weizhi, YANG Li, TAN Anhui, et al. Granularity selections in generalized incomplete multi-granular labeled decision systems[J]. Journal of Computer Research and Development, 2018, 55(6):149-158.
[13] 吴伟志,庄宇斌,谭安辉,等.不协调广义多尺度决策系统的尺度组合[J].模式识别与人工智能,2018,31(6):485-494. WU Weizhi, ZHUANG Yubin, TAN Anhui, et al. Scale combinations in inconsistent generalized multi-scale decision systems[J]. Pattern Recognition and Artificial Intelligence, 2018, 31(6):485-494.
[14] 牛东苒,吴伟志,李同军.广义多尺度决策系统中基于可变精度的最优尺度组合[J].模式识别与人工智能,2019,32(11):965-974. NIU Dongran, WU Weizhi, LI Tongjun. Variable precision based optimal scale combinations in generalized multi-scale decision systems[J]. Pattern Recognition and Artificial Intelligence, 2019, 32(11): 965-974.
[15] 郝晨,范敏,李金海,等. 多标记背景下基于粒标记规则的最优标记选择[J]. 模式识别与人工智能, 2016, 29(3):272-280. HAO Chen, FAN Min, LI Jinhai, et al. Optimal scale selection in multi-scale contexts based on granular scale rules[J]. Pattern Recognition and Artificial Intelligence, 2016, 29(3):272-280.
[16] 李金海, 吴伟志, 邓硕.形式概念分析的多粒度标记理论[J].山东大学学报(理学版), 2019,54(2):30-40. LI Jinhai, WU Weizhi, DENG Shuo. Multi-scale theory in formal concept analysis[J]. Journal of Shandong University(Natural Science), 2019, 54(2):30-40.
[17] BELOHLAVEK R, BAETS B D, KONECNY J. Granularity of attributes in formal concept analysis[J]. Information Sciences, 2014, 260(1):149-170.
[18] SHE Yanhong, HE Xiaoli, QIAN Ting, et al. A theoretical study on object-oriented and property-oriented multi-scale formal concept analysis[J]. International Journal of Machine Learning and Cybernetics, 2019, 10(11):3263-3271.
[19] LI Feng, HU Baoqing, WANG Jun. Stepwise optimal scale selection for multi-scale decision tables via attribute significance[J]. Knowledge-Based Systems, 2017, 129:4-16.
[20] LI Lifeng. Multi-level interval-valued fuzzy concept lattices and their attribute reduction[J]. International Journal of Machine Learning and Cybernetics, 2017, 8(1):45-56.
[21] 张文修, 仇国芳.基于粗糙集的不确定决策[M].北京:清华大学出版社,2005. ZHANG Wenxiu, QIU Guofang. Uncertain decision making based on rough sets[M]. Beijing: Tsinghua University Press, 2005.
[22] DEMPSTER A P. Upper and lower probability inferences based on a sample from a finite univariate population[J]. Biometrika, 1967, 54(3/4):515-528.
[23] SHAFER G.A mathematical theory of evidence[M]. Princeton: Princeton University Press, 1976.
[24] SKOWRON A. The relationship between rough set theory and evidence theory[J]. Bulletin of Polish Academy of Science: Mathematics, 1989, 37(1):87-90.
[25] SKOWRON A. The rough sets theory and evidence theory[J]. Fundamenta Informaticae, 1990, 13(3):245-262.
[26] YAO Yiyu, LINGRAS P J. Interpretations of belief functions in the theory of rough sets[J].Information Sciences, 1998, 104(1/2):81-106.
[27] WU Weizhi, LEUNG Yee, ZHANG Wenxiu. Connections between rough set theory and Dempster-Shafer theory of evidence[J]. International Journal of General Systems, 2002, 31(4):405-430.
[28] CHEN Degan, LI Wanlu, ZHANG Xiao, et al. Evidence-theory-based numerical algorithms of attribute reduction with neighborhood-covering rough sets[J]. International Journal of Approximate Reasoning, 2014, 55(3): 908-923.
[29] 车晓雅,李磊军,米据生.基于证据理论刻画多粒度覆盖粗糙集的数值属性[J].智能系统学报,2016,11(4):481-486. CHE Xiaoya, LI Leijun, MI Jusheng. Evidence-theory-based numerical characterization of multi-granulation covering rough sets[J]. CAAI Transactions on Intelligent Systems, 2016, 11(4):481-486.
[30] 张燕兰,李长清. 基于证据理论的覆盖决策信息系统的属性约简[J]. 模式识别与人工智能, 2018, 31(9):27-38. ZHANG Yanlan, LI Changqing. Attribute reduction of covering decision information system based on evidence theory[J]. Pattern Recognition and Artificial Intelligence, 2018, 31(9):797-808.
[31] 张燕兰,李长清,许晴媛. 基于证据理论的覆盖决策信息系统约简的数值刻画[J].南京航空航天大学学报,2019, 51(5):599-608. ZHANG Yanlan, LI Changqing, XU Qingyuan. Evidence-theory-based numerical characterization of attribute reduction in covering decision information system[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2019, 51(5):599-608.

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