Research of Inference Rules on Decision Implication and Variable Decision Implication

doi:10.3778/j.issn.1673-9418.2104118

Journal of Frontiers of Computer Science and Technology ›› 2022, Vol. 16 ›› Issue (10): 2357-2364.DOI: 10.3778/j.issn.1673-9418.2104118

• Artificial Intelligence • Previous Articles Next Articles

Research of Inference Rules on Decision Implication and Variable Decision Implication

XUE Dongqian¹, ZHAI Yanhui¹^,²^,⁺(), ZHANG Shaoxia¹, LI Deyu¹^,², XU Weihua³

1. School of Computer and Information Technology, Shanxi University, Taiyuan 030006, China
2. Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan 030006, China
3. School of Artificial Intelligence, Southwest University, Chongqing 400715, China

Received:2021-04-12 Revised:2021-05-25 Online:2022-10-01 Published:2021-05-31
About author:XUE Dongqian, born in 1997, M.S. His research interests include data mining and intelligent decision.
ZHAI Yanhui, born in 1981, associate professor, Ph.D. supervisor, member of CCF. His research interests include concept lattice and rough set.
ZHANG Shaoxia, born in 1991, Ph.D. Her research interest is concept lattice.
LI Deyu, born in 1965, professor, Ph.D. supervisor, senior member of CCF. His research interests include rough set, multi-label learning, etc.
XU Weihua, born in 1979, professor, Ph.D. supervisor. His research interests include rough set, concept lattice, etc.
Supported by:
National Natural Science Foundation of China(61972238);National Natural Science Foundation of China(62072294);National Natural Science Foundation of China(61806116)

决策蕴涵与可变决策蕴涵上的推理规则研究

薛东前¹, 翟岩慧¹^,²^,⁺(), 张少霞¹, 李德玉¹^,², 徐伟华³

1.山西大学计算机与信息技术学院,太原 030006
2.山西大学计算智能与中文信息处理教育部重点实验室,太原 030006
3.西南大学人工智能学院,重庆 400715

通讯作者: + E-mail: chai_yanhui@163.com
作者简介:薛东前（1997—）,男,山西运城人,硕士,主要研究方向为数据挖掘、智能决策。
翟岩慧（1981—）,男,山西文水人,副教授,博士生导师,CCF会员,主要研究方向为概念格、粗糙集。
张少霞（1991—）,女,山西浑源人,博士,主要研究方向为概念格。
李德玉（1965—）,男,山西临汾人,教授,博士生导师,CCF高级会员,主要研究方向为粗糙集、多标签学习等。
徐伟华（1979—）,男,山西浑源人,教授,博士生导师,主要研究方向为粗糙集、概念格等。
基金资助:
国家自然科学基金(61972238);国家自然科学基金(62072294);国家自然科学基金(61806116)

Abstract

Abstract:

Formal concept analysis is a data analysis method based on concept lattice, while decision implication and variable decision implication are two decision knowledge representations of formal concept analysis. Both decision implication and variable decision implication have complete inference rules for knowledge reasoning. In order to further clarify the differences between variable decision implication and decision implication, this paper first eliminates uncertainty from variable decision implication and introduces restricted variable decision impli-cation. Then, based on the related research on variable decision implication, this paper presents semantic and syntactic characteristics of restricted variable decision implication. On this basis, a complete set of inference rules is obtained for restricted variable decision implication, and decision implication and restricted variable decision implication are compared from the syntactic perspective. Besides, this paper further discusses the differences between the two decision types in knowledge representation and reasoning from the semantic perspective, and summarizes the characteristics of restricted variable decision implication relative to decision implication from the semantic and syntactic perspectives. These conclusions provide new ideas for comparative research of different decision types such as decision implication, variable decision implication, and fuzzy decision implication, as well as a new perspective for introducing more efficient and concise inference rules.

Key words: formal concept analysis, variable decision implication, inference rules, knowledge reasoning ability, knowledge representation

摘要：

形式概念分析是一种基于概念格的数据分析方法,决策蕴涵和可变决策蕴涵是形式概念分析的两种决策知识表示类型。决策蕴涵和可变决策蕴涵上已有完备的推理规则集。为了进一步厘清可变决策蕴涵和决策蕴涵在推理规则上的区别,首先对可变决策蕴涵进行不确定性剥离并提出了受限可变决策蕴涵,然后基于可变决策蕴涵的相关研究给出了受限可变决策蕴涵的语义特征和语构特征;在此基础上,得出了受限决策蕴涵的完备推理规则集,并且从语构角度比较了受限可变决策蕴涵和决策蕴涵;基于此,从语义角度得出了这两种决策类型在知识推理能力和知识表示形式上的差异,并从语义和语构角度总结了受限可变决策蕴涵相对于决策蕴涵所具有的特征。该研究为决策蕴涵、可变决策蕴涵和模糊决策蕴涵等不同决策类型的比较性研究提供了新的思路,为决策蕴涵更为高效、简洁的推理规则提供新的视角。

关键词: 形式概念分析, 可变决策蕴涵, 推理规则, 知识推理能力, 知识表示形式

CLC Number:

TP18

XUE Dongqian, ZHAI Yanhui, ZHANG Shaoxia, LI Deyu, XU Weihua. Research of Inference Rules on Decision Implication and Variable Decision Implication[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(10): 2357-2364.

薛东前, 翟岩慧, 张少霞, 李德玉, 徐伟华. 决策蕴涵与可变决策蕴涵上的推理规则研究[J]. 计算机科学与探索, 2022, 16(10): 2357-2364.

References 25

[1]	GANTER B, WILLE R. Formal concept analysis: mathe-matical foundations[M]. Berlin, Heidelberg: Springer, 1999.
[2]	WILLE R. Restructuring lattice theory: an approach based on hierarchies of concepts[C]// LNCS 5548: Proceedings of the 7th International Conference on Formal Concept Analysis, Darmstadt, May 21-24, 2009. Berlin, Heidelberg: Springer, 2009: 314-339.
[3]	李金海, 魏玲, 张卓, 等. 概念格理论与方法及其研究展望[J]. 模式识别与人工智能, 2020, 33(7): 619-642. DOI
	LI J H, WEI L, ZHANG Z, et al. Concept lattice theory and method and their research prospect[J]. Pattern Recognition and Artificial Intelligence, 2020, 33(7): 619-642. DOI
[4]	TU X D, WANG Y L, ZHANG M L, et al. Using formal concept analysis to identify negative correlations in gene expression data[J]. IEEE/ACM Transactions on Computa-tional Biology and Bioinformatics, 2016, 13(2): 380-391.
[5]	ZOU C F, ZHANG D Q, WAN J F, et al. Using concept lattice for personalized recommendation system design[J]. IEEE Systems Journal, 2017, 11(1): 305-314. DOI URL
[6]	QIN K Y, LI B, PEI Z. Attribute reduction and rule acqui-sition of formal decision context based on object (property) oriented concept lattices[J]. International Journal of Machine Learning and Cybernetics, 2019, 10(10): 2837-2850. DOI URL
[7]	CORNEJO M E, MEDINA J, RAMÍREZ-POUSSA E. Attri-bute and size reduction mechanisms in multi-adjoint concept lattices[J]. Journal of Computational and Applied Mathem-atics, 2017, 318: 388-402.
[8]	REN R S, WEI L. The attribute reductions of three-way con-cept lattices[J]. Knowledge Based Systems, 2016, 99: 92-102. DOI URL
[9]	ZHAI Y H, LI D Y. Knowledge structure preserving fuzzy attribute reduction in fuzzy formal context[J]. International Journal of Approximate Reasoning, 2019, 115: 209-220. DOI URL
[10]	LI J H, KUMAR C A, MEI C L, et al. Comparison of reduction in formal decision contexts[J]. International Journal of Approximate Reasoning, 2017, 80: 100-122. DOI URL
[11]	SHAO M W, LI K W. Attribute reduction in generalized one-sided formal contexts[J]. Information Sciences, 2016, 378: 317-327. DOI URL
[12]	LI J H, MEI C L, XU W H, et al. Concept learning via granular computing: a cognitive viewpoint[J]. Information Sciences, 2015, 298: 447-467. DOI PMID
[13]	SHI Y, MI Y L, LI J H, et al. Concept-cognitive learning model for incremental concept learning[J]. IEEE Transac-tions on Systems, Man, and Cybernetics: Systems, 2021, 51(2): 809-821.
[14]	李金海, 米允龙, 刘文奇. 概念的渐进式认知理论与方法[J]. 计算机学报, 2019, 42(10): 2233-2250.
	LI J H, MI Y L, LIU W Q. Incremental cognition of concepts: theories and methods[J]. Chinese Journal of Com-puters, 2019, 42(10): 2233-2250.
[15]	LI J H, HUANG C C, QI J J, et al. Three-way cognitive concept learning via multi-granularity[J]. Information Scie-nces, 2017, 378: 244-263.
[16]	QU K S, ZHAI Y H, LIANG J Y. Study of decision implications based on formal concept analysis[J]. Internat-ional Journal of General Systems, 2007, 36(2): 147-156.
[17]	ZHAI Y H, LI D Y, QU K S. Decision implications: a logical point of view[J]. International Journal of Machine Learning and Cybernetics, 2014, 5(4): 509-516. DOI URL
[18]	贾楠, 张少霞, 翟岩慧, 等. 决策蕴涵上的推理规则和推理过程研究[J]. 计算机科学与探索, 2020, 14(2): 344-352. DOI
	JIA N, ZHANG S X, ZHAI Y H, et al. Study of inference rules and deduction process on decision implications[J]. Journal of Frontiers of Computer Science and Technology, 2020, 14(2): 344-352. DOI
[19]	ZAKI M J, OGIHARA M. Theoretical foundations of association rules[C]// Proceedings of the 3rd ACM SIGMOD Workshop on Research Issues in Data Mining and Know-ledge Discovery, Seattle, Jun 13, 1998. New York:ACM, 1998: 71-78.
[20]	ZAKI M J. Mining non-redundant association rules[J]. Data Mining and Knowledge Discovery, 2004, 9(3): 223-248. DOI URL
[21]	BALCÁZAR J L. Minimum-size bases of association rules[C]// LNCS 5211: Proceedings of the 2008 European Confe-rence on Machine Learning and Knowledge Discovery in Databases, Belgium, Sep 15-19, 2008. Berlin, Heidelberg: Springer, 2008: 86-101.
[22]	ZHAI Y H, LI D Y, ZHANG J. Variable decision know-ledge representation: a logical description[J]. Journal of Computational Science, 2018, 25: 161-169. DOI URL
[23]	ZHANG S X, LI D Y, ZHAI Y H, et al. A comparative study of decision implication, concept rule and granular rule[J]. Information Sciences, 2020, 508: 33-49. DOI URL
[24]	ZHAI Y H, LI D Y, QU K S. Fuzzy decision implications[J]. Knowledge-Based Systems, 2013, 37: 230-236. DOI URL
[25]	ZHAI Y H, LI D Y, QU K S. Fuzzy decision implication canonical basis[J]. International Journal of Machine Learn-ing and Cybernetics, 2018, 9(11): 1909-1917.

Research of Inference Rules on Decision Implication and Variable Decision Implication

决策蕴涵与可变决策蕴涵上的推理规则研究

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