《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (11): 58-65.

• •

### 毕达哥拉斯模糊三支概念格

1. 1.西北大学数学学院, 陕西 西安 710127;2.西北大学概念、认知与智能研究中心, 陕西 西安 710127;3.咸阳师范学院数学与信息科学学院, 陕西 咸阳 712000
• 发布日期:2020-11-17
• 作者简介:姬儒雅(1995— ), 女, 硕士研究生, 研究方向为形式概念分析、粗糙集、粒计算等. E-mail:124988147@qq.com*通信作者简介:魏玲(1972— ), 女, 博士, 教授, 研究方向为形式概念分析、粗糙集、粒计算等. E-mail:wl@nwu.edu.cn
• 基金资助:
国家自然科学基金资助项目(61772021);陕西省教育厅科研计划资助项目(19JK0929)

### Pythagorean fuzzy three-way concept lattice

JI Ru-ya1,2, WEI Ling1,2*, REN Rui-si1,2, ZHAO Si-yu1,2,3

1. 1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China;
2. Institute of Concepts, Cognition and Intelligence, Northwest University, Xian 710127, Shaanxi, China;
3. College of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, Shaanxi, China
• Published:2020-11-17

Abstract: Pythagorean fuzzy set theory is introduced into fuzzy three-way concept lattice. The construction of Pythagorean fuzzy three-way concept lattice is studied under the Pythagorean fuzzy formal context. First, the relationships between objects and attributes are expressed by the membership degree and non-membership degree combined with the Pythagorean fuzzy set theory. On this foundation, the definition of the Pythagorean fuzzy formal context is given. Next, based on threshold α, β and the idea of three-way decision, the object sets(the attribute sets)are divided into three parts: positive region, negative region and boundary region. On this basis, the definitions and relevant theorems of two kinds of Pythagorean fuzzy three-way concepts(the object induced Pythagorean fuzzy three-way concept and the attribute induced Pythagorean fuzzy three-way concept)are given, and the corresponding Pythagorean fuzzy three-way concept lattices are constructed. Finally, the applications of Pythagorean fuzzy three-way concept lattice in real problems are explained in detail with examples.

• O29
 [1] YAO Yiyu. An outline of a theory of three-way decisions[C] //Proceedings of the 8th International Conference on Rough Sets and Current Trends in Computing. Berlin: Springer, 2012: 1-17.[2] 刘盾,李天瑞,李华雄.粗糙集理论:基于三支决策视角[J].南京大学学报(自然科学版), 2013, 49(5):574-581. LIU Dun, LI Tianrui, LI Huaxiong. Rough set theory: a three-way decisions perspective [J]. Journal of Nanjing University(Natural Sciences), 2013, 49(5):574-581.[3] YAO Yiyu. Granular computing and sequential three-way decisions[C] //Rough Sets and Knowledge Technology. Berlin: Springer, 2013: 16-27.[4] ZHANG Qinghua, LV Gongxun, CHEN Yuhong, et al. A dynamic three-way decision model based on the updating of attribute values[J]. Knowledge-Based Systems, 2017, 142:71-84.[5] MA Xi-ao, YAO Yiyu. Three-way decision perspectives on class-specific attribute reducts[J]. Information Sciences, 2018, 450:227-245.[6] WILLE R. Restructuring lattice theory: an approach based on hierarchies of concepts[J]. Orderd Sets D Reidel, 1982, 83:314-339.[7] GANTER B, WILLE R. Formal concept analysis: mathematical foundations[M]. New York: Springer Verlag, 1999.[8] 刘旭龙,洪文学,张涛.基于形式概念分析的中医辨证可视化方法[J].燕山大学学报, 2010, 34(2):162-168. LIU Xulong, HONG Wenxue, ZHANG Tao. TCM differentiation visualization methods based on formal concept analysis[J]. Journal of Yanshan University, 2010, 34(2):162-168.[9] MISSAOUI R, GODIN R, BOUJENOUI A. Extracting exact and approximate rules from databases[C] //Proceedings of SOFTEKS Workshop on Incompleteness and Uncertainty in Information Systems. Berlin: Springer, 1993: 209-222.[10] 郭显娥,王俊红.多维概念格与关联规则的发现[J].计算机应用,2010, 30(4):1072-1075. GUO Xiane, WANG Junhong. Multi-dimensional concept lattice and association rules discovery[J]. Journal of Computer Application, 2010, 30(4):1072-1075.[11] SUTTON A, MALETIC J I. Recovering UML class models from C++: a detailed explanation[J]. Information and Software Technology, 2007, 49(3):212-229.[12] GODIN R, MISSAOUI R. An incremental concept formation approach for learning from database[J]. Theoretical Computer Science, 1994, 133(2):387-419.[13] FREEMAN L, WHITE D. Using Galois lattices to represent network data[J]. Sociological Methodology, 1993, 23:127-146.[14] QI Jianjun, WEI Ling, YAO Yiyu. Three-way formal concept analysis[C] //International Conference on Rough Sets and Knowledge Technology. Berlin: Springer, 2014: 732-741.[15] QI Jianjun, QIAN Ting, WEI Ling. The connections between three-way and classical lattices[J]. Knowledge-Based Systems, 2016, 91:143-151.[16] 龙柄翰,徐伟华.模糊三支概念分析与模糊三支概念格[J].南京大学学报(自然科学版),2019,55(4):537-545. LONG Binghan, XU Weihua. Fuzzy three-way concept analysis and fuzzy three-way concept lattice[J]. Journal of Nanjing University(Natural Sciences), 2019, 55(4):537-545.[17] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-353.[18] YAGER R R. Pythagorean fuzzy subsets[C] //Proceedings Joint IFSA World Congress and NAFIPS Annual Meeting. Edmonton: IEEE, 2013: 7-61.[19] YAGER R R, ABBASOV A M. Pythagorean membership grades, complex numbers, and decision making[J]. International Journal of Intelligent Systems, 2013, 28(5):436-452.[20] YAGER R R. Pythagorean membership grades in multicriteria decision making[J]. IEEE Transactions on Fuzzy Systems, 2014, 22(4):958-965.[21] ZHANG Xiaolu, XU Zeshui. Extension of TOPSIS to multiple criteria decision making with pythagorean fuzzy sets[J]. International Journal of Intelligent Systems, 2014, 29(12):1061-1078.
 [1] 余鹰,吴新念,王乐为,张应龙. 基于标记相关性的多标记三支分类算法[J]. 《山东大学学报(理学版)》, 2020, 55(3): 81-88. [2] 刘国涛,张燕平,徐晨初. 一种优化覆盖中心的三支决策模型[J]. 山东大学学报（理学版）, 2017, 52(3): 105-110. [3] 张聪, 于洪. 一种三支决策软增量聚类算法[J]. 山东大学学报（理学版）, 2014, 49(08): 40-47. [4] 田海龙, 朱艳辉, 梁韬, 马进, 刘璟. 基于三支决策的中文微博观点句识别研究[J]. 山东大学学报（理学版）, 2014, 49(08): 58-65. [5] 杜丽娜, 徐久成, 刘洋洋, 孙林. 基于三支决策风险最小化的风险投资评估应用研究[J]. 山东大学学报（理学版）, 2014, 49(08): 66-72. [6] 张里博, 李华雄, 周献中, 黄兵. 人脸识别中的多粒度代价敏感三支决策[J]. 山东大学学报（理学版）, 2014, 49(08): 48-57.
Viewed
Full text

Abstract

Cited

Shared
Discussed