JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (3): 14-26.doi: 10.6040/j.issn.1671-9352.7.2023.9950

Previous Articles     Next Articles

Heuristic construction method of fuzzy concept set and its recommended application

Zhonghui LIU1(),Shuai JIANG1,Fan MIN1,2,*()   

  1. 1. School of Computer Science, Southwest Petroleum University, Chengdu 610500, Sichuan, China
    2. Institute for Artificial Intelligence, Southwest Petroleum University, Chengdu 610500, Sichuan, China
  • Received:2023-04-28 Online:2024-03-20 Published:2024-03-06
  • Contact: Fan MIN E-mail:lz_hui@126.com;minfan@swpu.edu.cn

RichHTML

1

PDF (PC)

172

Abstract:

Aiming at the problem that fuzzy formal concept analysis is difficult to apply to large-scale datasets in recommendation applications, a recommendation method based on a heuristic construction of fuzzy concept set is proposed. Sub-contexts are constructed for each user based on the similarity between users. Then, new heuristic information is used on the sub-contexts to generate fuzzy concepts with users and items as clues, respectively. Finally, using the internal information of fuzzy concepts, a recommendation confidence integrated with user weights is designed to achieve personalized recommendations for users. The experimental results on six real datasets show that the proposed method has higher recommendation efficiency, and can achieve better recommendation results on sparse data sets compared with classical collaborative filtering algorithms.

Key words: formal concept analysis, fuzzy concept, concept construction, recommender system, user similarity

CLC Number: 

  • TP181

Table 1

Main notations"

符号 含义 符号 含义
U 用户集 C 概念集合
M 属性集 Hu=(Uu, Mu, Ĩu) 用户u子背景
I 二元关系 D(u1, u2) 用户相似度
K=(U, M, I) 形式背景 S(c) 模糊概念大小
Ĩ 模糊关系 wc(u1, u2) 用户权重
H=(U, M, Ĩ) 模糊形式背景 Rc(u, m) 推荐置信度
μ(*) 隶属度 Au 用户u线索集合
φ(*) 模糊集 Bm 项目m线索集合
c=(φ(A), B) 模糊概念 L 推荐矩阵

Table 2

Formal context"

UM
m1 m2 m3 m4 m5
u1 1 1 1 0 0
u2 1 1 1 1 1
u3 1 0 1 0 1
u4 1 1 0 1 0
u5 0 0 1 0 0

Table 3

Fuzzy formal context"

UM
m1 m2 m3 m4 m5
u1 1.0 0.2 0.6 0.0 0.0
u2 0.8 0.4 0.8 0.6 0.8
u3 0.6 0.0 0.2 0.0 0.4
u4 0.6 0.2 0.0 0.6 0.0
u5 0.0 0.0 0.6 0.0 0.0

Table 4

The sub-background of u1"

Uu1Mu1
m1 m2 m3
u1 1.0 0.2 0.6
u2 0.8 0.4 0.8
u3 0.6 0.0 0.2
u4 0.6 0.2 0.0

Table 5

The process of concept generation by taking user as the clue under Hu1"

Au φ(Au**) Au* S(c)
{u1} {(u1, 0.2), (u2, 0.4)} {m1, m2, m3} 0.6
{u1, u2} {(u1, 0.2), (u2, 0.4)} {m1, m2, m3} 0.6
{u1, u2, u3} {(u1, 0.6), (u2, 0.8), (u3, 0.2)} {m1, m3} 0.9
{u1, u2, u3, u4} {(u1, 1.0), (u2, 0.8), (u3, 0.6), (u4, 0.6)} {m1} 0.7

Table 6

The process of concept generation by taking item as the clue under Hu1"

Bu φ(Bu*) Bu** S(c)
{m1} {(u1, 1.0), (u2, 0.8), (u3, 0.6), (u4, 0.6)} {m1} 0.7
{m1, m2} {(u1, 0.2), (u2, 0.4), (u4, 0.2)} {m1, m2} 0.9
{m1, m2, m3} {(u1, 0.2), (u2, 0.4)} {m1, m2, m3} 0.6

Table 7

Experimental datasets"

数据集 用户数 项目数 评分数 稠密度
movielens-100k 943 1 682 100 000 0.063 0
movielens-1m 6 040 3 952 1 000 000 0.041 9
eachmovie-2ku 2 000 1 628 38 571 0.011 8
eachmovie-3ku 3 000 1 628 59 247 0.012 1
filmtrust 1 508 2 071 35 497 0.011 3
jester-s 8 000 100 577 379 0.721 7

Fig.1

Influence of different θ on concept generation time and F1"

Fig.2

Influence of different α on F1"

Fig.3

Influence of different λ on F1"

Table 8

Comparison of RFCS recommendation effect with other algorithms"

数据集 算法 Pprecision Precall F1
movielens-100k RFCS 0.248 7 0.243 9 0.246 2
CSBR 0.192 5 0.239 3 0.213 2
kNN 0.199 4 0.344 2 0.252 5
IBCF 0.203 8 0.406 1 0.271 4
GreConD-kNN 0.199 6 0.342 4 0.252 1
NCF 0.194 6 0.335 2 0.246 1
movielens-1m RFCS 0.216 0 0.186 4 0.200 0
CSBR 0.142 1 0.204 0 0.167 6
kNN 0.188 3 0.339 0 0.242 0
IBCF 0.200 1 0.394 2 0.265 5
GreConD-kNN 0.188 5 0.338 0 0.242 1
NCF 0.139 5 0.359 3 0.200 8
eachmovie-2ku RFCS 0.223 6 0.251 8 0.236 8
CSBR 0.187 5 0.227 2 0.205 2
kNN 0.201 4 0.272 9 0.231 8
IBCF 0.148 6 0.352 0 0.208 9
GreConD-kNN 0.199 0 0.269 8 0.229 1
NCF 0.129 7 0.317 8 0.184 1
eachmovie-3ku RFCS 0.231 5 0.271 3 0.249 7
CSBR 0.203 0 0.236 2 0.218 3
kNN 0.112 3 0.276 8 0.159 6
IBCF 0.151 0 0.389 4 0.217 7
GreConD-kNN 0.104 3 0.247 8 0.146 6
NCF 0.131 9 0.363 2 0.193 4
filmtrust RFCS 0.486 2 0.477 6 0.481 4
CSBR 0.360 2 0.641 7 0.461 2
kNN 0.438 6 0.441 8 0.441 0
IBCF 0.182 6 0.532 8 0.271 7
GreConD-kNN 0.467 9 0.406 6 0.435 0
NCF 0.207 9 0.742 2 0.324 7
jester-s RFCS 0.714 8 0.846 9 0.775 3
CSBR 0.572 7 0.839 7 0.681 0
kNN 0.880 3 0.902 9 0.891 5
IBCF 0.891 0 0.851 7 0.870 9
GreConD-kNN 0.895 2 0.614 0 0.728 4
NCF 0.971 0 0.853 4 0.908 4
1 WILLE R. Restructuring lattice theory: an approach based on hierarchies of concepts[C]//Formal Concept Analysis: 7th International Conference. Berlin: Springer, 2009: 314-339.
2 KUZNETSOV S O. Machine learning and formal concept analysis[C]//Concept Lattices: Second International Conference on Formal Concept Analysis. Berlin: Springer, 2004: 287-312.
3 KANG Xiangping , LI Deyu , WANG Suge . A multi-instance ensemble learning model based on concept lattice[J]. Knowledge-Based Systems, 2011, 24 (8): 1203- 1213.
doi: 10.1016/j.knosys.2011.05.010
4 KUMAR C A . Fuzzy clustering-based formal concept analysis for association rules mining[J]. Applied Artificial Intelligence, 2012, 26 (3): 274- 301.
doi: 10.1080/08839514.2012.648457
5 TALLAM S , GUPTA N . A concept analysis inspired greedy algorithm for test suite minimization[J]. ACM SIGSOFT Software Engineering Notes, 2005, 31 (1): 35- 42.
6 ZOU Caifeng , ZHANG Daqiang , WAN Jiafu , et al. Using concept lattice for personalized recommendation system design[J]. IEEE Systems Journal, 2015, 11 (1): 305- 314.
7 陈昊文, 王黎明, 张卓. 基于概念邻域的Top-N推荐算法[J]. 小型微型计算机系统, 2017, 38 (11): 2553- 2559.
doi: 10.3969/j.issn.1000-1220.2017.11.025
CHEN Haowen , WANG Liming , ZHANG Zhuo . Top-N recommendation algorithm based on conceptual neighborhood[J]. Journal of Chinese Computer Systems, 2017, 38 (11): 2553- 2559.
doi: 10.3969/j.issn.1000-1220.2017.11.025
8 ZADEH L A . Fuzzy sets[J]. Information and Control, 1965, 8 (3): 338- 353.
doi: 10.1016/S0019-9958(65)90241-X
9 QUAN T T, HUI S C, CAO T H. A fuzzy FCA-based approach for citation-based document retrieval[C]//IEEE Conference on Cybernetics and Intelligent Systems, 2004. Piscataway: IEEE, 2004, 1: 578-583.
10 BURUSCO J A , FUENTES-GONZÁLEZ R . The study of the L-fuzzy concept lattice[J]. Mathware and Soft Computing, 1994, 1 (3): 209- 218.
11 刘宗田, 强宇, 周文, 等. 一种模糊概念格模型及其渐进式构造算法[J]. 计算机学报, 2007, 30 (2): 184- 188.
doi: 10.3321/j.issn:0254-4164.2007.02.004
LIU Zongtian , QIANG Yu , ZHOU Wen , et al. Fuzzy concept lattice model and its incremental construction algorithm[J]. Chinese Journal of Computers, 2007, 30 (2): 184- 188.
doi: 10.3321/j.issn:0254-4164.2007.02.004
12 KRAJCI S . Cluster based efficient generation of fuzzy concepts[J]. Neural Network World, 2003, 13 (5): 521- 530.
13 YAHIA S B , AROUR K , SLIMANI A , et al. Discovery of compact rules in relational databases[J]. Information Science Journal, 2000, 4 (3): 497- 511.
14 ZHANG Wenxiu , MA Jianmin , FAN Shiqing . Variable threshold concept lattices[J]. Information Sciences, 2007, 177 (22): 4883- 4892.
doi: 10.1016/j.ins.2007.05.031
15 BOFFA S, DE MAIO C, DI NOLA A, et al. Unifying fuzzy concept lattice construction methods[C]//2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). Piscataway: IEEE, 2016: 209-216.
16 SHAO Mingwen , LEUNG Y , WANG Xizhao , et al. Granular reducts of formal fuzzy contexts[J]. Knowledge-Based Systems, 2016, 114, 156- 166.
doi: 10.1016/j.knosys.2016.10.010
17 MI Yunlong , SHI Yong , LI Jinhai , et al. Fuzzy-based concept learning method: exploiting data with fuzzy conceptual clustering[J]. IEEE Transactions on Cybernetics, 2020, 52 (1): 582- 593.
18 XU Weihua , GUO Doudou , QIAN Yuhua , et al. Two-way concept-cognitive learning method: a fuzzy-based progressive learning[J]. IEEE Transactions on Fuzzy Systems, 2022, 31 (6): 1- 15.
19 SINGH P K , KUMAR C A , LI Jinhai . Knowledge representation using interval-valued fuzzy formal concept lattice[J]. Soft Computing, 2016, 20, 1485- 1502.
doi: 10.1007/s00500-015-1600-1
20 FANG Peici, ZHENG Siyao. A research on fuzzy formal concept analysis based collaborative filtering recommendation system[C]//2009 Second International Symposium on Knowledge Acquisition and Modeling. Piscataway: IEEE, 2009: 352-355.
21 张喜征, 蔡月月, 罗文. 基于模糊概念格的领先用户个性化知识推荐研究[J]. 科技管理研究, 2019, 39 (7): 183- 189.
ZHANG Xizheng , CAI Yueyue , LUO Wen . Research on personalized knowledge recommendation for leading users based on fuzzy concept lattice in innovation community[J]. Science and Technology Management Research, 2019, 39 (7): 183- 189.
22 LIU Zhonghui , ZHAO Qi , ZOU Lu , et al. A heuristic concept construction approach to collaborative recommendation[J]. International Journal of Approximate Reasoning, 2022, 146, 119- 132.
doi: 10.1016/j.ijar.2022.04.004
23 GANTER B , WILLE R . Formal concept analysis: mathematical foundations[M]. Berlin: Springer, 1999.
24 ZADEH L A . Fuzzy sets and information granularity[M]. Amsterdam: World Scientific Publisher, 1979.
25 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.
LI Jinhai , WEI Ling , ZHANG Zhuo , et al. Concept lattice theory and method and their research prospect[J]. Pattern Recognition and Artificial Intelligence, 2020, 33 (7): 619- 642.
26 POELMANS J , IGNATOV D I , KUZNETSOV S O , et al. Fuzzy and rough formal concept analysis: a survey[J]. International Journal of General Systems, 2014, 43 (2): 105- 134.
doi: 10.1080/03081079.2013.862377
27 于蒙, 何文涛, 周绪川, 等. 推荐系统综述[J]. 计算机应用, 2022, 42 (6): 1898- 1913.
YU Meng , HE Wentao , ZHOU Xuchuan , et al. Review of recommendation system[J]. Journal of Computer Applications, 2022, 42 (6): 1898- 1913.
28 BOUCHER-RYAN P D , BRIDGE D . Collaborative recommending using formal concept analysis[J]. Knowledge-Based Systems, 2006, 19 (5): 309- 315.
doi: 10.1016/j.knosys.2005.11.017
29 朵琳, 杨丙. 一种基于用户兴趣概念格的推荐评分预测方法[J]. 小型微型计算机系统, 2020, 41 (10): 2104- 2108.
DUO Lin , YANG Bing . Recommendation rating prediction based on user interest concept lattice[J]. Journal of Chinese Computer Systems, 2020, 41 (10): 2104- 2108.
30 MEZNI H , ABDELJAOUED T . A cloud services recommendation system based on fuzzy formal concept analysis[J]. Data & Knowledge Engineering, 2018, 116, 100- 123.
31 KUMAR C A , SINGH P K . Knowledge representation using formal concept analysis: a study on concept generation[M]. Hershey: IGI Global, 2014: 306- 336.
32 HARPER F M , KONSTAN J A . The movielens datasets: history and context[J]. ACM Transactions on Interactive Intelligent Systems, 2015, 5 (4): 1- 19.
33 PHUONG N D, PHUONG T M. Collaborative filtering by multi-task learning[C]//2008 IEEE International Conference on Research, Innovation and Vision for the Future in Computing and Communication Technologies. Piscataway: IEEE, 2008: 227-232.
34 GUO Guibing, ZHANG Jie, YORKE-SMITH N. A novel Bayesian similarity measure for recommender systems[C]//Proceedings of the Twenty-third International Joint Conference on Artificial Intelligence. Menlo Park: AAAI Press, 2013: 2619-2625.
35 GOLDBERG K , ROEDER T , GUPTA D , et al. Eigentaste: a constant time collaborative filtering algorithm[J]. Information Retrieval, 2001, 4, 133- 151.
36 IGNATOV D I, NENOVA E, KONSTANTINOVA N, et al. Boolean matrix factorisation for collaborative filtering: an FCA-based approach[C]//International Conference on Artificial Intelligence: Methodology, Systems, and Applications. Cham: Springer, 2014: 47-58.
37 HE Xiangnan, LIAO Lizi, ZHANG Hanwang, et al. Neural collaborative filtering[C]//Proceedings of the 26th International Conference on World Wide Web. Republic and Canton of Geneva: International World Wide Web Conferences Steering Committee, 2017: 173-182.
[1] HAN Pei-lei, WEI Ling, WANG Zhen, ZHAO Si-yu. Complementary concepts and their properties and generation in FCA [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(8): 60-67.
[2] Jie TANG,Ling WEI,Rui-si REN,Si-yu ZHAO. Granule description using possible attribute analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(1): 75-82.
[3] LI Jin-hai, HE Jian-jun, WU Wei-zhi. Optimization of class-attribute block in multi-granularity formal concept analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 1-12.
[4] LI Shuang-ling, YUE Xiao-wei, QIN Ke-yun. Granular structure in multi-source formal contexts [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 46-54.
[5] LIU Ying-ying, MI Ju-sheng, LIANG Mei-she, LI Lei-jun. Three-way interval-set concept lattice [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(3): 70-80.
[6] LI Jin-hai, WU Wei-zhi. Granular computing approach for formal concept analysis and its research outlooks [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 1-12.
[7] DENG Xiao-fang, ZHONG Yuan-sheng, L(¨overU)Lin-yuan, WANG Ming-wen, XIONG Nai-xue. Mass diffusion on coupled social networks [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(3): 51-59.
[8] HUANG Shu-qin, XU Yong, WANG Ping-shui. User similarity calculation method based on probabilistic matrix factorization and its recommendation application [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 37-43.
[9] AN Qiu-sheng, KONG Xiang-yu. New research of functional dependency and multi-valued dependency [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(08): 1-5.
[10] TANG Ya-qiang, FAN Min, LI Jin-hai. Cognitive system model and approach to transformation of information granules under triadic formal concept analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(08): 102-106.
[11] SUN Jing-yu, CHEN Jun-jie*, YU Xue-li, HE Xiu. A model for CBR-based collaborative Web search and its applications [J]. J4, 2012, 47(5): 19-24.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] HUO Yu-hong, JI Quan-bao. Synchronization analysis of oscillatory activities in a biological cell system[J]. J4, 2010, 45(6): 105 -110 .
[2] SHI Chang-guang . Multi-soliton solution of the Faddeev model[J]. J4, 2007, 42(7): 38 -40 .
[3] MA Jie-xiong,JIANG Li,QI Yu-yu,XIANG FEng-ning,XIA Guang-min . The growth of calli and regenerated plantlets of Gentiana Przewalskii Maxim. and the constituents analysis of its two effective components[J]. J4, 2006, 41(6): 157 -160 .
[4] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors[J]. J4, 2013, 48(1): 83 -88 .
[5] DONG Li-hong1,2, GUO Shuang-jian1. The fundamental theorem for weak Hopf module in  Yetter-Drinfeld module categories[J]. J4, 2013, 48(2): 20 -22 .
[6] CHENG Li-qing1,2, SHI Qiao-lian2. A new hybrid conjugate gradient method[J]. J4, 2010, 45(6): 81 -85 .
[7] WANG Kang, LI Hua. Analysis of the compound Haqing injection with hyphenated chromatography and chemometric resolution[J]. J4, 2009, 44(11): 16 -20 .
[8] CHEN Li, . Singular LQ suboptimal control problem with disturbance rejection[J]. J4, 2006, 41(2): 74 -77 .
[9] CHENG Zhi1,2, SUN Cui-fang2, WANG Ning1, DU Xian-neng1. On the fibre product of Zn and its property[J]. J4, 2013, 48(2): 15 -19 .
[10] ZHANG Ai-ping,LI Gang . LRquasinormalEhresmann semigroups[J]. J4, 2006, 41(5): 44 -47 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd