JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (9): 114-126.doi: 10.6040/j.issn.1671-9352.0.2022.504

Previous Articles    

Polytomous knowledge structure and learning path in formal context

Yujing LIN(),Jinjin LI*(),Huiqin CHEN   

  1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, Fujian, China
  • Received:2022-09-29 Online:2023-09-20 Published:2023-09-08
  • Contact: Jinjin LI E-mail:yujinglin_16@126.com;jinjinlimnu@126.com

RichHTML

1

PDF (PC)

282

Abstract:

Based on the polytomous evaluation system of problem solving, a method of formal concept analysis is employed to construct the polytomous knowledge structure, to find the learning path and to evaluate operation procedure, in order to effectively guide the learning of learners. Firstly, a method of constructing polytomous knowledge structure from the formal concept lattice of operation procedure is proposed. Secondly, the formal context of well-formed operating procedure is introduced, in which step-by-step learning and effective evaluation of operating procedures can be carried out. Finally, the algorithm steps to find the learning path under the disjunctive model are designed, and the effectiveness of the algorithm steps is illustrated with examples.

Key words: polytomous knowledge structure, operation procedure, formal context, learning path, operation procedure assessment

CLC Number: 

  • TP182

Fig.1

Hasse diagram of finite lattice $V$"

Fig.2

Problem level transition diagram of Example 3"

Table 1

The operation procedure formal context $\left(\mathit{\Omega}^{+}, S, \tau\right)$"

Ω+\S λ1 λ2 {λ1, λ2} λ1λ3
q1a 1 0 1 1
q1b 0 1 1 0
q1c 0 0 1 0
q21 1 0 1 1
q22 0 0 0 1

Fig.3

${ }_o L\left(\Omega^{+}, S, \tau\right)$"

Table 2

The operation procedure formal context $\left(\mathit{\Omega}^{+}, S, \tau\right)$ with $\nearrow$"

Ω+\S λ1 λ2 {λ1, λ2} λ1λ3
q1a $\nearrow$ 0 1 1
q1b 0 $\nearrow$ 1 0
q1c 0 0 $\nearrow$ 0
q21 $\nearrow$ 0 1 1
q22 0 0 0 $\nearrow$

Fig.4

Learning paths diagram for operation procedure set $S$"

Table 3

Operation procedure assessment of $\mathscr{K}$"

$\mathscr{K} \backslash S$ λ1 λ2 {λ1, λ2} λ1λ3
{q10, q20} × × × ×
{q1b, q20} × √ × ×
{q1a, q21} √ × × ×
{q1c, q21} √ √ √ ×
{q1a, q22} √ × × √
{q1c, q22} √ √ √ √
1 SCHREPP M . A generalization of knowledge space theory to problems with more than two answer alternatives[J]. Journal of Mathematical Psychology, 1997, 41 (3): 237- 243.
doi: 10.1006/jmps.1997.1169
2 BARTL E , BELOHLAVEK R . Knowledge spaces with graded knowledge states[J]. Information Sciences, 2011, 181 (8): 1426- 1439.
doi: 10.1016/j.ins.2010.11.040
3 STEFANUTTILl L , ANSELM P , DECHIUSOLE D , et al. On the polytomous generalization of knowledge space theory[J]. Journal of Mathematical Psychology, 2020, 94, 102306.
doi: 10.1016/j.jmp.2019.102306
4 HELLER J . Generalizing quasi-ordinal knowledge spaces to polytomous items[J]. Journal of Mathematical Psychology, 2021, 101, 102515.
doi: 10.1016/j.jmp.2021.102515
5 孙晓燕, 李进金. 技能映射通过析取模型诱导的多分知识结构[J/OL]. 华侨大学学报(自然科学版), 2022[2022-11-16]. http://kns.cnki.net/kcms/detail/35.1079.N.20220402.1013.002.html
SUN Xiaoyan, LI Jinjin. Polytomous knowledge structures delineated by skill map through disjunctive model[J/OL]. Journal of Huaqiao University(Natural Science), 2022[2022-11-16]. http://kns.cnki.net/kcms/detail/35.1079.N.20220402.1013.002.html.
6 孙晓燕, 李进金. 基于程序性知识学习的项目状态转移函数与多分知识结构[J]. 模式识别与人工智能, 2022, 35 (3): 223- 242.
SUN Xiaoyan , LI Jinjin . Item state transition functions and polytomous knowledge structures based on procedural knowledge learning[J]. Pattern Recognition and Artificial Intelligence, 2022, 35 (3): 223- 242.
7 WILLE R . Restructuring lattice theory: an approach based on hierarchies of concepts[J]. Lecture Notes in Computer Science, 2009, 5548 (1): 314- 339.
8 RUSCH A, WILLE R. Knowledge spaces and formal concept analysis[C]//BOCK H H, POLASEK W. Data Analysis and Information Systems. Berlin: Springer, 1996: 427- 436.
9 李进金, 孙文. 知识空间、形式背景和知识基[J]. 西北大学学报(自然科学版), 2019, 49 (4): 517- 526.
LI Jinjin , SUN Wen . Knowledge space, formal context and knowledge base[J]. Journal of Northwest University(Natural Science Edition), 2019, 49 (4): 517- 526.
10 DOIGNON J P , FALMAGNE J C . Learning spaces: interdisciplinary applied mathematics[M]. Berlin: Springer-Verlag, 2011.
11 冯丹露, 周银凤. 基于面向问题概念格的技能约简与推测关系[J]. 闽南师范大学学报(自然科学版), 2021, 34 (2): 36- 44.
FENG Danlu , ZHOU Yinfeng . Skill reduction and surmise relation based on object problem concept lattice[J]. Journal of Minnan Normal University(Natural Science), 2021, 34 (2): 36- 44.
12 周银凤, 李进金, 冯丹露, 等. 形式背景下的学习路径与技能评估[J]. 模式识别与人工智能, 2021, 34 (12): 1069- 1084.
ZHOU Yinfeng , LI Jinjin , FENG Danlu , et al. Learning paths and skills assessment in formal context[J]. Pattern Recognition and Artificial Intelligence, 2021, 34 (12): 1069- 1084.
13 BIRKHOFF G . Lattice theory[M]. New York: American Mathematical Society, 1967.
14 STEFANUTTI L . On the assessment of procedural knowledge: from problem spaces to knowledge spaces[J]. British Journal of Mathematical and Statistical Psychology, 2019, 72 (2): 185- 218.
doi: 10.1111/bmsp.12139
15 STEFANUTTI L , ALBERT D . Skill assessment in problem solving and simulated learning environments[J]. Journal of Universal Computer Science, 2003, 9 (12): 1455- 1468.
16 YAO Yiyu . A comparative study of formal concept analysis and rough sets theory in data analysis[J]. Lecture Notes in Computer Science, 2004, 3066 (1): 59- 68.
17 李进金, 李克典, 吴端恭. 基于粗糙集与概念格的知识系统模型[M]. 北京: 科学出版社, 2013: 24- 150.
LI Jinjin , LI Kedian , WU Duangong . Knowledge system model based on rough set and concept lattice[M]. Beijing: Science Press, 2013: 24- 150.
18 SUN Wen, LI Jinjin, LIN Fucai, et al. Constructing polytomous knowledge structures from fuzzy skills[J/OL]. Fuzzy Sets and Systems, 2022[2022-11-16]. https://doi.org/10.1016/j.fss.2022.09.003.
[1] FAN Min, LUO Shan, LI Jin-hai. Cognition of network concepts based on variable precision possibility operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(8): 1-12.
[2] Jing ZHANG,Jian-min MA. F-C variable threshold concept lattices based on dependence spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(1): 68-74.
[3] XIE Xiao-xian, LI Jin-jin, CHEN Dong-xiao, LIN Rong-de. Concept reduction of preserving binary relations based on Boolean matrix [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 32-45.
[4] 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.
[5] 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.
[6] 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.
[7] JI Ru-ya, WEI Ling, REN Rui-si, ZHAO Si-yu. Pythagorean fuzzy three-way concept lattice [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(11): 58-65.
[8] LI Jin-hai, WU Wei-zhi, DENG Shuo. Multi-scale theory in formal concept analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(2): 30-40.
[9] QIAN Ting, ZHAO Si-yu, HE Xiao-li. Rules acquisition of decision formal contexts based on attribute granular [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(10): 113-120.
[10] HUANG Tao-lin, NIU Jiao-jiao, LI Jin-hai. Reduct updating method in a dynamic formal context based on granular discernibility attribute matrix [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 13-21.
[11] LING Mi-ran, MI Ju-sheng, MA Li. Heterogeneous formal contexts for uncertainty reasoning [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(08): 28-32.
[12] WANG Bin-di, WEI Ling. The reduction theory of concept lattice based on its associated lattice [J]. J4, 2010, 45(9): 20-26.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] YANG Jun. Characterization and structural control of metalbased nanomaterials[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 1 -22 .
[2] DONG Wei-wei. A new method of DEA efficiency ranking for decision making units with independent subsystems[J]. J4, 2013, 48(1): 89 -92 .
[3] ZHANG Jing-you, ZHANG Pei-ai, ZHONG Hai-ping. The application of evolutionary graph theory in the design of knowledge-based enterprises’ organization strucure[J]. J4, 2013, 48(1): 107 -110 .
[4] MAO Ai-qin1,2, YANG Ming-jun2, 3, YU Hai-yun2, ZHANG Pin1, PAN Ren-ming1*. Study on thermal decomposition mechanism of  pentafluoroethane fire extinguishing agent[J]. J4, 2013, 48(1): 51 -55 .
[5] 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 .
[6] 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 .
[7] LUO Si-te, LU Li-qian, CUI Ruo-fei, ZHOU Wei-wei, LI Zeng-yong*. Monte-Carlo simulation of photons transmission at alcohol wavelength in  skin tissue and design of fiber optic probe[J]. J4, 2013, 48(1): 46 -50 .
[8] TIAN Xue-gang, WANG Shao-ying. Solutions to the operator equation AXB=C[J]. J4, 2010, 45(6): 74 -80 .
[9] HUO Yu-hong, JI Quan-bao. Synchronization analysis of oscillatory activities in a biological cell system[J]. J4, 2010, 45(6): 105 -110 .
[10] ZHAO Jun1, ZHAO Jing2, FAN Ting-jun1*, YUAN Wen-peng1,3, ZHANG Zheng1, CONG Ri-shan1. Purification and anti-tumor activity examination of water-soluble asterosaponin from Asterias rollestoni Bell[J]. J4, 2013, 48(1): 30 -35 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd