Probabilistic normalization conditions of polytomous knowledge structures
Constructing a probability distribution of knowledge states reasonably is a fundamental and important issue in dichotomous probabilistic knowledge structure (PKS). Recently, the dichotomous knowledge structure has been extended to the polytomous knowledge structure, but the establishment of the prob...
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| Published in | Communications in statistics. Theory and methods Vol. 54; no. 15; pp. 4877 - 4895 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis
03.08.2025
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0361-0926 1532-415X |
| DOI | 10.1080/03610926.2024.2430735 |
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| Abstract | Constructing a probability distribution of knowledge states reasonably is a fundamental and important issue in dichotomous probabilistic knowledge structure (PKS). Recently, the dichotomous knowledge structure has been extended to the polytomous knowledge structure, but the establishment of the probability distribution of the polytomous knowledge state has not yet been constructed. So it is necessary to find the relevant definition and normalization conditions for its establishment. To this end, this article builds two appropriate probability definitions of the polytomous knowledge state from different perspectives, and proves the equivalence of the two definitions. In addition, we obtain the probabilistic normalization conditions for the polytomous knowledge structure
(
Q
,
L
,
K
)
, where
(
L
,
≤
)
is a linear order and supply some examples. The results generalize the according conclusions of the dichotomous knowledge states of learning space. Moreover, such findings provide the way for the construction of a number of probabilistic models with polytomous data for the applications of knowledge structure theory (KST). |
|---|---|
| AbstractList | Constructing a probability distribution of knowledge states reasonably is a fundamental and important issue in dichotomous probabilistic knowledge structure (PKS). Recently, the dichotomous knowledge structure has been extended to the polytomous knowledge structure, but the establishment of the probability distribution of the polytomous knowledge state has not yet been constructed. So it is necessary to find the relevant definition and normalization conditions for its establishment. To this end, this article builds two appropriate probability definitions of the polytomous knowledge state from different perspectives, and proves the equivalence of the two definitions. In addition, we obtain the probabilistic normalization conditions for the polytomous knowledge structure
(
Q
,
L
,
K
)
, where
(
L
,
≤
)
is a linear order and supply some examples. The results generalize the according conclusions of the dichotomous knowledge states of learning space. Moreover, such findings provide the way for the construction of a number of probabilistic models with polytomous data for the applications of knowledge structure theory (KST). |
| Author | Wang, Bo Chen, Zhuoheng Xu, Bochi Li, Jinjin |
| Author_xml | – sequence: 1 givenname: Zhuoheng surname: Chen fullname: Chen, Zhuoheng organization: School of Mathematical Science, Huaqiao University – sequence: 2 givenname: Jinjin surname: Li fullname: Li, Jinjin organization: School of Mathematics and Statistics, Minnan Normal University – sequence: 3 givenname: Bo surname: Wang fullname: Wang, Bo organization: School of Mathematical Science, Huaqiao University – sequence: 4 givenname: Bochi surname: Xu fullname: Xu, Bochi organization: School of Mathematical Science, Huaqiao University |
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| Cites_doi | 10.1017/CBO9780511805967 10.1016/j.jmp.2006.07.003 10.1007/978-3-642-58625-5 10.1037/met0000050 10.1016/j.jmp.2020.102451 10.1111/j.1745-3984.2010.00119.x 10.1016/S0020-7373(85)80031-6 10.1007/s11336-020-09722-5 10.1016/j.jmp.2023.102770 10.1016/j.jmp.2021.102549 10.1111/j.2044-8317.1988.tb00884.x 10.1016/j.jmp.2021.102542 10.1016/j.endm.2013.05.144 10.1007/s11336-018-9645-6 10.3233/JIFS-212018 10.1016/0022-2496(88)90011-9 10.1007/978-1-4612-4308-3_6 10.1007/978-3-642-01039-2 10.1111/bmsp.12095 10.1016/j.jmp.2019.102306 10.1016/j.jmp.2021.102552 10.1007/s11336-015-9457-x 10.1016/j.jmp.2021.102515 10.1561/2000000043 10.1006/jmps.1997.1169 10.1111/bmsp.12283 10.3758/s13428-010-0036-x 10.1016/j.fss.2023.108540 10.1016/j.fss.2020.10.004 |
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| SubjectTerms | master fringe neighboring polytomous knowledge state polytomous knowledge state Probabilistic knowledge structure probabilistic normalization conditions well-graded |
| Title | Probabilistic normalization conditions of polytomous knowledge structures |
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