Minimal Generators from Positive and Negative Attributes: Analysing the Knowledge Space of a Mathematics Course

 

Abstract

Formal concept analysis is a data analysis framework based on lattice theory. In this paper, we analyse the use, inside this framework, of positive and negative (mixed) attributes of a dataset, which has proved to represent more information on the use of just positive attributes. From a theoretical point of view, in this paper we show the structure and the relationships between minimal generators of the simple and mixed concept lattices. From a practical point of view, the obtained theoretical results allow us to ensure a greater granularity in the retrieved information. Furthermore, due to the relationship between FCA and Knowledge Space theory, on a practical level, we analyse the marks of a Mathematics course to establish the knowledge structure of the course and determine the key items providing new relevant information that is not evident without the use of the proposed tools.

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Citation

Please, cite this work as:

[Oje+22] M. Ojeda-Hernández, F. Pérez-Gámez, D. López-Rodríguez, et al. “Minimal Generators from Positive and Negative Attributes: Analysing the Knowledge Space of a Mathematics Course”. In: Int. J. Comput. Intell. Syst. 15.1 (2022), p. 58. DOI: 10.1007/s44196-022-00123-3. URL: https://doi.org/10.1007/s44196-022-00123-3.

BibTeX

@article{MinGen-IJCIS,
     author = {Manuel Ojeda{-}Hernández and
     Francisco Pérez{-}Gámez and
     Domingo López{-}Rodríguez and
     Nicolás Madrid and
     Angel Mora},
     title = {Minimal Generators from Positive and Negative Attributes: Analysing
     the Knowledge Space of a Mathematics Course},
     journal = {Int. J. Comput. Intell. Syst.},
     volume = {15},
     number = {1},
     pages = {58},
     year = {2022},
     url = {https://doi.org/10.1007/s44196-022-00123-3},
     doi = {10.1007/s44196-022-00123-3},
     timestamp = {Mon, 15 Aug 2022 15:04:55 +0200},
     biburl = {https://dblp.org/rec/journals/ijcisys/Ojeda-Hernandez22.bib},
     bibsource = {dblp computer science bibliography, https://dblp.org}
}

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2

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2 Recent citations

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Papers citing this work

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[1] D. López-Rodríguez, M. Ojeda-Hernández, and C. Bejines. “New Simplification Rules for Databases with Positive and Negative Attributes”. In: Mathematics 13.2 (Jan. 2025), p. 309. ISSN: 2227-7390. DOI: 10.3390/math13020309. URL: http://dx.doi.org/10.3390/math13020309.

[2] D. López-Rodríguez, M. Ojeda-Hernández, and T. Pattison. “Systems of implications obtained using the Carve decomposition of a formal context”. In: Knowledge-Based Systems (Apr. 2025), p. 113475. ISSN: 0950-7051. DOI: 10.1016/j.knosys.2025.113475. URL: http://dx.doi.org/10.1016/j.knosys.2025.113475.