Fuzzy Algebras of Concepts

 

Abstract

Preconcepts are basic units of knowledge that form the basis of formal concepts in formal concept analysis (FCA). This paper investigates the relations among different kinds of preconcepts, such as protoconcepts, meet and join-semiconcepts and formal concepts. The first contribution of this paper, is to present a fuzzy powerset lattice gradation, that coincides with the preconcept lattice at its 1-cut. The second and more significant contribution, is to introduce a preconcept algebra gradation that yields different algebras for protoconcepts, semiconcepts, and concepts at different cuts. This result reveals new insights into the structure and properties of the different categories of preconcepts.

Citation

Please, cite this work as:

[OLC23] M. Ojeda-Hernández, D. López-Rodríguez, and P. Cordero. “Fuzzy Algebras of Concepts”. In: Axioms 12.4 (2023). ISSN: 2075-1680. DOI: 10.3390/axioms12040324. URL: https://www.mdpi.com/2075-1680/12/4/324.

BibTeX

@Article{axioms12040324,
    AUTHOR = {Ojeda-Hernández, Manuel and López-Rodríguez, Domingo and Cordero, Pablo},
    TITLE = {Fuzzy Algebras of Concepts},
    JOURNAL = {Axioms},
    VOLUME = {12},
    YEAR = {2023},
    NUMBER = {4},
    ARTICLE-NUMBER = {324},
    URL = {https://www.mdpi.com/2075-1680/12/4/324},
    ISSN = {2075-1680},
    ABSTRACT = {Preconcepts are basic units of knowledge that form the basis of formal concepts in formal concept analysis (FCA). This paper investigates the relations among different kinds of preconcepts, such as protoconcepts, meet and join-semiconcepts and formal concepts. The first contribution of this paper, is to present a fuzzy powerset lattice gradation, that coincides with the preconcept lattice at its 1-cut. The second and more significant contribution, is to introduce a preconcept algebra gradation that yields different algebras for protoconcepts, semiconcepts, and concepts at different cuts. This result reveals new insights into the structure and properties of the different categories of preconcepts.},
    DOI = {10.3390/axioms12040324}
}

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