Recent Advances and Prospects in Formal Concept Analysis (FCA)

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 10 June 2025 | Viewed by 624

Special Issue Editors


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Guest Editor
Department Teoría de Señal y Comunicaciones y Sistemas Telemáticos y Computación, University Rey Juan Carlos, Madrid, Spain
Interests: data mining; natural language processing; machine learning; information retrieval; information theory
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Guest Editor Assistant
Department de Matemática Aplicada, Universidad de Málaga, Andalucía Tech, 29071 Málaga, Spain
Interests: fuzzy set theory; formal concept analysis; non-classical logics

Special Issue Information

Dear Colleagues,

Formal Concept Analysis (FCA) was created in 1982 with the aim of re-activating, re-structuring, and finding applications for lattice theory. These past 40 years have accrued a wealth of results that highlight its fundamental role in making lattice theory ready to tackle mathematical, data, and social science applications. FCA has resulted in a mathematical framework to tackle data analysis and classification, as well as pattern mining in knowledge discovery, with a special emphasis on visualization and interaction with data and patterns, aside from the purely mathematical contributions to restructuring lattice theory.

This Special Issue aims to highlight contributions and recent advances to FCA in general, including, but not limited to, its foundations, applications, and methodologies. Prospective and historical papers from well-established researchers in the field are also welcome, provided they offer new insights into FCA overall. Review papers are not encouraged for this Special Issue.

We are pleased to invite you to submit original, unpublished, and highly-relevant contributions to be published in this Special Issue that reflect new results, ideas, and directions in the further development of FCA in any of its kinds. Innovative cases of data analysis and application are also welcome if they provide and highlight methodological, foundational, or otherwise highly relevant issues to FCA.

Research areas may include (but need not be limited to) the following:

  • FCA foundations;
  • FCA variants, including FCA in a fuzzy setting, FCA over idempotent semifields, Logical Concept Analysis, Relational Concept Analysis, Pattern Structures, etc.;
  • FCA in data modelling and analysis;
  • FCA in computational intelligence, including machine learning and artificial intelligence.

We look forward to receiving your contributions.

Dr. Francisco J. Valverde-Albacete
Guest Editor

Dr. Manuel Ojeda-Hernández
Guest Editor Assistant

Manuscript Submission Information

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Keywords

  • formal concept analysis
  • FCA-enabled data analysis using FCA
  • FCA-enabled machine learning and artificial intelligence
  • FCA-enabled data modelling

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Published Papers (1 paper)

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27 pages, 577 KiB  
Article
Approximate Description of Indefinable Granules Based on Classical and Three-Way Concept Lattices
by Hongwei Wang, Huilai Zhi and Yinan Li
Mathematics 2025, 13(4), 672; https://doi.org/10.3390/math13040672 - 18 Feb 2025
Viewed by 383
Abstract
Granule description is a fundamental problem in granular computing. However, how to describe indefinable granules is still an open, interesting, and important problem. The main objective of this paper is to give a preliminary solution to this problem. Before proceeding, the framework of [...] Read more.
Granule description is a fundamental problem in granular computing. However, how to describe indefinable granules is still an open, interesting, and important problem. The main objective of this paper is to give a preliminary solution to this problem. Before proceeding, the framework of approximate description is introduced. That is, any indefinable granule is characterized by an ordered pair of formulas, which form an interval set, where the first formula is the β-prior approximate optimal description and the second formula is the α-prior approximate optimal description. More concretely, given an indefinable granule, by exploring the description of its lower approximate granule, its β-prior approximate optimal description is obtained. Likewise, by consulting the description of its upper approximate granule, its α-prior approximate optimal description can also be derived. Following this idea, the descriptions of indefinable granules are investigated. Firstly, ∧-approximate descriptions of indefinable granules are investigated based on the classical concept lattice, and (,)-approximate descriptions of indefinable granules are given via object pictorial diagrams. And then, it is revealed from some examples that the classical concept lattice is no longer effective and negative attributes must be taken into consideration. Therefore, a three-way concept lattice is adopted instead of the classical concept lattice to study (,¬)-approximate descriptions and (,,¬)-approximate descriptions of indefinable granules. Finally, some discussions are presented to show the differences and similarities between our study and existing ones. Full article
(This article belongs to the Special Issue Recent Advances and Prospects in Formal Concept Analysis (FCA))
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