Fuzzy closure systems: Motivation, definition and properties

 

Abstract

The aim of this paper is to extend closure systems from being crisp sets with certain fuzzy properties to proper fuzzy sets. The presentation of the paper shows a thorough discussion on the different alternatives that could be taken to define the desired fuzzy closure systems. These plausible alternatives are discarded if they are proven impossible to be in a bijective correspondence with closure operators. Finally, a definition of fuzzy closure system is established and a one-to-one relation with closure operators is proved.

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Citation

Please, cite this work as:

[Oje+22] M. Ojeda-Hern’ndez, I. P. Cabrera, P. Cordero, et al. “Fuzzy closure systems: Motivation, definition and properties”. In: International Journal of Approximate Reasoning 148 (2022). Cited by: 4; All Open Access, Green Open Access, Hybrid Gold Open Access, p. 151 – 161. DOI: 10.1016/j.ijar.2022.06.004. URL: [https://www.scopus.com/inward/record.uri?eid=2-s2.0-85132519163&doi=10.1016

BibTeX

@ARTICLE{Ojeda-Hernandez2022151,
     author = {Ojeda-Hern’ndez, Manuel and Cabrera, Inma P. and Cordero, Pablo and Muñoz-Velasco, Emilio},
     title = {Fuzzy closure systems: Motivation, definition and properties},
     year = {2022},
     journal = {International Journal of Approximate Reasoning},
     volume = {148},
     pages = {151 – 161},
     doi = {10.1016/j.ijar.2022.06.004},
     url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85132519163&doi=10.1016%2fj.ijar.2022.06.004&partnerID=40&md5=d1a971a21900a5dc0f7c65e4de834098},
     type = {Article},
     publication_stage = {Final},
     source = {Scopus},
     note = {Cited by: 4; All Open Access, Green Open Access, Hybrid Gold Open Access}
}

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5

CITATIONS

5 Total citations

2 Recent citations

1.77 Field Citation Ratio

n/a Relative Citation Ratio

• Citations
• CrossRef - Citation Indexes: 5
• Scopus - Citation Indexes: 5

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• Mendeley - Readers: 5

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Cites

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Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

[1] C. Bejines, M. Ojeda-Hernández, and D. López-Rodríguez. “Analysis of Fuzzy Vector Spaces as an Algebraic Framework for Flag Codes”. In: Mathematics 12.3 (Feb. 2024), p. 498. ISSN: 2227-7390. DOI: 10.3390/math12030498. URL: http://dx.doi.org/10.3390/math12030498.

[2] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “Fuzzy closure structures as formal concepts”. In: Fuzzy Sets and Systems 463 (Jul. 2023), p. 108458. ISSN: 0165-0114. DOI: 10.1016/j.fss.2022.12.014. URL: http://dx.doi.org/10.1016/j.fss.2022.12.014.

[3] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “Fuzzy closure structures as formal concepts II”. In: Fuzzy Sets and Systems 473 (Dec. 2023), p. 108734. ISSN: 0165-0114. DOI: 10.1016/j.fss.2023.108734. URL: http://dx.doi.org/10.1016/j.fss.2023.108734.

[4] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “On the Commutative Diagrams Among Galois Connections Involved in Closure Structures”. In: Formal Concept Analysis. Springer Nature Switzerland, 2023, p. 49–63. ISBN: 9783031359491. DOI: 10.1007/978-3-031-35949-1_4. URL: http://dx.doi.org/10.1007/978-3-031-35949-1_4.

[5] Y. Zhong, S. Lin, and J. Chang. “Characterizations of M-fuzzifying topological operators and its applications”. In: Filomat 39.3 (2025), p. 905–919. ISSN: 2406-0933. DOI: 10.2298/fil2503905z. URL: http://dx.doi.org/10.2298/fil2503905z.