On (fuzzy) closure systems in complete fuzzy lattices

 

Abstract

Two alternative definitions of closure system in complete fuzzy lattices are introduced, first as a crisp set and then as a fuzzy one. It is valuated in a complete Heyting algebra and follows the classical definition on complete lattices. The classical bijection between closure systems and fuzzy closure operators is preserved. Then, the notion is compared with the most used definition given by Bělohlávek on the fuzzy powerset lattice.

Citation

Please, cite this work as:

[Oje+21] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “On (fuzzy) closure systems in complete fuzzy lattices”. In: 30th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2021, Luxembourg, July 11-14, 2021. IEEE, 2021, pp. 1-6. DOI: 10.1109/FUZZ45933.2021.9494404. URL: https://doi.org/10.1109/FUZZ45933.2021.9494404.

BibTeX

@InProceedings{OjedaHernandez2021,
     author = {Manuel Ojeda-Hern{’a}ndez and Inma P. Cabrera and Pablo Cordero and Emilio Mu~noz-Velasco},
     booktitle = {30th {IEEE} International Conference on Fuzzy Systems, {FUZZ-IEEE} 2021, Luxembourg, July 11-14, 2021},
     title = {On (fuzzy) closure systems in complete fuzzy lattices},
     year = {2021},
     pages = {1–6},
     publisher = {{IEEE}},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/conf/fuzzIEEE/Ojeda-Hernandez21.bib},
     doi = {10.1109/FUZZ45933.2021.9494404},
     timestamp = {Tue, 21 Mar 2023 00:00:00 +0100},
     url = {https://doi.org/10.1109/FUZZ45933.2021.9494404},
}

Bibliometric data

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6

CITATIONS

6 Total citations

4 Recent citations

3.23 Field Citation Ratio

n/a Relative Citation Ratio

• Citations
• Scopus - Citation Indexes: 8

• Captures
• Mendeley - Readers: 3

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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] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “Closure Systems as a Fuzzy Extension of Meet-subsemilattices”. In: Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP). ifsa-eusflat-agop-21. Atlantis Press, 2021. DOI: 10.2991/asum.k.210827.006. URL: http://dx.doi.org/10.2991/asum.k.210827.006.

[2] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “On Pseudointents in Fuzzy Formal Concept Analysis”. In: Graph-Based Representation and Reasoning. Springer Nature Switzerland, 2023, p. 36–40. ISBN: 9783031409608. DOI: 10.1007/978-3-031-40960-8_4. URL: http://dx.doi.org/10.1007/978-3-031-40960-8_4.

[3] 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.

[4] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “Relational Extension of Closure Structures”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer International Publishing, 2022, p. 77–86. ISBN: 9783031089718. DOI: 10.1007/978-3-031-08971-8_7. URL: http://dx.doi.org/10.1007/978-3-031-08971-8_7.