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.

Funding

Projects funding this work

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}
}