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Open AccessArticle
A Logifold Structure for Measure Space
by
Inkee Jung
Inkee Jung
and
Siu-Cheong Lau
Siu-Cheong Lau
Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(8), 599; https://doi.org/10.3390/axioms14080599 (registering DOI)
Submission received: 5 June 2025
/
Revised: 27 July 2025
/
Accepted: 29 July 2025
/
Published: 1 August 2025
Abstract
In this paper, we develop a geometric formulation of datasets. The key novel idea is to formulate a dataset to be a fuzzy topological measure space as a global object and equip the space with an atlas of local charts using graphs of fuzzy linear logical functions. We call such a space a logifold. In applications, the charts are constructed by machine learning with neural network models. We implement the logifold formulation to find fuzzy domains of a dataset and to improve accuracy in data classification problems.
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MDPI and ACS Style
Jung, I.; Lau, S.-C.
A Logifold Structure for Measure Space. Axioms 2025, 14, 599.
https://doi.org/10.3390/axioms14080599
AMA Style
Jung I, Lau S-C.
A Logifold Structure for Measure Space. Axioms. 2025; 14(8):599.
https://doi.org/10.3390/axioms14080599
Chicago/Turabian Style
Jung, Inkee, and Siu-Cheong Lau.
2025. "A Logifold Structure for Measure Space" Axioms 14, no. 8: 599.
https://doi.org/10.3390/axioms14080599
APA Style
Jung, I., & Lau, S.-C.
(2025). A Logifold Structure for Measure Space. Axioms, 14(8), 599.
https://doi.org/10.3390/axioms14080599
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