Lattice-valued coarse structures

Yongchao Wang; Bin Pang; Fu Gui Shi

doi:10.1016/j.fss.2024.109175

Lattice-valued coarse structures

Yongchao Wang, Bin Pang^*, Fu Gui Shi

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Based on a complete residuated lattice L, we propose a new approach to fuzzification of coarse structures. Firstly, we introduce the concepts of L-entourages and L-(quasi, semi)-coarse structures and study the maps between L-coarse spaces. Secondly, we provide some examples of L-coarse structures from the aspects of L-metrics, L-relations and L-hyperstructures. Thirdly, we introduce the notion of L-ball structures to characterize L-coarse structures. Finally, we establish the relationship among L-entourage spaces, L-quasi-coarse spaces, L-semi-coarse spaces and L-coarse spaces in a categorical viewpoint.

Original language	English
Article number	109175
Journal	Fuzzy Sets and Systems
Volume	499
DOIs	https://doi.org/10.1016/j.fss.2024.109175
Publication status	Published - 15 Jan 2025

Keywords

L-ball structure
L-bornologous map
L-bornology
L-coarse structure

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10.1016/j.fss.2024.109175

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Wang, Y., Pang, B., & Shi, F. G. (2025). Lattice-valued coarse structures. Fuzzy Sets and Systems, 499, Article 109175. https://doi.org/10.1016/j.fss.2024.109175

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abstract = "Based on a complete residuated lattice L, we propose a new approach to fuzzification of coarse structures. Firstly, we introduce the concepts of L-entourages and L-(quasi, semi)-coarse structures and study the maps between L-coarse spaces. Secondly, we provide some examples of L-coarse structures from the aspects of L-metrics, L-relations and L-hyperstructures. Thirdly, we introduce the notion of L-ball structures to characterize L-coarse structures. Finally, we establish the relationship among L-entourage spaces, L-quasi-coarse spaces, L-semi-coarse spaces and L-coarse spaces in a categorical viewpoint.",

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T1 - Lattice-valued coarse structures

AU - Wang, Yongchao

AU - Pang, Bin

AU - Shi, Fu Gui

PY - 2025/1/15

Y1 - 2025/1/15

N2 - Based on a complete residuated lattice L, we propose a new approach to fuzzification of coarse structures. Firstly, we introduce the concepts of L-entourages and L-(quasi, semi)-coarse structures and study the maps between L-coarse spaces. Secondly, we provide some examples of L-coarse structures from the aspects of L-metrics, L-relations and L-hyperstructures. Thirdly, we introduce the notion of L-ball structures to characterize L-coarse structures. Finally, we establish the relationship among L-entourage spaces, L-quasi-coarse spaces, L-semi-coarse spaces and L-coarse spaces in a categorical viewpoint.

AB - Based on a complete residuated lattice L, we propose a new approach to fuzzification of coarse structures. Firstly, we introduce the concepts of L-entourages and L-(quasi, semi)-coarse structures and study the maps between L-coarse spaces. Secondly, we provide some examples of L-coarse structures from the aspects of L-metrics, L-relations and L-hyperstructures. Thirdly, we introduce the notion of L-ball structures to characterize L-coarse structures. Finally, we establish the relationship among L-entourage spaces, L-quasi-coarse spaces, L-semi-coarse spaces and L-coarse spaces in a categorical viewpoint.

KW - L-ball structure

KW - L-bornologous map

KW - L-bornology

KW - L-coarse structure

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U2 - 10.1016/j.fss.2024.109175

DO - 10.1016/j.fss.2024.109175

M3 - Article

AN - SCOPUS:85208126706

SN - 0165-0114

VL - 499

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

M1 - 109175

ER -

Lattice-valued coarse structures

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Keywords

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