Lattice-valued coarse structures

Yongchao Wang, Bin Pang*, Fu Gui Shi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number109175
JournalFuzzy Sets and Systems
Volume499
DOIs
Publication statusPublished - 15 Jan 2025

Keywords

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

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