Combinations of lattice-valued coarse structures and groups

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 combine the lattice-valued coarse structures and group operations to propose the concept of L-fuzzifying coarse groups. Then we introduce the notion of L-fuzzifying group ideals and establish its one-to-one correspondence with L-fuzzifying coarse groups. Specifically, we examine how L-fuzzifying coarse structures align with the algebraic structures of the supporting group. Finally, we use L-fuzzifying group ideals to characterize a fuzzy coarse equivalence between L-fuzzifying coarse groups, presenting some results derived from the kernel of the group homomorphism.

Original languageEnglish
Article number109262
JournalFuzzy Sets and Systems
Volume505
DOIs
Publication statusPublished - 1 Apr 2025

Keywords

  • Fuzzy bornologous map
  • Fuzzy coarse equivalence
  • Fuzzy coarse group
  • Fuzzy coarse structure
  • Fuzzy group ideal

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Wang, Y., Pang, B., & Shi, F. G. (2025). Combinations of lattice-valued coarse structures and groups. Fuzzy Sets and Systems, 505, Article 109262. https://doi.org/10.1016/j.fss.2025.109262