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 language | English |
---|---|
Article number | 109262 |
Journal | Fuzzy Sets and Systems |
Volume | 505 |
DOIs | |
Publication status | Published - 1 Apr 2025 |
Keywords
- Fuzzy bornologous map
- Fuzzy coarse equivalence
- Fuzzy coarse group
- Fuzzy coarse structure
- Fuzzy group ideal
Fingerprint
Dive into the research topics of 'Combinations of lattice-valued coarse structures and groups'. Together they form a unique fingerprint.Cite this
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