Lattice structure of fuzzy groups in fuzzy approximation spaces
Pankajpankaj15@s.amity.eduDepartment of MathematicsAmity Institute of Applied SciencesAmity UniversityNoida, Uttar Pradesh, 201313, IndiaView full profile → , Rashmi Singhrsingh7@amity.eduDepartment of MathematicsAmity Institute of Applied SciencesAmity UniversityNoida, Uttar Pradesh, 201313, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Nov 2025
- Published Online:
- 30 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2851
- Pages:
- 3323–3333
Abstract
This paper presents a comprehensive of the algebraic and lattice structure of fuzzy groups in fuzzy approximation spaces. The structure of ℱ(𝒫, 𝒬), the collection of all fuzzy subgroups of a group 𝒫 in a fuzzy approximation space ℱ(𝒫, 𝒬) is systemically analysed. The main contributions include: (i) proving that ℱ(𝒫, 𝒬) forms a complete meet-semilattice under pointwise ordering. The infimum exists for any collection of fuzzy subgroups; (ii) ℱ(𝒫, 𝒬) does not generally form a complete lattice, as suprema may fail to preserve fuzzy subgroup properties and this is shown through counterexample; (iii) developing a comprehensive homomorphism theory including fuzzy isomorphism theorems, composition properties, and preservation results; and (iv) establishing that join-irreducible fuzzy subgroups generate all fuzzy subgroups through meets and directed joins. Every chain in ℱ(𝒫, 𝒬) admits both supremum and infimum. The framework extends classical group-theoretic concepts thereby giving a generalization of the concepts.
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References
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