Structural Analysis of Two-Fold Algebraic Systems Defined Over Fuzzy and Antifuzzy Groups

YAŞAR R.

Journal of Mathematics, cilt.2026, sa.1, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2026 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1155/jom/5407329
  • Dergi Adı: Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: antifuzzy group, two-fold algebra, two-fold fuzzy group, two-fold homomorphism
  • Ankara Üniversitesi Adresli: Evet

Özet

This study examines the structural properties of two-fold algebras defined over fuzzy groups and antifuzzy groups. The corresponding two-fold binary operations are introduced, and their fundamental algebraic features, such as associativity, identity elements, inverses, and finite order elements, are analyzed. In addition, several related substructures, including two-fold subalgebras, centers, normality conditions, and homomorphisms, are described and their relationships with the underlying groups are discussed. Illustrative examples are included to demonstrate the developed framework. The findings contribute to the theory of fuzzy algebraic systems and indicate possible applications in modeling uncertainty and multivalued logical systems.