New construction methods for uninorms on bounded lattices

ERTUĞRUL Ü., Yeşilyurt M.

Filomat, cilt.39, sa.15, ss.5335-5354, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 15
  • Basım Tarihi: 2025
  • Doi Numarası: 10.2298/fil2515335e
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.5335-5354
  • Anahtar Kelimeler: bounded lattice, construction method, sublattice, triangular conorm, triangular norm, Uninorm
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

After Karaçal and Mesiar introduced uninorms on a bounded lattice in [25] and showed their existence on an arbitrary bounded lattice, construction methods of uninorms on bounded lattices have been widely studied in which the existence of t-norms and t-conorms on sublattices of the bounded lattice L was generally exploited. In this paper, we introduce two new construction methods for uninorms on a bounded lattice L by exploiting the existence of a triangular norm T and triangular conorm S on a sublattice of L, where L \ {0, 1} has the bottom and the top elements. Then, we demonstrate that our new construction methods are also different from the existing construction methods in the literature. Additionally, some illustrative examples are provided. Finally, we generalize by induction our construction methods to a more general form.