Some construction methods of interval-valued implications on bounded lattices

KARAÇAL F., KARACAİR K., ERTUĞRUL Ü.

Iranian Journal of Fuzzy Systems, cilt.21, sa.6, ss.33-54, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 6
  • Basım Tarihi: 2024
  • Doi Numarası: 10.22111/ijfs.2024.48572.8569
  • Dergi Adı: Iranian Journal of Fuzzy Systems
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.33-54
  • Anahtar Kelimeler: bounded lattice, construction method, Implications, interval-valued fuzzy set, lattice of closed intervals, order preserving function, order reversing function
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In recent years, implication operators have been studied intensively from many perspectives. These include the study of construction methods of implication operators. Additionally, it has been investigated whether some aggregation operators such as t-norm in interval-valued L-fuzzy set theory are representable. In this paper, we present some construction methods to obtain interval-valued implications, which are i-representable or not depending on the lattice and fuzzy logic operators, via some fuzzy logic operators, order preserving and/or order reversing functions. Moreover, many illustrative examples are included.