Generalized convex combination of implications on bounded lattices
IRANIAN JOURNAL OF FUZZY SYSTEMS, cilt.17, sa.6, ss.75-91, 2020 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 17 Sayı: 6
- Basım Tarihi: 2020
- Doi Numarası: 10.22111/ijfs.2020.5602
- Dergi Adı: IRANIAN JOURNAL OF FUZZY SYSTEMS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
- Sayfa Sayıları: ss.75-91
- Recep Tayyip Erdoğan Üniversitesi Adresli: Evet
Özet
In this paper, the notions of the linear and g-convex combination for implications which extend the notion of convex combination of fuzzy implications on the unit interval to bounded lattices are introduced. A necessary and sufficient condition for the g-convex combination to be an implication is determined. Some basic properties of the g-convex combinations are discussed. Also, some sets which are defined by the linear (g-convex) combination of two implications on a bounded lattice are studied and the relationships between them are discussed. Moreover, the lattice theoretical structure of the mentioned sets is investigated.