Generalized convex combination of implications on bounded lattices

KESİCİOĞLU M. N., ERTUĞRUL Ü., KARAÇAL F.

IRANIAN JOURNAL OF FUZZY SYSTEMS, vol.17, no.6, pp.75-91, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.22111/ijfs.2020.5602
  • Journal Name: IRANIAN JOURNAL OF FUZZY SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.75-91
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

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.