Generalized convex combination of implications on bounded lattices
Publish place: Iranian Journal of Fuzzy Systems، Vol: 17، Issue: 6
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJFS-17-6_007
تاریخ نمایه سازی: 30 خرداد 1400
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.
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Authors
M. N. Kesicioglu
Department of Mathematics, Recep Tayyip Erdogan University, ۵۳۱۰۰ Rize, Turkey
U. Ertugrul
Department of Mathematics, Karadeniz Technical University, Trabzon, ۶۱۰۸۰, Turkey
F. Karacal
Department of Mathematics, Karadeniz Technical University, Trabzon, ۶۱۰۸۰, Turkey