Generalized convex combination of implications on bounded lattices

Document Type : Research Paper

Authors

1 Department of Mathematics, Recep Tayyip Erdogan University, 53100 Rize, Turkey

2 Department of Mathematics, Karadeniz Technical University, Trabzon, 61080, Turkey

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.

Keywords

Iranian Journal of Fuzzy Systems
Volume 17, Issue 6
November and December 2020
Pages 75-91

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