Generalized convex combination of implications on bounded lattices

被引：0
|
作者：
Kesicioglu, M. N. [1 ]
Ertugrul, U. [2 ]
Karacal, F. [2 ]
机构：
[1] Recep Tayyip Erdogan Univ, Dept Math, TR-53100 Rize, Turkey
[2] Karadeniz Tech Univ, Dept Math, TR-61080 Trabzon, Turkey
来源：
IRANIAN JOURNAL OF FUZZY SYSTEMS | 2020年 / 17卷 / 06期
关键词：
Fuzzy implication; linear combination; convex combination; bounded lattice; T-NORMS; FUZZY; CONSTRUCTION; LAW;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：75 / 91
页数：17
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