几类基于L~*上二元聚合算子的蕴涵(英文)

Several Classes of Implications Based on Binary Aggregation Operators on L~*

L*是区间值模糊与Atanassov意义下的直觉模糊集的基本格。本文首先基于单位区间上的三角模与三角余模,引入L*上两组对偶的二元聚合算子,然后,类似于剩余蕴涵与强蕴涵的构成方法,利用引入的对偶聚合算子生成几类L*上的蕴涵,并对其性质进行讨论。

Lattice L＊ is the underlying lattice of both interval-valued fuzzy sets and intuitionistic fuzzy sets in the sense of Atanassov. In this paper we introduce two groups of dual binary aggregation operators on L＊ based on t-norms and t-conorms on the unit interval. Similar to the constructions as for residual implications and strong implications, several classes of implications on L＊ are generated based on these binary aggregation operators on L＊ and their properties are discussed.