二型模糊集真值代数上重叠函数的扩展余蕴涵和分组函数的扩展蕴涵

Extended Coimplications of Overlap Functions and Extended Implications of Grouping Functions on Type-2 Fuzzy Truth Values

本文首先给出二型模糊集真值代数上重叠函数的扩展余蕴涵和分组函数的扩展蕴涵的定义,讨论重叠函数的扩展余蕴涵和分组函数的扩展蕴涵的封闭性,然后分别讨论它们与并∪,交∩,扩展并及扩展交的分配律,最后给出二型模糊集真值代数上重叠函数的扩展余蕴涵和分组函数的扩展蕴涵的一些表示。

This paper first introduces the concepts of an extended coimplication of a grouping function and an extended implication of a grouping function on type-2 fuzzy truth values,and discusses their closure.Then it presents the dis-tributive laws between the extended coimplication(resp.implication)and ∪(resp.∩,∪ and ∩).Finally,it gives some representations of the extended coimplications(resp.implications).