Abstract This paper deals with two sorts of interval fuzzy implications derived from interval overlap and grouping functions, viz., interval R O - and ( G , O , N ) -implications. Firstly, interval R O -implications, preserving the residuation property, are the interval generalization of R O -implications induced by overlap functions. We investigate their properties and their correlations with interval automorphisms. Secondly, interval ( G , O , N ) -operations are generalized from D-operations induced by tuples ( O , G , N ) . We obtain a necessary and sufficient condition for the interval ( G , O , N ) -operation to be an interval fuzzy implication, namely interval ( G , O , N ) -implication. And then, we investigate vital properties and conclusions regarding interval ( G , O , N ) -operations and interval ( G , O , N ) -implications. Finally, we study the intersections between families of interval fuzzy implications, including interval R O -, ( G , N ) -, ( O , G , N ) - and ( G , O , N ) -implications.

中文翻译：

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从区间重叠和分组函数推导出区间 RO- 和 (G,O,N)-含义

摘要 本文讨论了由区间重叠和分组函数导出的两类区间模糊蕴涵，即区间RO - 和( G , O , N ) -蕴涵。首先，区间RO -蕴涵，保留了残差性质，是由重叠函数引起的RO -蕴涵的区间推广。我们研究了它们的性质以及它们与区间自同构的相关性。其次，区间 ( G , O , N ) 操作是从由元组 ( O , G , N ) 诱导的 D 操作中推广的。我们得到区间( G , O , N ) - 运算为区间模糊蕴涵的充要条件，即区间( G , O , N ) -蕴涵。然后，我们研究关于区间 ( G , O , N ) - 操作和区间 ( G , O , N ) - 含义的重要属性和结论。最后，