中文摘要：

本文主要讨论了（L,M）-fuzzy凸空间的诱导理论。首先,利用三种Lowen算子ω、ι、[]得到了三种凸空间,并讨论了它们的基本性质。其次,引入了弱诱导的（L,M）-fuzzy凸空间,满层的（L,M）-fuzzy凸空间,以及诱导的（L,M）-fuzzy凸空间,并讨论了这三种空间的关系。最后,讨论了（L,M）-fuzzy凸商空间的诱导性质,并给出了（L,M）-fuzzy保凸映射和（L,M）-fuzzy凸凸映射的刻画。

英文摘要：

The aim of this paper is to discuss the induced theory of （L,M）-fuzzy convex spaces. Firstly, by using three Lowen operators, namely, ω,τ and [- ], we obtain three convex spaces and discuss there basic properties. Secondly, we introduce the notions of induced （L, M）-fuzzy convex spaces, weakly induced （L,M）-fuzzy convex spaces and stratified （L,M）-fuzzy convex spaces, and further discuss their relations. Finally, we discuss induced properties of （L,M）-fuzzy convex quotient spaces and obtain some characterizations of （L, M）-fuzzy convex preserving mappings and （L, M）-fuzzy convex-to-convex mappings.