Abstract
In this paper we introduce the concept of (weak) fuzzy subsupermodules based on (thin) supermodules different from fuzzy subhypermodules. In this study, the concept of α-cuts play a main role for constructing of extended (weak) fuzzy subsupermodules. In final, we introduce a notation of residual quotients of (weak) fuzzy subsupermodules and obtain some conditions to be a (weak) fuzzy subsupermodule. Also obtained some applied results in residual quotients of (weak) fuzzy subsupermodules of superrings as specially subsupermodules.
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