Abstract: Let, M be a unitary R-module over R be a commutative ring with identity and let X be a fuzzy module of an R-module M . In this study, we present two concepts: the frist concept is a weakly T-ABSO fuzzy submodule where a proper fuzzy submodule A of fuzzy module X of an R-module M is called a weakly T-ABSO fuzzy submodule of X if whenever fuzzy singletons as, bl of R, xν⊆X, ∀s, l, νεL and 01≠asblxν⊆ then either asbl⊆(A:RX) or as xv⊆ or blxν⊆A. And the second concept is an almost T-ABSO fuzzy submodule where let R be an integral domain, X be fuzzy module of an R-module M and A a proper fuzzy submodule of X. A is called an almost T-ABSO fuzzy submodule of X if for fuzzy singletons as, bl of R and xν⊆X with asblxν⊆A-(A:RX)A, then either asbl⊆(A:RX) or asxν⊆ or blxν⊆. We study some basic properties and characterizations of weakly T-ABSO fuzzy submodules and almost T-ABSO fuzzy submodules. We present almost T-ABSO fuzzy submodules of X as a new generalization of T-ABSO fuzzy and weakly T-ABSO fuzzy submodules and relationships between them concepts are given.
Wafaa H. Hanoon and Hatam Y. Khalaf, 2019. Weakly and Almost T-ABSO Fuzzy Submodules. Journal of Engineering and Applied Sciences, 14: 10459-10466.