Atanassov’s intuitionistic fuzzy submodules with respect to a t-norm

In this paper, t-norm based intuitionistic fuzzy submodules are defined, and their various properties are investigated. We also show that if an intuitionistic fuzzy set of a module is an intuitionistic fuzzy submodule with respect to a t-norm, then it is also an intuitionistic fuzzy submodule with respect to the annihilation t-norm. We investigate the nature of intuitionistic fuzzy submodules of a module with the help of their respective cut sets. We obtain some results based on (α, β)-level sets and t-norm based α-cut sets of an intuitionistic fuzzy submodule with respect to a t-norm T.

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