Lattices of Intuitionistic Fuzzy Submodules

Abstract

In this paper, we provide a technique of generating an intuitionistic fuzzy submodule from a given intuitionistic fuzzy set. It is shown that (i) the sum of two intuitionistic fuzzy submodules of a module M is the intuitionistic fuzzy submodule generated by their union and (ii) the set of all intuitionistic fuzzy submodules of a given module forms a bounded complete lattice. Consequently it is established that the collection of all intuitionistic fuzzy submodules, having the same value at zero, of M constitute a complete distributive sublattice of the lattice of intuitionistic fuzzy submodules.