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We use a neutrosophic set, instead of an intuitionistic fuzzy because the neutrosophic set is more general, and it allows for independent and partial independent components μ (χ) , γ (χ) , ζ (χ), while in an intuitionistic fuzzy set, all components are totally dependent. In this article, we present and demonstrate the concept of neutrosophic invariant subgroups. We delve into the exploration of this notion to establish and study the neutrosophic quotient group. Further, we give the concept of a neutrosophic normal subgroup as a novel concept. [ABSTRACT FROM AUTHOR]

In this paper we consider the category M-FQMod of M-fuzzy (left) Q-modules over a given quantale Q. We introduce and investigate the notion of M-fuzzy Q-submodule of a left Q-module. Also, the notions of M-fuzzy module nuclei and conuclei on a left Q-module are defined, and the elementary properties of both are studied. The relationships between such notions and M-fuzzy Q-submodule are discussed. Finally, the relationship between the category of M-fuzzy Q-modules and the category of (L, M)-quasi-fuzzy topological spaces is discussed. [ABSTRACT FROM AUTHOR]