Hybrid models of fuzzy sets and soft sets were extensively applied in different fields of mathematics, in particular they were extremely applied in classical

algebraic structures. This was started by Rosenfeld in 1971 [27] when he established the idea of fuzzy subgroup, by applying fuzzy sets to the theory of groups.

In particular, as

algebraic structures are particular cases of structures satisfying first-order theories, model theory has naturally several applications to algebra.

M'ller's (1934-2014) mathematical community honor his contributions to algebra with papers on the

algebraic structures rings and modules.

Actually, the operations of the loop homology algebra of a manifold are very difficult to compute, but there are several conjectures connecting the string topology with

algebraic structures on the Hochschild cohomology of algebras related to the manifold.

In fact, the structure is nonassociative and noncommutative but it possesses many properties which usually hold in associative and commutative

algebraic structures. Also, defining a new operation on this algebra gives a commutative and associative algebra.

They stress the importance of learning activities that assist students to recognise and use numerical structures that can be easily translated for understanding of

algebraic structures at a later time.

The notion of neutrosophic

algebraic structures was introduced by Kandasamy and Smarandache in 2006, see [12, 13].

The notion of BL-algebras was introduced by Hajek [6] as the

algebraic structures for his Basic Logic.

[3] Florentin Smarandache, Special

algebraic structures, University of Maxico, Craiova, 1973.

They write for mathematicians, physicists, and computer scientists interested in theoretical relationships between graph theory,

algebraic structures, and physics.

The notion of a combinatorial Hopf algebra is a heuristic one, referring to rich

algebraic structures arising naturally on the linear spans of various families of combinatorial objects.

The classification of such

algebraic structures was performed in [43].