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  when he established the idea of fuzzy subgroup, by applying fuzzy sets to the theory of groups.
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  as the algebraic structures
for his Basic Logic.
 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 .