intuitionistic l-fuzzy ideals and subalgebras of novikovalgebras

In this paper, a new concept of intuitionistic l-fuzzy sets (ilfss) is applied to novikov algebras and some fundamental notions including ilf subspace, ilf ideal and ilf subalgebra of novikov algebras are introduced alongside operations such as multiplication, union, and intersection on ilfss. additionally, throughout this paper, some necessary and sufficient conditions including an ilf subspace is an ilf ideal are obtained and key structural properties are established. moreover, it is demonstrated that a quotient algebra $x/a$ of a ilf ideal $a=(mu_a,nu_a)$ is isomorphic to $x/x_a$ of a non-ilf ideal $x_a$. furthermore, the algebraic properties of the surjective homomorphic image and preimage of an ilf ideal is explored which helps reach deeper insights into the algebraic structure of novikov algebras and further research of ilfss.