New structure of bipolar fuzzy rho-ideals in rho-algebraic semigroups

In algebraic semigroups when we deal with classical sets every ρ-ideal does not have to be ρ–-ideal. As a result, it is demonstrated in this study with their expansion in some kinds of sets as fuzzy set (FS) & bipolar fuzzy set (BFS) is held. Also, a new construction of (BFS) is demonstrated in ρ-algebras. The study of novel notions such as ρ-semigroup (ρ-SG), ρ-subsemigroup (ρ-SSG), ρ–-ideal semigroup (ρ–-ISG), ρ-ideal semigroup (ρ-ISG), and other are given. Moreover, their extensions in fuzzy logic (FL) using Bipolar fuzzy are introduced. Additionally, a number of basic characteristics of our concepts are investigated and explored.