The concept of hesitant fuzzy set in the abstract mathematical notion of nearring for further development of hesitant fuzzy set on a theoretical model is introduced in this paper. An attempt is made to study the algebraic nature of interval-valued hesitant fuzzy subnearring of a nearring under homomorphism and anti-homomorphism.

hesitant fuzzy set, interval-valued hesitant fuzzy set, interval-valued hesitant fuzzy subset, interval-valued hesitant fuzzy subnearring, interval-valued anti-hesitant fuzzy subnearring.