The hesitant fuzzy MP filter and the hesitant fuzzy congruence relation of algebra are introduced in this study, and their properties are investigated. The comparable characterization of a hesitant fuzzy MP filter is then provided. Furthermore, we established that the set of all hesitant fuzzy congruence relations and the set of all hesitant fuzzy MP filters of R₀-algebra are complete lattice isomorphism based on the features of the hesitant fuzzy congruence relation in R₀-algebra.