small Polygroups are multi-valued systems that satisfy group-like axioms. Using the notion of "belonging (2)" and "quasi-coincidence (q)" of fuzzy points with fuzzy sets, the concept of (2,2 _q)-fuzzy subpolygroups is introduced. The study of (2,2 _q)-fuzzy normal subpolygroups of a polygroup are dealt with. Characterization and some of the fundamental properties of such fuzzy subpolygroups are obtained. (2,2 _q)-fuzzy cosets determined by (2,2 _q)-fuzzy subpolygroups are discussed. Finally, a fuzzy subpolygroup with thresholds, which is a generalization of an ordinary fuzzy subpolygroup and an (2,2,_q)-fuzzy subpolygroup, is defined and relations between two fuzzy subpolygroups are discussed.