GENERALIZED FUZZY POLYGROUPS

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