Note on fuzzy groups

Abstract

Motivated by various applications of finite algebraic structures, we give general solutions to the following problems, implicitly stated in [1] and [2]: for which groups is every fuzzy subgroupoid a fuzzy subgroup ? and: for which groups are all fuzzy subgroup of finite order ? The solutions are given for lattice valued fuzzy subgroups, and particularly for interval valued ones ([0,1] fuzzy subgroups).