Fuzzy Subgroups and Fuzzy Normal Subgroups

In this chapter, we introduced the notions of some fuzzy analog of the concept of a subgroupoid of a groupoid, a subgroup of a group, a normal subgroup of a group, a level subgroup of a group, and cosets of a subgroup of a group. Further, it has been exhibited how some basic notions of group theory should be extended in an elementary way to develop the theory of fuzzy subgroupoids, fuzzy subgroups, and homomorphism between fuzzy groups, sup property, fuzzy groups redefined, fuzzy level subgroups, fuzzy normal subgroups, and fuzzy cosets. Also, we have here the fuzzy version of the famous “Lagrange’s theorem’ and the fundamental homomorphism theorem. We should be familiar with fuzzy subgroups, and fuzzy normal subgroups are generalizations of their classical counterpart.