Counting the number of intuitionistic fuzzy subgroups of groups order 12

One of the most important topics in the theory of fuzzy groups is the classification of fuzzy subgroups of a finite group. Enumeration of fuzzy subgroups has been done in the theory of fuzzy groups using the equivalence relation defined by Murali and Makamba. Using this idea, Neeraj and Sharma enumerated Intuitionistic fuzzy subgroups of a finite Abelian group by concept of double pinned flags.We are in thisWe do this in another way for some finite Abelian and non-Abelian groups. In fact, with the help of a suitable equivalence relation on Intuitionistic fuzzy subgroups and the lattice of subgroups, we obtain the enumeration of Intuitionistic fuzzy subgroups of finite groups of order 12. Also, we obtain the enumeration of Intuitionistic fuzzy subgroups of finite groups $Z_{p^k}\times Z_q$ and $Z_{p^k}$ with a different method from the article [9]. Finally, with the help of the results obtained in this paper, we present the number of Intuitionistic fuzzy subgroups on a group with order less than 16 in a table.