A fuzzy application of the group $$\mathbb {Z}_n$$ to complete hypergroups

The purpose of this paper is the study of intuitionistic fuzzy subhypergroups of some special finite complete hypergroups. More exactly, in this paper we determine all m-tuples, characterizing the considered complete hypergroups, such that the grade intuitionistic fuzzy set $$(\overline{\mu },\overline{\lambda })$$ is an intuitionistic fuzzy subhypergroup of such hypergroups. Here, we deal with complete hypergroups obtained from groups isomorphic with the additive groups of integers modulo $$p^2$$ or modulo pq, with p and q distinct odd primes. This article is a continuation of a previous work, concerning the complete hypergroups obtained from groups isomorphic with the additive groups of integers modulo p or modulo 2p, with p a prime number. It represents the starting point, the mathematical base, for writing a general algorithm for characterizing all complete hypergroups obtained from a group G and having the grade intuitionistic fuzzy set as an intuitionistic fuzzy subhypergroup.