Refined neutrosophic quadruple (po-)hypergroups and their fundamental group

Abstract

After introducing the notion of hyperstructures about 80 years ago by F. Marty, a number of researches on
 its theory, generalization, and it’s applications have been done. On the other hand, the theory of Neutrosophy, the study
 of neutralities, was developed in 1995 by F. Smarandache as an extension of dialectics. This paper aims at finding
 a connection between refined neutrosophy of sets and hypergroups. In this regard, we define refined neutrosophic
 quadruple hypergroups, study their properties, and find their fundamental refined neutrosophic quadruple groups.
 Moreover, some results related to refined neutrosophic quadruple po-hypergroups are obtained.