An Introduction to NeutroHX-Groups

Abstract

The chapter aims to introduce the concept of NeutroHX-Group. Starting with HX-groups and using the newly defined concept of NeutroAlgebra, the authors define the NeutroHX-Group. Using the HX-groups associated with the dihedral group, they obtain the Chinese hypergroup associated with them. They present some examples to illustrate situations when the NeutroHX-Groups and AntiHX-Groups are obtained. Also, they determine a way to obtain commutative hyperstructure, considering the set of all HX-Groups with the dihedral group as support. The important result of this chapter is given by Theorem 1, where it is establishing a connection between NeutroHX-Groups and NeutroSemihypergroups.