Introduction to NeutroHyperGroups

Abstract

NeutroSophication and AntiSophication are processes through which NeutroAlgebraic and AntiAlgebraic structures can be generated from any classical structures. Given any classical structure with $m$ operations (laws and axioms) where $m\geq 1$ we can generate $(2^m-1)$ NeutroStructures and $(3^m-2^m)$ AntiStructures. In this paper, we introduce for the first time the concept of NeutroHyperGroups. Specifically, we study a particular class of NeutroHyperGroups called $[2,3]-$ NeutroHyperGroups and present their basic properties and several examples. It is shown that the intersection of two $[2,3]-$ NeutroSubHyperGroups is not necessarily a $[2,3]-$NeutroSubHypergroup but their union may produce a $[2,3]-$ NeutroSubhypergroup. Also, the quotient of a $[2,3]-$NeutroHyperGroup factored by a $[2,3]-$ NeutroSubHyperGroup is shown to be a $[2,3]-$NeutroHyperGroup. Examples are provided to show that in the neutrosophic environment, $[2,3]-$ NeutroHyperGroups are associated with dismutation reactions in some chemical reactions and biological processes.