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 ≥ 1 we can generate (2m − 1) NeutroStructures and (3m − 2m) AntiStructures. In this paper, we introduce for the first time the concept of NeutroHyperGroups. Specifically, we study a particular class of NeutroHy perGroups 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 neutro sophic environment, [2, 3]− NeutroHyperGroups are associated with dismutation reactions in some chemical reactions and biological processes.

Keywords

• neutrohypergroup
• neutrosubhypergroup
• neutrohypergrouphomomorphism