On Quasi-Ordering Hypergroups, Ordered Hyperstructures and Their Applications in Genetics

Abstract

The study of hypercompositional structures (introduced by Marty) is now considered of a great value because of its applications in various sciences. In this paper, we focus on a special hypercompositional structure; quasi-ordering hypergroup. In this regard, we discuss some of the quasi-ordering hypergroup’s properties and investigate some relations on it. Then, we present an application of quasi-ordering hypercompositional structures in genetics and define ordered hypercompositional structures for both sets: phenotypes and genotypes of F2-offspring.

Keywords

• quasi-ordering hypergroup
• po-hypergroup
• fundamental group
• phenotype
• genotype