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

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 quasiordering 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.