Algebraic properties of ordered power semigroups on Semihypergroups induced by Posets

Abstract

Based on the development of fuzzy mathematics, all kinds of algebraic structure are upgraded from its universes to its power sets. We construct a new algebraic structure which is called a power semigroup on a semihypergroup and then study some of its algebraic properties such as homomorphism theorems. In this thesis, we focus on the study of the algebraic structure called an ordered power semigroup on a semihypergroup induced by a poset. This algebraic structure is constructed by combining the concept of power semigroups on semihypergroups and the concept of power ordered set together and then study its algebraic properties such as pure ideals, C-ideals and regularities.