Makgeolli Structure on Hoops

Abstract

The aim of this paper is to define the concept of makgeolli structures on hoops. For this aim, we use the notions and results in fuzzy and soft set theory and apply them to hoops. Then, we introduce the notion of makgeolli algebra and makgeolli filter in hoops and study some properties of them. Some equivalence definitions of makgeolli filter and several examples are given. Then, we investigate the conditions that under that makgeolli filters and makgeolli algebras can be equivalence. Finally, by using the level subset of makgeolli filters, we try to introduce a congruence relation and show that the quotient structure is a hoop.