Soft Set Theory Applied to Hoops

Abstract

In this paper, we introduced the concept of a soft hoop and we investigated some of their properties. Then, we established different types of intersections and unions of the family of soft hoops. We defined two operations ⊙ and → on the set of all soft hoops and we proved that with these operations, it is a hoop and also is a Heyting algebra. Finally we introduced a congruence relation on the set of all soft hoops and we investigated the quotient of it.

Keywords

• soft set
• hoop
• soft hoop
• heyting algebra
• 06f35
• 03g25
• 06d72