The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between ...

The notions of (implicative) soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions ...