Falling Shadow Theory with Applications in Hoops - Borzooei, Rajab Ali; Rezaei, Gholam Reza; Kologhani, Mona Aaly; Jun, Young Bae (Bulletin of the Section of Logic, 2021)
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 falling fuzzy subhoops and falling fuzzy filters are discussed, and conditions for a falling fuzzy subhoop to be a falling fuzzy filter are provided. Also conditions for a falling shadow of a random set to be a falling fuzzy filter are displayed.