The Decomposition for the α-level Fuzzy Soft Sets

In this paper, the properties of α-level fuzzy soft sets and α-level fuzzy soft lattices are discussed. Firstly, some soft operations between α-level fuzzy soft sets (lattices) are dened, such as the soft union and intersection operations, and illustrates them by the examples. Secondly, the relation between the α-level fuzzy soft lattices and the α-level fuzzy soft sets are studied, we mainly verify the properties not valid in the case discussed, but tenable in the classical soft set theory.
Thirdly, the decomposition theorem for the α-level fuzzy soft sets is proved. Lastly, a simple application in skin disease diagnosis is illustrated.