The Decomposition for the α-level Fuzzy Soft Sets
Li Fu
School of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai 810000, P. R. China.
Luo Tai Qie
School of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai 810000, P. R. China.
Qiao Yun Liu
School of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai 810000, P. R. China.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Soft lattice, fuzzy soft sets (lattices), level sets, a-level fuzzy soft set (lattices), decomposition theorem.