LL-fuzzy soft sets based on complete Boolean lattices

In this paper, the concept of LL-fuzzy soft sets based on complete Boolean lattices, which can be seen as a generalization of fuzzy soft sets, is introduced. The topological and lattice structure of LL-fuzzy soft sets are obtained. Some operations on LL-fuzzy soft sets are discussed, and new types of LL-fuzzy soft sets such as full, keeping intersection and keeping union LL-fuzzy soft sets are defined and supported by some illustrative examples. A pair of LL-fuzzy soft rough approximations is proposed and their properties are given. Based on LL-fuzzy soft rough approximations, the concept of LL-fuzzy soft rough sets is introduced and their structures are studied. The fact that every finite LL-fuzzy topological space is an LL-fuzzy soft approximation space is revealed. In addition, we obtain two one-to-one correspondence relationships associated with LL-fuzzy soft sets, which expounds the broad application prospect of LL-fuzzy soft sets.