Lattice Structures of Multi-Fuzzy Soft Sets

The multi-fuzzy soft set theory has recently been introduced and it has started to be applied in some fields such as decision making and medical diagnosis. In this paper, algebraic structure of multi-fuzzy soft sets is studied. Several related properties of some operations on multi-fuzzy soft sets are investigated. Two lattice structures of multi-fuzzy soft sets are constructed. It is shown that these lattices are distributive and whence modular. Additionally, the ordering relations on the lattices of multi-fuzzy soft sets are presented. Moreover, by giving an example, it is indicated that some pairs of operations on multi-fuzzy soft sets do not satisfy the absorption rule which is necessary to form a lattice. So it is proved that a lattice structure cannot be constructed by using these operations.