Interval-valued fuzzy soft β-covering approximation spaces

The concept of interval-valued fuzzy soft β-covering approximation spaces (IFSβCASs) is introduced to combine the theories of soft sets, rough sets and interval-valued fuzzy sets, and some fundamental propositions concerning interval-valued fuzzy soft β-neighborhoods and soft β-neighborhoods of IFSβCASs are explored. And then four kinds of interval-valued fuzzy soft β-coverings based fuzzy rough sets are researched. Finally, the relationships of four kinds of interval-valued fuzzy soft β-coverings based fuzzy rough sets are investigated.