Interval-valued fuzzy soft $β$-covering approximation spaces
Shizhan Lu
TL;DR
The paper addresses uncertainty in information systems by unifying soft sets, interval-valued fuzzy sets, and rough sets through interval-valued fuzzy soft $β$-covering approximation spaces. It develops interval-valued fuzzy soft $β$-neighborhoods and soft $β$-neighborhoods, then introduces four types of β-coverings-based fuzzy rough sets with corresponding lower and upper approximations. It provides formal definitions, key properties, and interrelations among the four kinds, enabling definability tests and robust approximation behavior under interval-valued fuzzy-soft β-settings. This framework advances decision-making and data analysis under multi-criteria uncertainty by offering a rigorous algebraic apparatus for interval-valued fuzzy-soft rough reasoning.
Abstract
The concept of interval-valued fuzzy soft $β$-covering approximation spaces (IFS$β$CASs) 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 IFS$β$CASs 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.