Hierarchical structures and uncertainty measures for intuitionistic fuzzy approximation space

An intuitionistic fuzzy graded covering rough set

“…The affirmation, negation, and hesitation cardinalities of N β C can also be defined as follows: [20] to IF β-neighborhood systems as follows. …”

“…The IF rough entropy for IF granular structures [20] is generalized to IF granular structures to characterize the uncertainty of an IF βneighborhood approximation space as follows. …”

“…Exploring rough sets from the perspective of multi-granulation represents a promising direction in rough set theory, where concepts are approximated by multiple granular structures represented by binary relations [20,29,43,47] . In the literature, the uncertainty measures of the multi-granulation approximation space are studied [20] .…”

“…In the literature, the uncertainty measures of the multi-granulation approximation space are studied [20] . In this section, we investigate the distance-based uncertainty measures for a multi-granulation IF β-neighborhood approximation space and discuss the multi-granulation IF rough sets based on IF graded neighborhood.…”

“…Yang et al [63] generalized the MGRS model into a fuzzy environment. Huang et al [20,21] examined multigranulation IF approximation, IF rough sets, and their matrix-based reduction methods.…”