id: 05599503
dt: j
an: 05599503
au: Li, Tong-Jun
ti: Rough approximation operators on two universes of discourse and their fuzzy
    extensions.
so: Fuzzy Sets Syst. 159, No. 22, 3033-3050 (2008).
py: 2008
pu: Elsevier Science B.V. (North-Holland), Amsterdam
la: EN
cc: 
ut: fuzzy generalization; fuzzy rough approximation operators; fuzzy sets;
    rough sets; two universes of discourse
ci: 
li: doi:10.1016/j.fss.2008.04.008
ab: Summary: Based on a crisp binary relation between two universes of
    discourse, one crisp covering and three crisp binary relations on the
    single universe of discourse are introduced in this paper. Based on
    these induced notions, four pairs of rough approximation operators are
    formulated so that the approximating sets and the approximated sets are
    on the same universe of discourse. Furthermore, basic properties of the
    new approximation operators are investigated, and the relationships
    among the operators are also examined. Subsequently, conditions under
    which some or all of these approximation operators are equivalent are
    obtained. On the other hand, the generalizations of these rough
    approximation operators are also made in a fuzzy approximation space
    via a fuzzy implicator $\cal I$ and a triangular norm ${\cal T}$.
    Consequently, four pairs of fuzzy rough approximation operators are
    constructed. Basic properties and comparison of the fuzzy rough
    approximation operators are discussed. If ${\cal I}$ is an
    $R$-implicator with respect to a t-norm ${\cal T}$, then it is shown
    that three pairs of the fuzzy rough approximation operators are
    identical iff the induced fuzzy covering is a fuzzy ${\cal
    T}$-partition.
rv: