Notes on “the lower and upper approximations in a fuzzy group” and “rough ideals in semigroups”

In this note, we show by examples that Propositions 2.4 and 2.5 in [N. Kuroki, P.P. Wang, The lower and upper approximations in a fuzzy group, Information Sciences 90 (1996) 203] and Theorem 2.5 in [N. Kuroki, Rough ideals in semigroups, Information Sciences 100 (1997) 139] are incorrect and offer their modified versions.