A. Khan, Y. B. Jun and M. Shabir
Fuzzy ideals in ordered semigroups I
We prove that: a regular ordered semigroup S is
left simple if and only if every fuzzy left ideal of S is a
constant function. We also show that an ordered semigroup S is
left (resp. right) regular if and only if for every fuzzy
left (resp. right) ideal f of S we have, f(a)=f(a2) for
every a in S. Further, we characterize some semilattices of
ordered semigroups in terms of fuzzy left(resp. right) ideals. In
this respect, we prove that an ordered semigroup S is a
semilattice of left (resp. right) simple semigroups if and only if
for every fuzzy left(resp. right) ideal f of S we have,
f(a)=f(a2) and f(ab)=f(ba) for all a,b in S.