• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.527-537
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• 2005

The intuitionistic fuzzification of the notion of a bi-ideal in ordered semigroups is considered. In terms of intuitionistic fuzzy set, conditions for an ordered semigroup to be completely regular is provided. Characterizations of intuitionistic fuzzy bi-ideals in ordered semigroups are given. Using a collection of bi-ideals with additional conditions, an intuitionistic fuzzy bi-ideal is constructed. Natural equivalence relations on the set of all intuitionistic fuzzy bi-ideals of an ordered semigroup are investigated.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.225-229
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• 2013

According to the paper in [3], the kernel of an ordered semigroup S is a completely regular subsemigroup of S. In this note we show that the kernel of an ordered semigroup S is not a completely regular subsemigroup of S, in general.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.627-637
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• 2013

Let [$n$] = {1, 2, ${\ldots}$, $n$} be ordered in the standard way. The order-preserving full transformation semigroup ${\mathcal{O}}_n$ is the set of all order-preserving singular full transformations on [$n$] under composition. For this semigroup we describe maximal subsemibands, maximal regular subsemibands, locally maximal regular subsemibands, and completely obtain their classification.