• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1217-1225
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• 2010

In this paper we define fuzzy interior $\Gamma$-ideals in ordered $\Gamma$-semigroups. We prove that in regular(resp. intra-regular) ordered $\Gamma$-semigroups the concepts of fuzzy interior $\Gamma$-ideals and fuzzy $\Gamma$-ideals coincide. We prove that an ordered $\Gamma$-semigroup is fuzzy simple if and only if every fuzzy interior $\Gamma$-ideal is a constant function. We characterize intra-regular ordered $\Gamma$-semigroups in terms of interior (resp. fuzzy interior) $\Gamma$-ideals.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.583-606
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• 2013

We generalize the idea of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered semi-group and give the concept of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered $\mathcal{LA}$-semigroup. We show that (${\in}$, ${\in}{\vee}q_k$)-fuzzy left (right, two-sided) ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy (generalized) bi-ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy interior ideals and (${\in}$, ${\in}{\vee}q_k$)-fuzzy (1, 2)-ideals need not to be coincide in an ordered $\mathcal{LA}$-semigroup but on the other hand, we prove that all these (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideals coincide in a left regular class of an ordered $\mathcal{LA}$-semigroup. Further we investigate some useful conditions for an ordered $\mathcal{LA}$-semigroup to become a left regular ordered $\mathcal{LA}$-semigroup and characterize a left regular ordered $\mathcal{LA}$-semigroup in terms of (${\in}$, ${\in}{\vee}q_k$)-fuzzy one-sided ideals. Finally we connect an ideal theory with an (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideal theory by using the notions of duo and (${\in}{\vee}q_k$)-fuzzy duo.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.1-6
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• 1998

The paper refers to ordered semigroups in which $x^2 (x \in S)$ are left ideal elements. We mainly show that this $po$-semigroup is left regular if and only if S is a union of left simple subsemigroups of S.

• Journal of architectural history
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• v.17 no.5
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• pp.23-37
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• 2008

Hyeunryungwon is a tomb for Crown Prince Sado, who was the father of King Jeongjo, the twenty second king of Joseon dynasty. The tomb had been originally in the Eastern part of Seoul, but was relocated in 1789 to the downtown Suwon, which was renowned as a good tomb site among the Royal family at that time. King Jeongjo looked through the records from the previous generations for the ideal location and direction for the tomb. He personally studied Feng Shui theory and designated its location and direction. He ordered for lavish decorations for the stone adornments of the surroundings of the grave mound, which was against the regulations of the royal family. He found his reasons in the precedent that allowed sumptuous decoration. However, for the arrangements of Jeongjagahk(T shaped building) and other attached facilities, he made unusual choice that other precedent royal tombs did not have. Instead of following the conventions that Jeongjagak should be facing south of a grave mound, he put it on the right side of grave mound. Also conventionally, Subokbang(a place where guards can stay) and Suragan(a kitchen that prepares food for sacrificial rites) should be facing symmetrically, but they too, were on the same side with Jeongjagak. It was a measurement that the grave mound of Hyeunryungwon can have a full view without being obstructed by other facilities and it was also personally ordered by King Jeongjo. The distinguishing features of Hyeunryuwon was motivated by King Jeongjo's filial affection, and his academic pursuit of precedent royal tombs initiated the unconventional and innovative challenges.