• Korean Journal of Mathematics
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• 제30권3호
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• pp.443-458
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• 2022

In this paper, we apply the concept of intuitionistic Q-fuzzy set to PMS-algebras. We study the concept of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras and investigate some related properties of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras. We provide the relationship between an intuitionistic Q-fuzzy PMS-subalgebra and an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. We establish a condition for an intuitionistic Q-fuzzy set in a PMS-algebra to be an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. Characterizations of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras in terms of their level sets are given.

• 호남수학학술지
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• 제34권4호
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• pp.549-557
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• 2012

The notion of vague $q$-ideals of BCI-algebras is introduced, and several properties of them are investigated. Relations between a vague ideal and a vague $q$-ideal are discussed. Characterizations of a vague $q$-ideal are considered.

• 충청수학회지
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• 제25권2호
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• pp.241-251
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• 2012

The notion of an enlarged $q$-ideal and a fuzzy $q$-ideal in BCI-algebras with degree are introduced. Related properties of them are investigated.

• 호남수학학술지
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• 제29권2호
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• pp.289-297
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• 2007

In this paper, we show that BCI-algebras P and Q are injective if and only if its direct sum P $\oplus$ Q is injective. Moreover, we obtain the equivalent conditions for a p-semisimple BCI-algebra to be p-injective.

• Kyungpook Mathematical Journal
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• 제63권3호
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• pp.463-484
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• 2023

An examination is conducted on the multinomial coefficients derived from generalized quantum deformed algebras, and on their recurrence relations. The 𝓡(p, q)-deformed multinomial probability distribution and the negative 𝓡(p, q)-deformed multinomial probability distribution are constructed, and the recurrence relations are determined. From our general result, we deduce particular cases that correspond to quantum algebras considered in the literature.

• 대한수학회논문집
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• 제25권3호
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• pp.365-372
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• 2010

In this paper, we show that the mapping ${\varphi}(x)\;=\;0*x$ is an endomorphism of a Q-algebra X, which induces a congruence relation "~" such that X/$\varphi$ is a medial Q-algebra. We also study some decompositions of ideals in Q-algebras and obtain equivalent conditions for closed ideals. Moreover, we show that if I is an ideal of a Q-algebra X, then $I^g$ is an ignorable ideal of X.

• 대한수학회논문집
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• 제27권3호
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• pp.489-496
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• 2012

In this paper, we introduce the notions of Smarandache weak BE-algebra, Q-Smarandache filters and Q-Smarandache ideals. We show that a nonempty subset F of a BE-algebra X is a Q-Smarandache filter if and only if $A(x,y){\subseteq}F$, which A($x,y$) is a Q-Smarandache upper set The relationship between these notions are stated and proved.

• 호남수학학술지
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• 제36권3호
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• pp.623-635
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• 2014

Classications of (${\alpha},{\beta}$)-fuzzy subalgebras of BCK/BCI-algebras are discussed. Relations between (${\in},{\in}{\vee}q$)-fuzzy subalgebras and ($q,{\in}{\vee}q$)-fuzzy subalgebras are established. Given special sets, so called t-q-set and t-${\in}{\vee}q$-set, conditions for the t-q-set and t-${\in}{\vee}q$-set to be subalgebras are considered. The notions of $({\in},q)^{max}$-fuzzy subalgebra, $(q,{\in})^{max}$-fuzzy subalgebra and $(q,{\in}{\vee}q)^{max}$-fuzzy subalgebra are introduced. Conditions for a fuzzy set to be an $({\in},q)^{max}$-fuzzy subalgebra, a $(q,{\in})^{max}$-fuzzy subalgebra and a $(q,{\in}{\vee}q)^{max}$-fuzzy subalgebra are considered.

• 호남수학학술지
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• 제44권1호
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• pp.78-97
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• 2022

In this study, new properties of various filters on a Sheffer stroke BL-algebra are studied. Then some new results in filters of Sheffer stroke BL-algebras are given. Also, stabilizers of nonempty subsets of Sheffer stroke BL-algebras are defined and some properties are examined. Moreover, it is shown that the stabilizer of a filter with respect to a/n (ultra) filter of a Sheffer stroke BL-algebra is its (ultra) filter. It is proved that the stabilizer of the subset {0} of a Sheffer stroke BL-algebra is {1}. Finally, it is stated that the stabilizer St(P, Q) of P with respect to Q is an ultra filter of a Sheffer stroke BL-algebra when P is any filter and Q is an ultra filter of this algebra.

• 호남수학학술지
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• 제17권1호
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• pp.7-14
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• 1995

The purpose of this study is to construct the structure of the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$, which conforms to Stellmacher's [4] Pushing Up. The main idea of this paper comes from Stellmacher's [4] Pushing Up. Stelhnacher considered Pushing Up under a finite p-group. This paper, however, considers Pushing Up under the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$. In this paper, $O_p(G)$ in [4] is Q=exp(q), where q=nilrad(g) and a Sylow p-subgroup S in [7] is S=exp(s), where $s=q{\oplus}\{\(\array{0&*\\0&0}\){\mid}*{\in}\mathbb{F}\}$. Showing the properties of the connected Lie group and the subgroups of the connected Lie group with relations between a connected Lie group and its Lie algebras under the exponential map, this paper constructs the subgroup series C_z(G)