• Title, Summary, Keyword: quasi-coincident with

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FUZZY SUBGROUPS BASED ON FUZZY POINTS

  • Jun, Young-Bae;Kang, Min-Su;Park, Chul-Hwan
    • Communications of the Korean Mathematical Society
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    • v.26 no.3
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    • pp.349-371
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    • 2011
  • Using the "belongs to" relation and "quasi-coincident with" relation between a fuzzy point and a fuzzy subgroup, Bhakat and Das, in 1992 and 1996, initiated general types of fuzzy subgroups which are a generalization of Rosenfeld's fuzzy subgroups. In this paper, more general notions of "belongs to" and "quasi-coincident with" relation between a fuzzy point and a fuzzy set are provided, and more general formulations of general types of fuzzy (normal) subgroups by Bhakat and Das are discussed. Furthermore, general type of coset is introduced, and related fundamental properties are investigated.

ON (α, β)-FUZZY SUBALGEBRAS OF BCK/ BCI-ALGEBRAS

  • Jun, Young-Bae
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.4
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    • pp.703-711
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    • 2005
  • Using the belongs to relation ($\in$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (${\alpha},\;{\beta}$)-fuzzy subalgebras where ${\alpha},\;{\beta}$ are any two of $\{\in,\;q,\;{\in}\;{\vee}\;q,\;{\in}\;{\wedge}\;q\}$ with $\;{\alpha}\;{\neq}\;{\in}\;{\wedge}\;q$ is introduced, and related properties are investigated.

MORE GENERALIZED FUZZY SUBSEMIGROUPS/IDEALS IN SEMIGROUPS

  • Khan, Muhammad Sajjad Ali;Abdullah, Saleem;Jun, Young Bi;Rahman, Khaista
    • Honam Mathematical Journal
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    • v.39 no.4
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    • pp.527-559
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    • 2017
  • The main motivation of this article is to generalized the concept of fuzzy ideals, (${\alpha},{\beta}$)-fuzzy ideals, (${\in},{\in}{\vee}q_k$)-fuzzy ideals of semigroups. By using the concept of $q^{\delta}_K$-quasi-coincident of a fuzzy point with a fuzzy set, we introduce the notions of (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy left ideal, (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy right ideal of a semigroup. Special sets, so called $Q^{\delta}_k$-set and $[{\lambda}^{\delta}_k]_t$-set, condition for the $Q^{\delta}_k$-set and $[{\lambda}^{\delta}_k]_t$-set-set to be left (resp. right) ideals are considered. We finally characterize different classes of semigroups (regular, left weakly regular, right weakly regular) in term of (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy left ideal, (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy right ideal and (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy ideal of semigroup S.

FUZZY SUBALGEBRAS WITH THRESHOLDS IN BCK/BCI-ALGEBRAS

  • Jun, Young-Bae
    • Communications of the Korean Mathematical Society
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    • v.22 no.2
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    • pp.173-181
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    • 2007
  • Using the belongs to relation ($\in$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of ($\alpha,\;\beta$)-fuzzy subalgebras where $\alpha,\;\beta$ are any two of $\{{\in},\;q,\;{\in}\;{\vee}\;q,\;{\in}\;{\wedge}\;q\}$ with ${\alpha}\;{\neq}\;{\in}\;{\wedge}\;q$ was introduced, and related properties were investigated in [3]. As a continuation of the paper [3], in this paper, the notion of a fuzzy subalgebra with thresholds is introduced, and its characterizations are obtained. Relations between a fuzzy subalgebra with thresholds and an (${\in},\;{\in}\;{\vee}\;q$)-fuzzy subalgebra are provided.

C*-compactness in L-Fuzzy Topological Spaces

  • Saad, Ali Kandil;Tantawy, Osama A. E.;Yakout, Mohammed Mostafa;Saleh, Salem Ali M.
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.9 no.4
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    • pp.261-268
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    • 2009
  • In this paper we introduce stronger form of the notion of cover so-called p-cover which is more appropriate. According to this cover we introduce and study another type of compactness in L-fuzzy topology so-called $C^*$-compact and study some of its properties with some interrelation.

Fuzzy Subalgebras of Type (α, β) in BCK/BCI-Algebras

  • Jun, Young Bae
    • Kyungpook Mathematical Journal
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    • v.47 no.3
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    • pp.403-410
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    • 2007
  • Using the belongs to relation (${\in}$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (${\alpha}$, ${\beta}$)-fuzzy subalgebras where ${\alpha}$ and ${\beta}$ areany two of {${\in}$, q, ${\in}{\vee}q$, ${\in}{\wedge}q$} with ${\alpha}{\neq}{\in}{\wedge}q$ was already introduced, and related properties were investigated (see [3]). In this paper, we give a condition for an (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra to be an (${\in}$, ${\in}$)-fuzzy subalgebra. We provide characterizations of an (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra. We show that a proper (${\in}$, ${\in}$)-fuzzy subalgebra $\mathfrak{A}$ of X with additional conditions can be expressed as the union of two proper non-equivalent (${\in}$, ${\in}$)-fuzzy subalgebras of X. We also prove that if $\mathfrak{A}$ is a proper (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra of a CK/BCI-algebra X such that #($\mathfrak{A}(x){\mid}\mathfrak{A}(x)$ < 0.5} ${\geq}2$, then there exist two prope non-equivalent (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebras of X such that $\mathfrak{A}$ can be expressed as the union of them.

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Moving Support Elements for Dynamic Finite Element Analysis of Statically Determinate Beams Subjected to Support Motions (지점운동을 받는 정정보의 동해석을 위한 동지점 유한요소 개발)

  • Kim, Yong-Woo;Jhung, Myung Jo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.37 no.4
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    • pp.555-567
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    • 2013
  • A finite element formulation for a Rayleigh-damped Bernoulli-Euler beam subjected to support motions, which accompanies quasi-static rigid-body motion, is presented by using the quasi-static decomposition method. Moving support beam elements, one of whose nodes is coincident with the moving support, are developed to represent the effect of a moving support. Statically determinate beams subjected to support motions can be modeled successfully by using moving support elements. Examples of cantilever and simply-supported beams subjected to support motions are illustrated, and the numerical results are compared with the analytical solutions. The comparison shows good agreement.