• Title, Summary, Keyword: lattice ideal

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LI-ideals in lattice implication algebras

  • Jun, Young-Bae;Roh, Eun-Hwan;Yang Xu
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.13-24
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    • 1998
  • We define an LI-ideal of a lattice implication algebra and show that every LI-ideal is a lattice ideal. We give an exampl that a lattice ideal may not be an LI-ideal, and show that every lattice ideal is an LI-ideal in a lattice H implication algebra. we discuss the relationship between filters and LI-ideals, and study how to generate an LI-ideal by a set. We construct the quotient structure by using an LI-ideal, and study the properties of LI-ideals related to implication homomorphisms.

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FUZZY LATTICES

  • Chon, Inheung
    • Korean Journal of Mathematics
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    • v.16 no.3
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    • pp.403-412
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    • 2008
  • We define the operations ${\vee}$ and ${\wedge}$ for fuzzy sets in a lattice, characterize fuzzy sublattices in terms of ${\vee}$ and ${\wedge}$, develop some properties of the distributive fuzzy sublattices, and find the fuzzy ideal generated by a fuzzy subset in a lattice and the fuzzy dual ideal generated by a fuzzy subset in a lattice.

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ON LI-IDEALS AND PRIME LI-IDEALS OF LATTICE IMPLICATION ALGEBRAS

  • Jun, Young-Bae
    • Journal of the Korean Mathematical Society
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    • v.36 no.2
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    • pp.369-380
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    • 1999
  • As a continuation of the paper [3], in this paper we investigate the further properties on LI-ideals, and show that how to generate an LI-ideal by both and LI-ideal and an element. We define a prime LI-ideal, and give an equivalent condition for a proper LI-ideal to be prime. Using this result, we establish the extension property and prime LI-ideal theorem.

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𝛿;-FUZZY IDEALS IN PSEUDO-COMPLEMENTED DISTRIBUTIVE LATTICES

  • ALABA, BERHANU ASSAYE;NORAHUN, WONDWOSEN ZEMENE
    • Journal of applied mathematics & informatics
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    • v.37 no.5_6
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    • pp.383-397
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    • 2019
  • In this paper, we introduce ${\delta}$-fuzzy ideals in a pseudo complemented distributive lattice in terms of fuzzy filters. It is proved that the set of all ${\delta}$-fuzzy ideals forms a complete distributive lattice. The set of equivalent conditions are given for the class of all ${\delta}$-fuzzy ideals to be a sub-lattice of the fuzzy ideals of L. Moreover, ${\delta}$-fuzzy ideals are characterized in terms of fuzzy congruences.

L-fuzzy ideals of a poset

  • Alaba, Berhanu Assaye;Taye, Miheret Alamneh;Engidaw, Derso Abeje
    • Annals of Fuzzy Mathematics and Informatics
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    • v.16 no.3
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    • pp.285-299
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    • 2018
  • Many generalizations of ideals of a lattice to an arbitrary poset have been studied by different scholars. In this paper, we introduce several L-fuzzy ideals of a poset which generalize the notion of an L-fuzzy ideal of a lattice and give several characterizations of them.

Remarks on the Valid Equations in Lattice Implication Algebras

  • JEONG, JOOHEE
    • Kyungpook Mathematical Journal
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    • v.43 no.4
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    • pp.539-545
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    • 2003
  • We present a set of equations that axiomatizes the class of all lattice implication algebras. The construction is different from the one given in [7], and the proof is direct: i.e., it does not rely on results from outside the realm of the lattice implication algebras, such as the theory of BCK-algebras. Then we show that the lattice H implication algebras are nothing more than the familiar Boolean algebras. Finally we obtain some negative results for the embedding of lattice implication algebras into Boolean algebras.

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ON INTERVAL-VALUED FUZZY LATTICES

  • LEE, JEONG GON;HUR, KUL;LIM, PYUNG KI
    • Honam Mathematical Journal
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    • v.37 no.2
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    • pp.187-205
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    • 2015
  • We discuss the relationship between interval-valued fuzzy ideals and interval-valued fuzzy congruence on a distributive lattice L and show that for a generalized Boolean algebra the lattice of interval-valued fuzzy ideals is isomorphic to the lattice of interval-valued fuzzy congruences. Finally we consider the products of interval-valued fuzzy ideals and obtain a necessary and sufficient condition for an interval-valued fuzzy ideal on the direct sum of lattices to be representable as a direct sum of interval-valued fuzzy ideals on each lattice.

Development of Effective Stiffness and Effective Strength for a Truss-Wall Rectangular model combined with Micro-Lattice Truss (트러스 벽면과 미세격자 트러스로 구성된 정육면체 단위모델의 강성 및 강도 개발)

  • Choi, Jeong-Ho
    • Journal of the Korean Society of Industry Convergence
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    • v.19 no.3
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    • pp.133-143
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    • 2016
  • The objective in here is to find the density, stiffness, and strength of truss-wall rectangular (TWR) model which is combined with lattice truss (MLT) inside space. The TWR unit-cell model is defined as a unit cell originated from a solid-wall rectangular (SWR) model and it has an empty space inside. Thus, the empty space inside of the TWR is filled with lattice truss model defined as TWR-MLT. The ideal solutions derived of TWR-MLT are based on TWR with MLT model and it has developed by Gibson-Ashby's theory. To validate the ideal solutions of the TWR-MLT, ABAQUS software is applied to predict the density, strength, and stiffness, and then each of them are compared with the Gibson-Ashby's ideal solution as a log-log scale. Applied material property is stainless steel 304 because of cost effectiveness and easy to get around. For the analysis, SWR and TWR-MLT models are 1mm, 2mm, and 3mm truss diameter separately within a fixed 20mm opening width. In conclusion, the relative Young's modulus and relative yield strength of the TWR-MLT unit model is reasonably matched to the ideal expectations of the Gibson-Ashby's theory. In nearby future, TWR-MLT model can be verified by advanced technologies such as 3D printing skills.t.

THE LATTICE OF INTERVAL-VALUED FUZZY IDEALS OF A RING

  • Lee, Keon-Chang;Hur, Kul;Lim, Pyung-Ki
    • Honam Mathematical Journal
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    • v.34 no.3
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    • pp.351-373
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    • 2012
  • We investigate the lattice structure of various sublattices of the lattice of interval-valued fuzzy subrings of a given ring. We prove that a special class of interval-valued fuzzy ideals of a ring. Finally, we show that the lattice of interval-valued fuzzy ideals of R is not complemented[resp. has no atoms(dual atoms)].

RESOLUTION OF UNMIXED BIPARTITE GRAPHS

  • Mohammadi, Fatemeh;Moradi, Somayeh
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.3
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    • pp.977-986
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    • 2015
  • Let G be a graph on the vertex set $V(G)=\{x_1,{\cdots},x_n\}$ with the edge set E(G), and let $R=K[x_1,{\cdots},x_n]$ be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials $x_i,x_j$ with $\{x_i,x_j\}{\in}E(G)$, and the vertex cover ideal $I_G$ generated by monomials ${\prod}_{x_i{\in}C}{^{x_i}}$ for all minimal vertex covers C of G. A minimal vertex cover of G is a subset $C{\subset}V(G)$ such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers $L_G$ and we explicitly describe the minimal free resolution of the ideal associated to $L_G$ which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice.