• Title/Summary/Keyword: prime fuzzy ideal

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Fuzzy Prime Ideals of Pseudo- ŁBCK-algebras

  • Dymek, Grzegorz;Walendziak, Andrzej
    • Kyungpook Mathematical Journal
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    • v.55 no.1
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    • pp.51-62
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    • 2015
  • Pseudo-ŁBCK-algebras are commutative pseudo-BCK-algebras with relative cancellation property. In the paper, we introduce fuzzy prime ideals in pseudo-ŁBCK-algebras and investigate some of their properties. We also give various characterizations of prime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo-ŁBCKalgebra to be a pseudo-ŁBCK-chain.

INTUITIONISTIC FUZZY FILTERS OF ORDERED SEMIGROUPS

  • Shabir, M.;Khan, A.
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.1071-1084
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    • 2008
  • The notion of intuitionistic fuzzy filters in ordered semigroups is introduced and relation between intuitionistic fuzzy filters and intuitionistic fuzzy prime ideals is investegated. The notion of intuitionistic fuzzy bi-ideal subsets and intuitionistic fuzzy bi-filters are provided and relation between intuitionistic fuzzy bi-filters and intuitionistic fuzzy prime bi-ideal subsets is established. The concept of intuitionistic fuzzy right filters(1eft filters) is given and their relation with intuitionistic fuzzy prime right (left) ideals is discussed.

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𝛽-FUZZY FILTERS OF STONE ALMOST DISTRIBUTIVE LATTICES

  • ALEMAYEHU, TEFERI GETACHEW;GUBENA, YESHIWAS MEBRAT
    • Journal of applied mathematics & informatics
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    • v.40 no.3_4
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    • pp.445-460
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    • 2022
  • In this paper, we studied on 𝛽-fuzzy filters of Stone almost distributive lattices. An isomorphism between the lattice of 𝛽-fuzzy filters of a Stone ADL A onto the lattice of fuzzy ideals of the set of all boosters of A is established. The fact that any 𝛽-fuzzy filter of A is an e-fuzzy filter of A is proved. We discuss on some properties of prime 𝛽-fuzzy filters and some topological concepts on the collection of prime 𝛽-fuzzy filters of a Stone ADL. Further we show that the collection 𝓣 = {X𝛽(λ) : λ is a fuzzy ideal of A} is a topology on 𝓕Spec𝛽(A) where X𝛽(λ) = {𝜇 ∈ 𝓕Spec𝛽(A) : λ ⊈ 𝜇}.

FUZZY MULTIPLICATION RINGS

  • Lee, Dong-Soo;Park, Chul-Hwan;Kim, Jong-Heon
    • East Asian mathematical journal
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    • v.21 no.2
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    • pp.183-190
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    • 2005
  • We will introduce the notion of fuzzy multiplication ring using fuzzy ideal. In this paper we will show that a fuzzy ideal I is primary if radI is prime. And we will investigate some properties related the theorem.

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QUOTIENT RINGS INDUCED VIA FUZZY IDEALS

  • Liu, Yong-Lin;Meng, Jie;Xin, Xiao-Long
    • Journal of applied mathematics & informatics
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    • v.8 no.3
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    • pp.855-867
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    • 2001
  • This note we give a construction of a quotient ring $R/{\mu}$ induced via a fuzzy ideal ${\mu}$ in a ring R. The Fuzzy First, Second and Third Isomorphism Theorems are established. For some applications of this construction of quotient rings, we show that if ${\mu}$ is a fuzzy ideal of a commutative ring R, then $\mu$ is prime (resp. $R/{\mu}$ is a field, every zero divisor in $R/{\mu}$ is nilpotent). Moreover we give a simpler characterization of fuzzy maximal ideal of a ring.

The Fuzzy Jacobson Radical of a κ-Semiring

  • Kim, Chang-Bum
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.3
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    • pp.423-429
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    • 2007
  • We define and study the fuzzy Jacobson radical of a ${\kappa}$-semiring. Also it is shown that the Jacobson radical of the quotient semiring R/FJR(R) of a ${\kappa}$-semiring by the fuzzy Jacobson radical FJR(R) is semisimple. And the algebraic properties of the fuzzy ideals FJR(R) and FJR(S) under a homomorphism from R onto S are also discussed.

CLOSURE FILTERS AND PRIME FUZZY CLOSURE FILTERS OF MS-ALGEBRAS

  • Noorbhasha, Rafi;Bandaru, Ravikumar;Shum, Kar Ping
    • Korean Journal of Mathematics
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    • v.28 no.3
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    • pp.509-524
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    • 2020
  • The notion of fuzzy closure filters is introduced and discussed in an MS-algebra. In particular, we characterize the prime fuzzy closure filters in terms of boosters. Some relationship between the lattice of fuzzy closure filters and the fuzzy ideal lattice of boosters are explored and investigated.