• Title/Summary/Keyword: prime fuzzy ideal

Search Result 25, Processing Time 0.02 seconds

SOME RESULTS ON FUZZY COSETS AND HOMOMORPHISMS OF N-GROUPS

  • Satyanarayana, Bhavanari;Syam Prasad, Kuncaham;Venkata Pradeep Kumar, Tumurukora;Thota, Srinivas
    • East Asian mathematical journal
    • /
    • v.23 no.1
    • /
    • pp.23-36
    • /
    • 2007
  • In this paper we consider the fuzzy ideals of N-group G where N is a nearring. We introduce fuzzy ideal ${\theta}_{\mu}$ of the quotient N-group $G/{\mu}$ with respect to a fuzzy ideal $\mu$ of G. If $\mu$ is a fuzzy ideal of G and $\theta$ a fuzzy ideal of $G/{\mu}$ such that ${\theta}_{\mu}\;{\subseteq}\;{\theta}$ and ${\theta}_{\mu}(0)\;=\;{\theta}(0)$, then corresponding ${\sigma}_{\theta}\;:\;G\;{\rightarrow}\;[0,\;1]$ is defined and proved that it is a fuzzy ideal of G such that ${\mu}\;{\subseteq}\;{\sigma}_{\theta}$ and ${\mu}(0)\;=\;{\sigma}_{\theta}(0)$. We also prove some results on homomorphisms and fuzzy ideals of N-groups. The image and preimage of fuzzy ideal $\mu$ under N-group homomorphism were studied. Finally it is obtained that if $f\;:\;G\;{\rightarrow}\;G^1$ is an epimorphism of N-groups, then there is an order preserving bijection between the fuzzy ideals of $G^1$ and the fuzzy ideals of G that are constant on kerf. Some examples related to these concepts were illustrated.

  • PDF

Semiprime and Semiprimary Fuzzy Ideals

  • Jeong, Tae-Eun
    • Journal of the Korean Institute of Intelligent Systems
    • /
    • v.9 no.5
    • /
    • pp.509-512
    • /
    • 1999
  • We study semiprime fuzzy ideals semiprimary fuzzy ideals and their properties. We investigate that if a fuzzy ideal is semiprime and semiprimary then it is prime.

  • PDF

ON INTUITIONISTIC FUZZY PRIME ${\Gamma}$-IDEALS OF ${\Gamma}$-LA-SEMIGROUPS

  • Abdullah, Saleem;Aslam, Muhammad
    • Journal of applied mathematics & informatics
    • /
    • v.30 no.3_4
    • /
    • pp.603-612
    • /
    • 2012
  • In this paper, we introduce and study the intuitionistic fuzzy prime (semi-prime) ${\Gamma}$-ideals of ${\Gamma}$-LA-semigroups and some interesting properties are investigated. The main result of the paper is: if $A={\langle}{\mu}_A,{\gamma}_A{\rangle}$ is an IFS in ${\Gamma}$-LA-semigroup S, then $A={\langle}{\mu}_A,{\gamma}_A{\rangle}$ is an intuitionistic fuzzy prime (semi-prime) ${\Gamma}$-ideal of S if and only if for any $s,t{\in}[0,1]$, the sets $U({\mu}_A,s)=\{x{\in}S:{\mu}_A(x){\geq}s\}$ and $L({\gamma}_A,t)=\{x{\in}S:{\gamma}_A(x){\leq}t\}$ are prime (semi-prime) ${\Gamma}$-ideals of S.

FUZZY IDEALS IN NEAR-RINGS

  • Hong, Sung-Min;Jun, Young-Bae;Kim, Hee-Sik
    • Bulletin of the Korean Mathematical Society
    • /
    • v.35 no.3
    • /
    • pp.455-464
    • /
    • 1998
  • In this paper, we give another proof of Theorem 2.13 of [4] without using the sup property. For the homomorphic image $f(\mu)$ and preimage $f^{-1}(\nu)$ of fuzzy left (resp. right) ideals $\mu$ and $\nu$ respectively, we establish the chains of level left (resp. right) ideals of $f(\mu)$ and $f^{-1}(\nu)$, respectively. Moreover, we prove that a necessary condition for a fuzzy ideal $\mu$ of a near-ring $R$ to be prime is that $\mu$ is two-valued.

  • PDF

𝛽-FUZZY FILTERS IN MS-ALGEBRAS

  • Alaba, Berhanu Assaye;Alemayehu, Teferi Getachew
    • Korean Journal of Mathematics
    • /
    • v.27 no.3
    • /
    • pp.595-612
    • /
    • 2019
  • In this paper, we introduce the concept of ${\beta}$-fuzzy filters in MS-algebras and ${\beta}$-fuzzy filters are characterized in terms of boosters. It is proved that the lattice of ${\beta}$-fuzzy filters is isomorphic to the fuzzy ideal lattice of boosters.