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Existence and Uniqueness of Anti-fuzzy Ideal

  • Min Li
  • Yanping Feng
  • Ying Han
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 54)

Abstract

Let S ⊆ [0,1] satisfying \(\underline{s}=infS\in S \) and C = {I t |t ∈ S} be an ascending chain of ideals in commutative ring R . This article presented and studied the following problem:

(1) Whether is there an anti-fuzzy ideal μ of R such that μ(R) = {μ(x)| x ∈ R}= S and \(C_{\mu}=\{\mu^{t}|t\in\mu(R)\}=C\) ?

(2) If the anti-fuzzy ideal satisfying (1) exists, then whether is it unique ? We built theorems of existence and uniqueness of anti-fuzzy ideal.

Keywords

Anti-fuzzy ideal order-isomorphic cut set 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Min Li
    • 1
  • Yanping Feng
    • 2
  • Ying Han
    • 3
  1. 1.School of Mathematics and Quantitative EconomicsDongbei University of Finance and EconomicsDalianP.R. China
  2. 2.School of MathematicsLiaoning Normal UniversityDalianChina
  3. 3.Department of Mathematics and ComputerChaoyang Teacher’s CollegeDalianP.R. China

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