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.
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© 2009 Springer-Verlag Berlin Heidelberg
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Li, M., Feng, Y., Han, Y. (2009). Existence and Uniqueness of Anti-fuzzy Ideal. In: Cao, By., Zhang, Cy., Li, Tf. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88914-4_13
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DOI: https://doi.org/10.1007/978-3-540-88914-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88913-7
Online ISBN: 978-3-540-88914-4
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