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Uniformly strongly prime fuzzy ideals
2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2014In this paper we define the concept of uniformly strongly prime fuzzy ideal for associative rings with unity. This concept is proposed without dependence of level cuts. We show a pure fuzzy demonstration that all uniformly strongly prime fuzzy ideals are a prime fuzzy ideal according to the newest definition given by Navarro, Cortadellas and Lobillo [1]
F. Bergamaschi, R. Santiago
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Fuzzy ideals and fuzzy prime ideals of a ring
Fuzzy Sets and Systems, 1991Firstly, the authors focus on the generalization of the well-known classical property: the union of two ideals of a ring is again an ideal iff one of them is contained in the other. By means of a counterexample it is proven that this property does not hold in general for fuzzy ideals.
Naseem Ajmal
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A characterization of L-fuzzy prime ideals
Fuzzy Sets and Systems, 1991A definition is given for the concept of an \(L\)-fuzzy prime ideal that is more restrictive than the concept introduced by \textit{Y. Zhang} [ibid. 27, 345-350 (1988; Zbl 0663.13001)]. The new definition is based on the concept of an \(L\)-fuzzy point, where even the value zero is allowed, which means that the \(L\)-fuzzy set \(\phi: X\to \{0\}\) is ...
M M Zahedi
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Fuzzy prime ideals and invertible fuzzy ideals in BCK-algebras
Fuzzy Sets and Systems, 2001Let \(\mu\) and \(\nu\) be fuzzy ideals of a commutative BCK-algebra \(X\). \(\mu\) is called prime iff it is non-constant and \(\mu(x\wedge y)=\max\{\mu(x), \mu(y)\}\) for all \(x,y\in X\). If \(\nu^+ (x)=1-\inf\{\nu(y) |y\wedge x=0\}\) is a fuzzy ideal of \(X\), then \(\nu\) is called invertible.
Young Bae Jun
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On properties of Uniformly Strongly Prime fuzzy ideals
2015 Annual Conference of the North American Fuzzy Information Processing Society (NAFIPS) held jointly with 2015 5th World Conference on Soft Computing (WConSC), 2015The main purpose of this paper is to continue the study of uniform strong primeness in fuzzy setting started in 2014. A pure fuzzy notion of this structure allows us to develop specific fuzzy results on Uniformly Strongly Prime (USP) ideals over commutative and noncommutative rings.
F. Bergamaschi, R. Santiago
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Fuzzy Sets and Systems, 1990
Abstract This paper characterizes all fuzzy prime ideals P of an arbitrary ring R. We show that a nonconstant fuzzy ideal P of R is prime if and only if P0 ={;x ϵ R: P(x) = P(0)}; is a prime ideal of R, P is two-valued, and P(0) = 1. Examples are given showing that P0 is a prime ideal is not sufficient for P to be a fuzzy prime ideal and that P0 may ...
A.S. Malik, John N. Mordeson
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Abstract This paper characterizes all fuzzy prime ideals P of an arbitrary ring R. We show that a nonconstant fuzzy ideal P of R is prime if and only if P0 ={;x ϵ R: P(x) = P(0)}; is a prime ideal of R, P is two-valued, and P(0) = 1. Examples are given showing that P0 is a prime ideal is not sufficient for P to be a fuzzy prime ideal and that P0 may ...
A.S. Malik, John N. Mordeson
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Prime Fuzzy Ideals, Completely Prime Fuzzy Ideals of Po-\Gamma -Semigroups Based on Fuzzy Points
, 2015Using fuzzy points the notions of prime fuzzy ideals, weakly prime fuzzy ideals, completely prime fuzzy ideals, and weakly completely prime fuzzy ideals of a po-\(\Gamma \)-semigroup have been introduced. Some important properties and characterizations of these ideals have been obtained.
Pavel Pal, S. Sardar, R. Pal
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Fuzzy radicals and prime fuzzy ideals of ordered semigroups
Information Sciences, 2008Let \(S\) be an ordered semigroup, \(f\) a fuzzy subset of \(S\) and \(t\in [0,1]\). Then, the set \(f_t:=\{x\in S\mid f(x)\geq t\}\) is called the level subset of \(f\) (introduced by the same authors in an earlier paper). The authors prove first that a fuzzy subset of \(S\) is a fuzzy ideal of \(S\) if and only if the level subset of \(f\), if it is ...
Xiang-Yun Xie, Jian Tang
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Equiprime, 3-prime and c-prime fuzzy ideals of nearrings
Soft Computing, 2009The notion of primeness for fuzzy ideals of near-rings is not new, but the approach of the authors to this topic is in the sense that they deal with fuzzy ideals with thresholds. This opens up more possibilities and leads to a wider and more interesting class of examples.
B. S. Kedukodi, S. Kuncham, S. Bhavanari
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Information Sciences, 2008 This paper is a continuation of ideas presented by Davvaz [Roughness in rings, Inform. Sci., 164 (2004) 147-163; Roughness based on fuzzy ideals, Inform. Sci., 176 (2006) 2417-2437].
Osman Kazanci, Bijan Davvaz
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