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Rough prime ideals and rough fuzzy prime ideals in semigroups
Information Sciences, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qi-Mei Xiao, Zhen-Liang Zhang
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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, Xiao Long Xin 0001
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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]
Flaulles Boone Bergamaschi +1 more
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Fuzzy prime ideals and prime fuzzy ideals
Fuzzy Sets and Systems, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fuzzy prime ideals and fuzzy radical ideals
Information Sciences, 1990Abstract Some properties of the fuzzy prime ideals and radical ideals are studied. Also we study the structure of fuzzy principal ideals.
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2003
In this chapter, we characterize prime fuzzy ideals of a semigroup S. Sections 7.1–7.11 are essentially from [151]. We show that a nonconstant fuzzy ideal f of a semigroup S is prime if and only if f is two-valued and there exists an element x0 in S such that f(x0) = 1 and f1 = {x ∈ S | f(x) = 1} is a prime ideal of S.
John N. Mordeson +2 more
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In this chapter, we characterize prime fuzzy ideals of a semigroup S. Sections 7.1–7.11 are essentially from [151]. We show that a nonconstant fuzzy ideal f of a semigroup S is prime if and only if f is two-valued and there exists an element x0 in S such that f(x0) = 1 and f1 = {x ∈ S | f(x) = 1} is a prime ideal of S.
John N. Mordeson +2 more
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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 0002
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FUZZY PRIME IDEALS OF A SEMIRING AND FUZZY PRIME SUB-SEMIMODULES OF A SEMIMODULE OVER A SEMIRING [PDF]
New Mathematics and Natural Computation, 2006 In this paper we define fuzzy prime right ideals and fuzzy prime subsemimodules of a right R-semimodule. We characterize those semirings for which each fuzzy ideal is prime and those semirings for which each fuzzy right ideal is prime.
J. AHSAN, K. SAIFULLAH, M. SHABIR
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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.
Flaulles Boone Bergamaschi +1 more
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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 +2 more
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