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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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2018 6th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS), 2018
In this paper, we offer a general prime fuzzy ideal principle for proving that certain fuzzy ideals of a commutative ring are prime. For this purpose, we introduce the concepts of Ako and Oka for some families of fuzzy ideals of a commutative ring and then by these concepts, we can state some familiar results of commutative algebra in fuzzy case. Also,
Esmaeil Rostami, Azadeh Rajabi Khabisi
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In this paper, we offer a general prime fuzzy ideal principle for proving that certain fuzzy ideals of a commutative ring are prime. For this purpose, we introduce the concepts of Ako and Oka for some families of fuzzy ideals of a commutative ring and then by these concepts, we can state some familiar results of commutative algebra in fuzzy case. Also,
Esmaeil Rostami, Azadeh Rajabi Khabisi
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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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Fuzzy rough prime and semi-prime ideals in semigroups
AIP Conference Proceedings, 2019The purpose of this paper is to introduce the concept of fuzzy rough prime ideals and fuzzy rough semi-prime ideals in semigroups. Some results based on fuzzy rough prime and fuzzy rough semi-prime ideals are established.The purpose of this paper is to introduce the concept of fuzzy rough prime ideals and fuzzy rough semi-prime ideals in semigroups ...
V. S. Subha +2 more
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Spectrum of prime fuzzy ideals
Fuzzy Sets and Systems, 1994An attempt has been made to introduce an appropriate topology on the set of prime fuzzy ideals. Instead of appealing to other definitions of prime fuzzy ideals, as in literature, the author has taken his own definition introduced earlier; such prime fuzzy ideals in a commutative ring \(R\) with identity are denoted by \(F \text{spec} (R)\); the author ...
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Prime L-fuzzy ideals and primary L-fuzzy ideals
Fuzzy Sets and Systems, 1988The author introduces the concepts of a primary L-fuzzy ideal and a primary L-fuzzy ideal belonging to a prime L-fuzzy ideal where L is a complete distributive lattice. Let A be an L-fuzzy ideal of a ring X and \(X_ A=\{x\in X| A(x)=A(0)\}\). A is called prime if for \(a,b\in X\), \(A(ab)=A(0)\) implies \(A(a)=A(0)\) or \(A(b)=A(0)\).
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Prime and primary L-fuzzy ideals of L-fuzzy rings
Fuzzy Sets and Systems, 1999This paper elaborates on the earlier introduced concept of a fuzzy ideal of an \(L\)-fuzzy ring where \(L\) denotes a totally distributive bounded lattice. More concretely the following notions are (re-)introduced in this framework: fuzzy prime ideal, primary fuzzy ideal and fuzzy radical of a fuzzy ideal.
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THE STRONGLY PRIME RADICAL OF A FUZZY IDEAL
Decision Making and Soft Computing, 2014proposed Strongly PrimeFuzzy(SP) ideals for commutative and noncommutative rings with unity, andinvestigated their properties. This paper goes a step further since it providesthe concept of Strongly Prime Radical of a fuzzy ideal and its propertiesare investigated. It is shown that Zadeh’s extension preserves strongly primeradicals.
Flaulles B. Bergamaschi +1 more
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