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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), 2015
The 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, Regivan H. N. Santiago   +1 more
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Prime Fuzzy Ideals, Completely Prime Fuzzy Ideals of Po-$$\Gamma $$-Semigroups Based on Fuzzy Points

2015
Using 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, Sujit Kumar Sardar, Rajlaxmi Mukherjee Pal   +2 more
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CO - FUZZY BI-IDEALS AND CO - FUZZY PRIME IDEALS OF A FINITE Г- NEAR RINGS

Strad Research, 2021

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Prime and primary L-fuzzy ideals of L-fuzzy rings

Fuzzy Sets and Systems, 1999
This 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, 2014
proposed 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, Regivan H.N. Santiago   +1 more
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Fuzzy prime ideals of pseudo-MV algebras

Soft Computing, 2007
Pseudo-MV algebras, as a non-commutative generalization of MV-algebras, are an algebraic counterpart of the non-commutative Łukasiewicz infinite-valued propositional logic. The paper deals with fuzzy ideals of pseudo-MV algebras. The author gives a new construction of the fuzzy ideal generated by a fuzzy set of a pseudo-MV algebra. Further, fuzzy prime
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On Prime Hesitant Fuzzy Ideals in Semigroups

2022
Theory of hesitant fuzzy sets is an important tool in algebraic systems, fuzzy sets theory, partially ordered sets, data mining, etc. The aim of this chapter is to apply prime hesitant fuzzy ideal for dealing with several kinds of theories in semigroups. The concepts of prime hesitant fuzzy, weakly prime hesitant fuzzy, completely prime hesitant fuzzy,
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On prime, quasi-prime, weakly quasi-prime fuzzy left ideals of semigroups

Fuzzy Sets and Systems, 2001
First the author introduces the concepts of a fuzzy left (right) ideal of a semigroup. Then the concept of a prime fuzzy left ideal is introduced and characterized in terms of fuzzy singletons. It is shown that this prime notion is a natural fuzzification of the crisp notion.
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ON PRIME FUZZY BI-IDEALS OF SEMIGROUPS

2010
In this paper, we introduce and study the prime, strongly prime, semiprime and irreducible fuzzy bi-ideals of a semigroup. We characterize those semigroups for which each fuzzy bi-ideal is semiprime. We also characterize those semigroups for which each fuzzy bi-ideal is strongly prime.
Shabir, Muhammad, Jun, Young Bae, Bano, Mahwish   +2 more
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