• Title/Summary/Keyword: Fuzzy ideal

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FUZZY MULTIPLICATION RINGS

  • Lee, Dong-Soo;Park, Chul-Hwan;Kim, Jong-Heon
    • East Asian mathematical journal
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    • v.21 no.2
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    • pp.183-190
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    • 2005
  • We will introduce the notion of fuzzy multiplication ring using fuzzy ideal. In this paper we will show that a fuzzy ideal I is primary if radI is prime. And we will investigate some properties related the theorem.

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FSI-IDEALS AND FSC-IDEALS OF BCI-ALGEBRAS

  • Liu, Yong-Lin;Liu, San-Yang;Meng, Jie
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.1
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    • pp.167-179
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    • 2004
  • The notions of FSI-ideals and FSC-ideals in BCI-algebras are introduced. The characterization properties of FSI-ideals and FSC-ideals are obtained. We investigate the relations between FSI-ideals (resp. FSC-ideals) and other fuzzy ideals, between FSI-ideals (resp. FSC-ideals) and BCI-algebras, and show that a fuzzy subset of a BCI-algebra is an FSI-ideal if and only if it is both an FSC-ideal and a fuzzy BCI-positive implicative ideal.

𝛿;-FUZZY IDEALS IN PSEUDO-COMPLEMENTED DISTRIBUTIVE LATTICES

  • ALABA, BERHANU ASSAYE;NORAHUN, WONDWOSEN ZEMENE
    • Journal of applied mathematics & informatics
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    • v.37 no.5_6
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    • pp.383-397
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    • 2019
  • In this paper, we introduce ${\delta}$-fuzzy ideals in a pseudo complemented distributive lattice in terms of fuzzy filters. It is proved that the set of all ${\delta}$-fuzzy ideals forms a complete distributive lattice. The set of equivalent conditions are given for the class of all ${\delta}$-fuzzy ideals to be a sub-lattice of the fuzzy ideals of L. Moreover, ${\delta}$-fuzzy ideals are characterized in terms of fuzzy congruences.

Intuitionistic Fuzzy Bi-ideals of Ordered Semigroups

  • Jun, Young Bae
    • Kyungpook Mathematical Journal
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    • v.45 no.4
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    • pp.527-537
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    • 2005
  • The intuitionistic fuzzification of the notion of a bi-ideal in ordered semigroups is considered. In terms of intuitionistic fuzzy set, conditions for an ordered semigroup to be completely regular is provided. Characterizations of intuitionistic fuzzy bi-ideals in ordered semigroups are given. Using a collection of bi-ideals with additional conditions, an intuitionistic fuzzy bi-ideal is constructed. Natural equivalence relations on the set of all intuitionistic fuzzy bi-ideals of an ordered semigroup are investigated.

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FALLING SUBALGEBRAS AND IDEALS IN BH-ALGEBRAS

  • Kim, Eun-Mi;Ahn, Sun-Shin
    • The Pure and Applied Mathematics
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    • v.19 no.3
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    • pp.251-262
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    • 2012
  • Based on the theory of a falling shadow which was first formulated by Wang([14]), a theoretical approach of the ideal structure in BH-algebras is established. The notions of a falling subalgebra, a falling ideal, a falling strong ideal, a falling $n$-fold strong ideal and a falling translation ideal of a BH-algebra are introduced. Some fundamental properties are investigated. Relations among a falling subalgebra, a falling ideal and a falling strong ideal, a falling $n$-fold strong ideal are stated. A relation between a fuzzy subalgebra/ideal and a falling subalgebra/ideal is provided.

STRONGLY PRIME FUZZY IDEALS AND RELATED FUZZY IDEALS IN AN INTEGRAL DOMAIN

  • Kim, Myeong Og;Kim, Hwankoo
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.333-351
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    • 2009
  • We introduce the concepts of strongly prime fuzzy ideals, powerful fuzzy ideals, strongly primary fuzzy ideals, and pseudo-strongly prime fuzzy ideals of an integral domain R and we provide characterizations of pseudo-valuation domains, almost pseudo-valuation domains, and pseudo-almost valuation domains in terms of these fuzzy ideals.

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Interval-Valued Fuzzy Ideals of a Ring

  • Lee, Keon-Chang;Hur, Kul;Lim, Pyung-Ki
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.12 no.3
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    • pp.198-204
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    • 2012
  • We introduce the notions of interval-valued fuzzy prime ideals, interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals. And we give a characterization of interval-valued fuzzy ideals and establish relationships between interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals.