• Title/Summary/Keyword: fuzzy k-ideal

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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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COINCIDENCES OF DIFFERENT TYPES OF FUZZY IDEALS IN ORDERED Γ-SEMIGROUPS

  • Kanlaya, Arunothai;Iampan, Aiyared
    • Korean Journal of Mathematics
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    • v.22 no.2
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    • pp.367-381
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    • 2014
  • The notion of ${\Gamma}$-semigroups was introduced by Sen in 1981 and that of fuzzy sets by Zadeh in 1965. Any semigroup can be reduced to a ${\Gamma}$-semigroup but a ${\Gamma}$-semigroup does not necessarily reduce to a semigroup. In this paper, we study the coincidences of fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy interior ideals and fuzzy ideals in regular, left regular, right regular, intra-regular, semisimple ordered ${\Gamma}$-semigroups.

EXTENSIONS OF FUZZY IDEALS IN NEAR-RINGS

  • Lee, Young Chan;Hur, Chang Kyu
    • Journal of the Chungcheong Mathematical Society
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    • v.10 no.1
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    • pp.1-7
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    • 1997
  • We characterize fuzzy ideals in near-rings and extensions of such ideals with the sup property.

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FUZZY IDEALS AND FUZZY SUBRINGS UNDER TRIANGULAR NORMS

  • Chon, Inheung
    • Korean Journal of Mathematics
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    • v.10 no.2
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    • pp.149-155
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    • 2002
  • We develop some basic properties of $t$-fuzzy ideals in a monoid or a group and find the sufficient conditions for a fuzzy set in a division ring to be a $t$-fuzzy subring and the necessary and sufficient conditions for a fuzzy set in a division ring to be a $t$-fuzzy ideal.

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ROUGH SET THEORY APPLIED TO INTUITIONISTIC FUZZY IDEALS IN RINGS

  • Jun, Young-Bae;Park, Chul-Hwan;Song, Seok-Zun
    • Journal of applied mathematics & informatics
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    • v.25 no.1_2
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    • pp.551-562
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    • 2007
  • This paper concerns a relationship between rough sets, intuitionistic fuzzy sets and ring theory. We consider a ring as a universal set and we assume that the knowledge about objects is restricted by an intuitionistic fuzzy ideal. We apply the notion of intutionistic fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring. Some properties of the lower and upper approximations are investigated.

INTUITIONISTIC FUZZY SEMIPRIME IDEALS OF ORDERED SEMIGROUPS

  • Kim, Kyung Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.2
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    • pp.235-243
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    • 2009
  • In this paper, we introduce the notion of intuitionistic fuzzy semiprimality in an ordered semigroup, which is an extension of fuzzy semiprimality and investigate some properties of intuitionistic fuzzification of the concept of several ideals.

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