• Title/Summary/Keyword: interval-valued fuzzy left(right) ideal

Search Result 4, Processing Time 0.018 seconds

Interval-valued Fuzzy Ideals and Bi-ideals of a Semigroup

  • Cheong, Min-Seok;Hur, Kul
    • International Journal of Fuzzy Logic and Intelligent Systems
    • /
    • v.11 no.4
    • /
    • pp.259-266
    • /
    • 2011
  • We apply the concept of interval-valued fuzzy sets to theory of semigroups. We give some properties of interval-valued fuzzy ideals and interval-valued fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of interval-valued fuzzy ideals and intervalvalued fuzzy bi-ideals.

INTERVAL-VALUED FUZZY IDEALS GENERATED BY AN INTERVAL-VALUED FUZZY SUBSET IN SEMIGROUPS

  • NARAYANAN AL.;MANIKANTAN T.
    • Journal of applied mathematics & informatics
    • /
    • v.20 no.1_2
    • /
    • pp.455-464
    • /
    • 2006
  • In this paper, we introduce the concept of an interval-valued fuzzy left (right, two-sided, interior, bi-) ideal generated by an interval-valued fuzzy subset in semigroups. Some characterizations of such generated interval-valued fuzzy ideals are also discussed.

Interval-valued Fuzzy Quasi-ideals in a Semigroups

  • Kim, Sang-Mok;Hur, Kul;Cheong, Min-Seok;Chae, Gab-Byung
    • International Journal of Fuzzy Logic and Intelligent Systems
    • /
    • v.12 no.3
    • /
    • pp.215-225
    • /
    • 2012
  • We initiate the study of interval-valued fuzzy quasi-ideal of a semigroup. In Section 2, we list some basic definitions in the later sections. In Section 3, we investigate interval-valued fuzzy subsemigroups and in Section 4, we define interval-valued fuzzy quasi-ideals and establish some of their basic properties. In Section 5, we obtain characterizations of regular and intraregular semigroups using the machinery developed in the preceding sections.

THE LATTICE OF INTERVAL-VALUED FUZZY IDEALS OF A RING

  • Lee, Keon-Chang;Hur, Kul;Lim, Pyung-Ki
    • Honam Mathematical Journal
    • /
    • v.34 no.3
    • /
    • pp.351-373
    • /
    • 2012
  • We investigate the lattice structure of various sublattices of the lattice of interval-valued fuzzy subrings of a given ring. We prove that a special class of interval-valued fuzzy ideals of a ring. Finally, we show that the lattice of interval-valued fuzzy ideals of R is not complemented[resp. has no atoms(dual atoms)].