• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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• pp.259-266
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• 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.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.455-464
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• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.3
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• pp.215-225
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• 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.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.351-373
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• 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)].