# INTUITIONISTIC FUZZY LIE IDEALS OF LIE ALGERBAS

Jun, Young-Bae;Park, Chul-Hwan

• Accepted : 2007.04.24
• Published : 2007.06.25
• 32 3

#### Abstract

The notion of intuitionistic fuzzy Lie ideal of a Lie algebra is introduced, and related properties are investigated. Characterizations of an intuitionistic fuzzy Lie ideal are provided. Using a collection of Lie ideals, an intuitionistic fuzzy Lie ideal is established.

#### Keywords

Lie algebra;Lie ideal;intuitionistic fuzzy Lie ideal

#### References

1. K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
2. K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems 61 (1994), 137-142. https://doi.org/10.1016/0165-0114(94)90229-1
3. K. T. Atanassov, Intuitionistic fuzzy sets. Theory and applications, Studies in Fuzziness and Soft Computing, 35. Heidelberg; Physica-Verlag 1999.
4. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, 1972.
5. Y. B. Jun, K. H. Kim and E. H. Roh, On fuzzy ideals of Lie algebras, J. Appl. Math. Computing 10 (2002), no. 1-2, 251-259.
6. S. E. Yehia, Fuzzy ideals and fuzzy subalgebras of Lie algebras, Fuzzy Sets and Systems 80 (1996), 237-244. https://doi.org/10.1016/0165-0114(95)00109-3
7. S. E. Yehia, The adjoint representation of fuzzy Lie algebras, Fuzzy Sets and Systems 119 (2001), 409-417. https://doi.org/10.1016/S0165-0114(99)00069-X
8. L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X