Intuitionistic Fuzzy Points in Semigroups

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun and S.Z. Song introduced the notion of intuitionistic fuzzy points. In this paper we find some relations between the intuitionistic fuzzy ideals of a semigroup S and the set of all intuitionistic fuzzy points of S.

Authors:

• Sujit Kumar Sardar Manasi Mandal Samit Kumar Majumder

Keywords:

• Semigroup
• Regular(intra-regular) semigroup
• Intuitionistic fuzzy point
• Intuitionistic fuzzy subsemigroup
• Intuitionistic fuzzy ideal
• Intuitionistic fuzzy interior ideal
• Intuitionistic fuzzy semiprime ideal
• Intuitionistic fuzzy prime ideal.

References:

[1] K. Atanassov; Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986)
87-96.
[2] K. Atanassov; New operations defined over the intuitionistic fuzzy sets,
Fuzzy Sets and Systems, 61(1994) 137-142.
[3] K. Atanassov; Intuitionistic fuzzy sets, theory and Applications, Studies
in Fuzziness and Soft Computing., 35(1999) Physica-Verlag, Heidelberg.
[4] J.M. Howie; Fundamentals of semigroup theory, London Mathematical
Society Monographs. New Series, 12. Oxford Science Publications. The
Clarendon Press, Oxford University Press, New York, 1995.
[5] Y.B. Jun, S.M. Hong and J. Meng; Fuzzy interior ideals in semigroups,
Indian J. of Pure Appl. Math., 26(9)(1995) 859-863.
[6] Y.B. Jun and S.Z. Song; Intuitionistic fuzzy semipreopen sets and
intuitionistic fuzzy semiprecontinuous mappings, Journal of Appl. Math.
and Computing, 19(1-2)(2005) 467-474.
[7] K.H. Kim; On fuzzy points in semigroups, International Journal of
Mathematics and Mathematical Sciences, 26(11) (2001) 707-712.
[8] N. Kuroki; On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy
Sets and Systems, 5(1981) 203-215.
[9] N. Kuroki; On fuzzy semigroups, Information Sciences, 53(1991)
203-236.
[10] N. Kuroki ; Fuzzy semiprime quasi ideals in semigroups, Inform. Sci.,
75(3)(1993) 201-211.
[11] Mordeson et all; Fuzzy semigroups, Springer-Verlag (2003), Heidelberg.
[12] P.M. Pu and Y.M. Liu; Fuzzy topology I, neighbourhood structure of
a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76(2)
(1980) 571-599.
[13] A. Rosenfeld; Fuzzy groups, J. Math. Anal. Appl., 35 (1971) 512-517.
[14] S.K. Sardar, M. Mandal and S.K. Majumder; On intuitionistic fuzzy
magnified translation in semigroups,(Communicated).
[15] X.P. Wang, Z.W. Mo and W.J. Liu; Fuzzy ideals generated by fuzzy
point in semigroups, Sichuan Shifan Daxue Xuebao Ziran Kexue Ban.,
15(4) (1992) 17-24.
[16] X.Y. Xie; Fuzzy ideal extensions of semigroups,, Soochow Journal of
Mathematics, 27(2)(April 2001) 125-138.
[17] X.Y. Xie; Fuzzy ideal extensions of ordered semigroups, Lobach Journal
of Mathematics, 19(2005) 29-40.
[18] Y.H. Yon; The semigroup of fuzzy points, Submitted in Comm. Algebra.
[19] L.A. Zadeh; Fuzzy sets, Information and Control, 8 (1965) 338-353.