Intuitionistic Fuzzy Points in Semigroups
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
Intuitionistic Fuzzy Points in Semigroups

Authors: Sujit Kumar Sardar Manasi Mandal Samit Kumar Majumder

Abstract:

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.

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071664

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1862

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.