On Intuitionistic Fuzzy Normal Groups

Dr. Hakimuddin Khan

doi:https://doi.org/10.14445/22315373/IJMTT-V64P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 64 | Number 1 | Year 2018 | Article Id. IJMTT-V64P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V64P507

On Intuitionistic Fuzzy Normal Groups

Dr. Hakimuddin Khan

Citation :

Dr. Hakimuddin Khan, "On Intuitionistic Fuzzy Normal Groups," International Journal of Mathematics Trends and Technology (IJMTT), vol. 64, no. 1, pp. 46-50, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V64P507

Abstract

In this present paper the Author discussed the concepts of Intutionistic fuzzy normal subgroups. The concepts of ordinary groups and ordinary normal groups are already in existence. Zadeh [1] Introduced the notion of fuzzy set theory , over an extra edge on ordinary set theory. A remarkable and beneficial research work is done in the field of fuzzy set theory, then the researchers started to think about the applications of fuzzy groups and fuzzy subgroups and fuzzy normal subgroups. The Intutionistic fuzzy sets and the Intutionistic fuzzy groups are same as Vague sets and vague groups, as justified by Bustince and Burillo in [2]. Consequently, in this paper the two terminologies ‘vague set’ and ‘Intutionistic fuzzy set’ have been used with same meaning and objectives.

Keywords

Fuzzy Sets, Fuzzy Groups, Fuzzy Relations , Intutionistic Fuzzy Sets, Intutionistic Fuzzy Relations, Intutionistic Fuzzy Groups, Intutionistic Fuzzy Normal Groups

References

[1] Zadeh,L.A., Fuzzy sets ,Infor. and Control.8 (1965),338-353.
[2] Bustince,H .and Burillo,P., Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems 79 (1996)403-405
[3] Dubois,D. and Prade,H., Fuzzy Sets and Systems :Theory and Applications, Academic Press,(London)1980.
[4] Klir, G. J. and Yuan, B. Fuzzy Sets and Fuzzy Logic :Theory and Applications. Englewood Clifis,NJ :Prentice-Hall,1995.
[5] Lin,T.Y., Fuzzy reasoning and rough sets, in Rough Sets, Fuzzy Sets and Knowledge Discovery (W.P.Ziarko, Ed.), Springer-Verlag,London,343 - 348,1994.
[6] Lin,T.Y., and Liu,Q., Rough approximate operators : Axiomatic rough set theory, in Rough Sets, Fuzzy Sets and Knowledge Discovery (W. P. Ziarko, Ed.), Springer- Verlag,London,256-260,1994.
[7] Yazici,A., George,R., Buckles,B.P. and Petry,F.E., A survey of conceptual and logical data models for uncertainty management in : Fuzzy Logic for the Management of Uncertainty, eds. L.Zadeh and J.Kacprzyk (John Wiely, New York,1992)607 -643.
[8] Zimmermann, H.-J., Fuzzy Set Theory and Its Applications (Kluwer Academic Publisher,Dordrecht,1985)
[9] Zimmermann,H.-J., Results of empirical studies in fuzzy set theory, in : Klir,G.J.(Eds).,Applied General System Research, Plenum, New york,1978.
[10] Zimmermann,H.-J., Fuzzy Set Theory and Its Applications, Kluwer Ac. Press., Dordrecht,1991.
[11] Zimmermann,H.-J., Zadeh,L.A. and Gaines,B.R., Fuzzy Sets and Decision Analysis, North Holland,1984.
[12] Zimmermann,H.-J., Fuzzy Sets, Decision Making and Expert Systems. Boston, MA: Kluwer Academic Publishers,1987.