On Cubic Fuzzy Groups and Cubic Fuzzy Normal Subgroups

Authors

  • Kardo Sleman Haso Dept. of Mathematics, College of Science, University of Duhok, Kurdistan Region, Iraq
  • Alias Barakat Khalaf Dept. of Mathematics, College of Science, University of Duhok, Kurdistan Region, Iraq

DOI:

https://doi.org/10.25271/sjuoz.2022.10.3.907

Keywords:

KEYWORS: Fuzzy set, interval-valued fuzzy set, Cubic fuzzy group, (Internal, External) cubic set, (P-,R-) intersection and (P-,R-) union.

Abstract

In this paper, the notions of cubic fuzzy groups and cubic fuzzy normal subgroups are introduced. The internal,
external of cubic sets, (P-,R-) order, (P-,R-) intersection and (P-,R-) union of cubic fuzzy groups are investigated and
some related properties were obtained. It is proved that a cubic fuzzy group which is both (internal, external) cubic
set. Also we provide condition on cubic fuzzy group to be an internal cubic set. We show that (P-,R-) intersection and
(P-,R-) union of cubic fuzzy groups are also cubic fuzzy groups. Also the (P-,R-) intersection, (P-,R-) union of cubic
fuzzy normal subgroups are proved to be cubic fuzzy normal subgroup.

Author Biographies

Kardo Sleman Haso, Dept. of Mathematics, College of Science, University of Duhok, Kurdistan Region, Iraq

Dept. of Mathematics, College of Science, University of Duhok, Kurdistan Region, Iraq
(kardo.haso@uod.ac)

Alias Barakat Khalaf, Dept. of Mathematics, College of Science, University of Duhok, Kurdistan Region, Iraq

Dept. of Mathematics, College of Science, University of Duhok, Kurdistan Region, Iraq
(aliasbkhalaf@uod.ac)

References

[1 ]A.Rosenfeld. Fuzzy groups,Journal Of Mathematical Analysis And Applications,35,1971,512-517
[2] L.A.Zadeh. Fuzzy sets,Information and Control,Vol.8,1965,338-353.
[3] L.A.Zadeh. The concept of a linguistic variable and it's application to approximate reasoning,part1,Infor.Sci.Vol.8,1975,199-249.
[4] N.P.Mukherjee. Fuzzy normal subgroups and fuzzy cosets,Information Scinces,34,1984,225-239.
[5] P.Loganayaki. On cubic sets and cubic topological space,Reg.No.17PHMAP001,2020.
[6] Y.B.Jun. Cubic sets,Vol.4,No.1,2012,83-98.

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Published

2022-07-23

How to Cite

Haso, K. S., & Khalaf, A. B. (2022). On Cubic Fuzzy Groups and Cubic Fuzzy Normal Subgroups. Science Journal of University of Zakho, 10(3), 105–111. https://doi.org/10.25271/sjuoz.2022.10.3.907

Issue

Vol. 10 No. 3 (2022): July - September  Issue

Section

Science Journal of University of Zakho

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