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.

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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

Issue

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

Section

Science Journal of University of Zakho

License

Copyright (c) 2022 Kardo Sleman Haso, Alias Barakat Khalaf

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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

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