Study Of Fuzzy Groups In Z_p-{0 ̅ } Group

Authors

  • Imelda Bo’bo’ Batunna Jurusan Matematika dan Statistika, Fakultas MIPA, Universitas Papua
  • Harina O.L Monim Jurusan Matematika dan Statistika, Fakultas MIPA, Universitas Papua
  • Junianto Sesa Jurusan Matematika dan Statistika, Fakultas MIPA, Universitas Papua

DOI:

https://doi.org/10.20956/j.v20i3.31827

Keywords:

Fuzzy subgroup, Group, Modulo, Subgroup

Abstract

Group theory is a field of abstract algebra that studies the structure of sets. Some concepts that are developments of group theory are fuzzy subgroups. Suppose that G is a group, a fuzzy subset μ of G is called a fuzzy subgroup of G if it satisfies  and  for each . However, not all groups have fuzzy subgroups. The aim of this research is to show that  is a classical group with multiplication operations in the group and determine fuzzy subgroups in the group . From the research results, it is found that the subset  with prime modulo integers  and  is a classical group with group multiplication operations and the fuzzy subset in the group  is a fuzzy subgroup and in general The properties of the classical group apply to the fuzzy subgroup, namely the singularity of the identity and the singularity of the inverse. However, there are properties of classical groups that do not apply to fuzzy subgroups, namely the law of cancellation

References

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Published

2024-05-15

Issue

Vol. 20 No. 3 (2024): May 2024

Section

Research Articles

License

Copyright (c) 2024 Author and publisher

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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