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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Junianto Sesa
Jurusan Matematika dan Statistika, Fakultas MIPA, Universitas Papua
Mathematics

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Study Of Fuzzy Groups In Z_p-{0 ̅ } Group Imelda Bo’bo’ Batunna; Harina O.L Monim; Junianto Sesa
Jurnal Matematika, Statistika dan Komputasi Vol. 20 No. 3 (2024): May 2024
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v20i3.31827

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
Co-Authors Harina O.L Monim Imelda Bo’bo’ Batunna