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All Journal Epsilon: Jurnal Matematika Murni dan Terapan
Mahfuz Tarmizi
Program Studi Matematika FMIPA ULM
Decision Sciences, Operations Research & Management Transportation

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GRUP FAKTOR YANG DIBANGUN DARI SUBGRUP NORMAL FUZZY Mahfuz Tarmizi; Saman Abdurrahman; Muhammad Mahfuzh Shiddiq
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 13, No 1 (2019): JURNAL EPSILON VOLUME 13 NOMOR 1
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (975.233 KB) | DOI: 10.20527/epsilon.v13i1.3189

Abstract

A Quotient group is a set which contains coset members and satisfies group definition. These cosets are formed by group and its normal subgroup. A set which contains fuzzy coset members is also called a quotient group. These fuzzy cosets are formed by a group and its fuzzy normal subgroup. The purpose of this research is to explain quotient groups induced by fuzzy normal subgroups and isomorphic between them. This research construct sets which contain fuzzy coset members, define an operation between fuzzy cosets and prove these sets under an operation between fuzzy coset satisfy group definition, and prove theorems relating to qoutient groups and homomorphism. The results of this research are ????????⁄={????????|????∈????} is a qoutient group induced by a fuzzy normal subgroup, where ???? is a fuzzy normal subgroup of a group ????, ???????? is a fuzzy coset, and the binary operation is “∘” where ????????∘????????=???????????? for every ????????,????????∈????????⁄. An epimorphism ???? from a group ???? to a group ????′ and a fuzzy normal subgroup ???? of ???? which is constant on ???????????????? cause quotient goup ????????⁄ and ????′????????⁄ are isomorphic.
Co-Authors Muhammad Mahfuzh Shiddiq Saman Abdurrahman