Open AccessGRUP FAKTOR YANG DIBANGUN DARI SUBGRUP NORMAL FUZZY
Author(s) -
Mahfuz Tarmizi,
Saman Abdurrahman
Publication year - 2019
Publication title -
epsilon /epsilon
Language(s) - English
Resource type - Journals
eISSN - 2656-7660
pISSN - 1978-4422
DOI - 10.20527/epsilon.v13i1.1240
Subject(s) - coset , mathematics , quotient group , group (periodic table) , quotient , normal subgroup , fuzzy logic , binary operation , homomorphism , combinatorics , torsion subgroup , discrete mathematics , algebra over a field , pure mathematics , cyclic group , abelian group , artificial intelligence , computer science , chemistry , organic chemistry , elementary abelian group
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.