GRUP FAKTOR YANG DIBANGUN DARI SUBGRUP NORMAL FUZZY

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 𝐺𝜇⁄={𝜇𝑥|𝑥∈𝐺} is a qoutient group induced by a fuzzy normal subgroup, where 𝜇 is a fuzzy normal subgroup of a group 𝐺, 𝜇𝑥 is a fuzzy coset, and the binary operation is “∘” where 𝜇𝑥∘𝜇𝑦=𝜇𝑥𝑦 for every 𝜇𝑥,𝜇𝑦∈𝐺𝜇⁄. An epimorphism 𝑓 from a group 𝐺 to a group 𝐺′ and a fuzzy normal subgroup 𝜇 of 𝐺 which is constant on 𝑘𝑒𝑟𝑓 cause quotient goup 𝐺𝜇⁄ and 𝐺′𝑓𝜇⁄ are isomorphic.