Fuzzy partitions and fuzzy-quotient rings
The cosets of a fuzzy ideal \(M\) in a ring \(A\) form another ring \(A/M\), called the fuzzy-quotient ring of \(A\) by \(M\). We show that \(A/M\) is always a fuzzy partition of \(A\), and a fuzzy partition of \(A\) will be a fuzzy-quotient ring (with respect to some fuzzy ideal) if and only if its associated fuzzy similarity relation is compatible with the ring operations.
scientific article; zbMATH DE number 487501