Fuzzy prime ideals and invertible fuzzy ideals in BCK-algebras
Let \(\mu\) and \(\nu\) be fuzzy ideals of a commutative BCK-algebra \(X\). \(\mu\) is called prime iff it is non-constant and \(\mu(x\wedge y)=\max\{\mu(x), \mu(y)\}\) for all \(x,y\in X\). If \(\nu^+ (x)=1-\inf\{\nu(y) |y\wedge x=0\}\) is a fuzzy ideal of \(X\), then \(\nu\) is called invertible. Every fuzzy prime ideal is invertible, but not conversely. If all fuzzy ideals of a bounded implicative BCK-algebra \(X\) are invertible, then for all fuzzy prime ideals \(\mu\), \(\nu\), the ideals \(\mu\cup\nu\) and \(\mu\cap\nu\) are also prime.
scientific article; zbMATH DE number 1563553