On fuzzy ideals in BCK/BCI-algebras
For BCI- and BCK-algebras, the authors define the notion of a fuzzy ideal generated by a fuzzy set. They then show that for a BCI-algebra, the set of all fuzzy ideals forms a complete lattice in an obvious way, and the set of closed fuzzy ideals is a modular sublattice of it. Some comments are made in the BCK-algebra case. This reviewer observes that the definition implies that for a BCK-algebra with largest element 1, if \(f\) is a fuzzy set with maximal value at 1, then the fuzzy ideal generated by it is constant with value \(f(1)\).
scientific article; zbMATH DE number 2131588
scientific article