Semantics of quotient operators in fuzzy relational databases

The quotient operator plays an important role for query evaluation in relational databases. Its extension to fuzzy databases raises the question of the intended interpretation of the intermediary degrees attached to the items in the fuzzy relations. This note points out that the fuzzy quotient operator should be defined in slightly different ways depending on the possible interpretations of the degrees: levels of satisfaction of a gradual property, levels of importance of a required property, uncertainty pertaining to the membership of an element to a subset.