On the division of bipolar fuzzy relations

In this paper, we deal with the relational division operation and extend it so that it can handle bipolar fuzzy relations, i.e., relations where each tuple t is attached a pair of grades in the unit interval expressing the extent to which t satisfies a flexible constraint and a flexible wish tied by a consistency condition. The framework considered is that of an extended relational algebra. It is shown that the result of a division of bipolar relations can be characterized as a twofold quotient. The question of the (non-) primitivity of the operator is also tackled.