On the division of bipolar fuzzy relations
Patrick Bosc, Olivier Pivert · 2010
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.