A relational division based on a fuzzy bipolar R-implication operator

We introduce in this paper a new relational division operator based on a bipolar implication operator involving fuzzy bipolar relations. The considered bipolarity encompasses two kinds of bipolar conditions: the former is of type “and if possible”, and the latter is of type “or else”. This new division operator allows as to express a division of bipolar relations regardless of the nature of the dividend and the divisor (Boolean, fuzzy, bipolar, homogeneous, heterogeneous). We have also shown that the proposed relational division operator satisfies the bipolar quotient properties and can be an alternative to the already proposed operator in [1]-[3] which is based on the quantities involved in the division operation. The new proposed operator is aimed to be integrated into the bipolar SQLf language for flexible querying of relational databases.