On the negation of bipolar fuzzy conditions

This paper deals with the negation operator in the context of a bipolar fuzzy relational algebra which makes it possible to handle bipolar fuzzy queries (involving flexible constraints and wishes) and relations. Several possible definitions of the negation are studied and assessed with respect to some desirable properties. A negation operator which complies with all those desirable properties is proposed, and serves as a basis for the definition of the set difference operation in the extended relational algebraic framework considered.