A generalization of the t-norm and t-conorm called the uni-norm is def
ined. These operators allow for an identity element lying anywhere in
the unit interval rather than at one or zero as in the case of t-norms
and t-conorms, respectively. Various important properties of these un
i-norms are investigated. We next introduce two particular families of
these uni-norms, R and R*, study their behavior and suggest some sem
antics. Finally, withdrawing the requirement of associativity, we intr
oduce a class of operators called R(Q-star) aggregation operators whic
h are useful for aggregations guided by imperatives such as ''if most
of the scores are above the identity take the Max else use the Min''.