Uninorm aggregation operators

A generalization of the t-norm and t-conorm called the uni-norm is defined. 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 uni-norms are investigated. We next introduce two particular families of these uni-norms, R* and R*, study their behavior and suggest some semantics. Finally, withdrawing the requirement of associativity, we introduce a class of operators called R(Q-star) aggregation operators which 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''.