Uni-norms: a unification of t-norms and t-conorms

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. Some properties of these uni-norms are discussed. Two particular families of uni-norms (R* and R_*) are introduced. Weighted aggregations using these operators are described. Withdrawing the requirement of associativity, a class of operators called R_Q-star aggregation operators are discussed, which are useful for aggregations guided by imperatives such as “if most of the scores are above the identity then take the Max, else use the Min”