Noble reinforcement in disjunctive aggregation operators

We discuss the role of disjunctive aggregation operators in prototype based reasoning systems such as recommender systems. We indicate a need for these aggregation operators to have the additional property of noble reinforcement: Allowing a collection of high valued arguments to reinforce each other to give complete satisfaction while avoiding the situation in which a collection of low valued arguments act in the same way. We describe the difficulty that most t-conorms have in realizing this feature of noble reinforcement. We show that by relaxing the requirement of associativity we can provide disjunctive type aggregation operators that manifest noble reinforcement.