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 tconorms 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.