Aggregating truth and falsity values
Résumé
We propose an axiom set for the aggregation of truth values which leads to the characterization of two truth-aggregation families, a prudent and an enthusiastic. The first one has a cautious attitude choosing between two observed values, one of which is more uncertain. The second one has no enthusiastic behavior and will reinforce the result if it observes twice the truth or twice the falsity. When observing falsity and truth, the operator gives a compensated value. We finish by expounding the use of these operators and their relationship with the traditionally used truth aggregation operators: t-norms and t-conorms. Actually the presented operators should be used for the aggregation of different observed truth values for the same phrase vs. the calculus of the truth of a logical phrase.