 A t-norm formula_7 has to satisfy the properties of
Notably absent from this list is the property of "idempotence" formula_18; the closest one gets is that formula_19.It may seem strange to be less confident in ‘formula_5 and formula_5’ than in just formula_5, but we generally do want to allow for letting the confidence formula_8 in a combined ‘formula_5 and formula_6’ be less than both the confidence formula_26 in formula_5 and the confidence formula_28 in formula_6, and then the ordering formula_30 by monotonicity requires formula_31.Another way of putting it is that the t-norm can only take into account the confidences as numbers, not the reasons that may be behind ascribing those confidences; thus it cannot treat ‘formula_5 and formula_5’ differently from ‘formula_5 and formula_6, where we are equally confident in both’.