Aggregation function; evaluation; lattice dominance points; probability distribution; t-conorm.

Finding the maximum and minimum values of a given collection of real inputs is critical in many decision-making and evaluationmodels. In often encountered evaluation problems where information iscollected based on survey or statistics and embodied by a collection of normalized distributions on lattice, we cannot directly obtain the corresponding concept of ?maximum? and ?minimum.? To process such situationsand related evaluation problem, we first define the distributions poset on agiven lattice structure and then propose the concept of lattice dominancepoints, which can sometimes be seen as a type generalized ?maximum?points. Often there may be infinite dominance points to choose from. Inorder to find some more suitable ones according with our intuition andwith mathematical completeness, we propose an optimization method anddistribution t-conorm methods to elicit lattice dominances based on givencollection of normalized distributions. The distribution and bilinear distribution t-conorms examples are well defined, and some related propertiesare proposed with strict proofs. In addition, a commonly used evaluationmodel is proposed with results for comparing differently elicited latticedominance points.