Eliciting Different Lattice Dominance Points to Evaluate Distribution Information

Finding the maximum and minimum values of a given collection of real inputs is critical in many decision-making and evaluation models. In often encountered evaluation problems where information is collected 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 situations and related evaluation problem, we first define the distributions poset on a given lattice structure and then propose the concept of lattice dominance points, which can sometimes be seen as a type generalized “maximum” points. Often there may be infinite dominance points to choose from. In order to find some more suitable ones according with our intuition and with mathematical completeness, we propose an optimization method and distribution t-conorm methods to elicit lattice dominances based on given collection of normalized distributions. The distribution and bilinear distribution t-conorms examples are well defined, and some related properties are proposed with strict proofs. In addition, a commonly used evaluation model is proposed with results for comparing differently elicited lattice dominance points.