A Note on Numerical Representations of Nested System of Strict Partial Orders

This note provides two numerical representations of a nested system strict partial orders. The first representation is based on utility and threshold functions. We generalize the menu-dependent preferences by allowing to depend not only menu but also pair alternatives under comparison. function can be interpreted as distance between alternatives. second aggregation multi-dimensional preference. describes decision-making procedure where multiple criteria are gradually aggregated into an overall assessment.