Data-Driven Nonlinear Preference Learning Methods for Multiple Criteria Sorting with Ordinal Relationship Consistency Check

The multiple criteria-sorting (MCS) problem based on preference learning is a research hotspot. In this paper, an improved method for the piecewise cubic polynomial value function based on monotonicity constraints is proposed, which can effectively overcome classification errors in the existing methods. Moreover, a construction method for the piecewise quadratic polynomial value function is raised to further explore the impact of flexibility on MCS, which can ensure the monotonicity of the nonlinear marginal value function in any subinterval by concise linear constraints. Second, a nonlinear preference learning model that minimizes the classification error and maximizes the difference between category thresholds is advanced through an improved UTilites Additives DIScriminanteś (UTADIS) method, which can improve the flexibility and universality of value-driven MCS methods. Third, an ordinal relationship consistency (ORC) check method is constructed to screen and handle outliers in MCS. Finally, the feasibility and superiority of the proposed methods are verified through comparison analysis.