DC optimization for constructing discrete Sugeno integrals and learning nonadditive measures

Abstract

Defined solely by means of order-theoretic operations meet (min) and join (max), weighted lattice polynomial functions are particularly useful for modelling data on an ordinal scale. A special case, the discrete Sugeno integral, defined with respect to a nonadditive measure (a capacity), enables accounting for the interdependencies between input variables. However, until recently the problem of identifying the fuzzy measure values with respect to various objectives and requirements has not received a great deal of attention. By expressing the learning problem as the difference of convex functions, we are able to apply DC (difference of convex) optimization methods. Here we formulate one of the global optimization steps as a local linear programming problem and investigate the improvement under different conditions. Abbreviation: DC: difference of convex; LP: linear programming