Using 2-additive measures in nonlinear multiregressions

Abstract

When a nonlinear integral with respect to a signed fuzzy measure is used in multiregression, people face a serious problem that, comparing to the number of variables (attributes), there are exponentially many unknown parameters in the model. However, in many real-world problems, the higher-order interactions among the variables can be omitted, and then only consider the second-order one with an acceptable small error in the result. Thus, a 2-additive measure based on the Mőbius transformation and its inverse can be used to replace the signed fuzzy measure. In such a way, the complexity of the computation will be significantly reduced.