Using Pseudo Gradient Search for Solving Nonlinear Multiregression Based on 2-Additive Measures

In an optimization problem, when the objective function is not differentiate, such as nonlinear multiregressions based on the generalized Choquet integral, the traditional gradient search fails. In this case, we may replace gradient with a pseudo gradient to determine the optimal search direction. Nonetheless, the complexity of the algorithm is very high. When a nonlinear integral with respect to signed fuzzy measure is used in multiregression, people encounter the problem that, comparing to the number of variables, there are exponentially many unknown parameters in the model. However, in real-world problems, the higher-order interactions among the variables can be omitted, and then only second-order one with an acceptable small error in the results. Thus, a 2-additive measure based on the Mobius 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