線形回帰分析を用いたChoquet積分モデルの構造最適化

Abstract

There are many cases where fuzzy integral has been applied to identification problems or for predicting the behavior of an unknown N-inputs 1-output system. But these models using fuzzy integral are usually made to over-fit to the case data of the system which includes some noise. This is because the model using fuzzy integral has too many parameters, called fuzzy measures. Some methods to reduce the parameters using the concept of inclusion-exclusion covering have been already proposed. But they are complicated and they cannot be applied to a system that has no inclusion-exclusion covering. This paper proposes a way to reduce the parameters of the model of the Choquet integral. This method reduces the number of parameters by introducing new concepts of independent and dependent fuzzy measures, and then by changing the process to make Choquet integral model into a process to solve a linear regression function. This method is very simple and the structure of the model optimized by this method is easy to understand. This method is an improved and superior method over conventional methods using the inclusion-exclusion covering.