A new nonlinear integral used for information fusion

Abstract

The integral is a common tool of aggregations in information fusion. In real problems, various backgrounds require a variety of integrals. The weighted average method is the simplest one and can be regarded as a linear integral (the Lebesgue integral). However, due to the nonadditivity of the concerned set functions such as fuzzy measures, which is used to describe the interaction among attributes, the integral is generally nonlinear. The fuzzy extension have been used. This paper introduces a new nonlinear integral. Its primary properties are discussed. This integral has a natural explanation and, therefore, it has a wide applicability. The paper also shows a comparison between this new integral and other nonlinear integrals. The algorithm for calculating the new integral is given when the set of all information sources is finite. © 1998 IEEE