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A new type of nonlinear integrals and the computational algorithm

机译：一种新型的非线性积分及其计算算法

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摘要

In information fusion, aggregations with various background require a variety of integrals to handle. These integrals are generally nonlinear since the set functions considered are nonnegative and vanishing at the empty set. They are a class of set functions including fuzzy measures and even imprecise probabilities. A new type of nonlinear integrals with respect to such a set function for nonnegative functions is introduced and its primary properties are deterred. These type of integrals has a natural explanation and, therefore, has wide applicability. We also show a comparison between the newly introduced nonlinear integral and other nonlinear integrals, such as the Choquet integral, the natural extension in the theory of imprecise probabilities, and the common pan-integral. With a flowchart, the algorithm for calculating the integral is given in this paper when the universe of discourse (the set of all information sources) is finite.
机译：在信息融合中，具有各种背景的聚合需要处理各种积分。这些积分通常是非线性的，因为所考虑的集合函数是非负的，并且在空集合处消失。它们是一类集合函数，包括模糊测度甚至不精确的概率。针对这种非负函数的集合函数，引入了一种新型的非线性积分，并确定了其主要性质。这些类型的积分具有自然的解释，因此具有广泛的适用性。我们还展示了新引入的非线性积分与其他非线性积分之间的比较，例如Choquet积分，不精确概率理论中的自然扩展以及常见的泛积分。借助流程图，本文给出了在话语范围（所有信息源的集合）有限的情况下计算积分的算法。

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