区间值测度的上积分和下积分

Upper and Lower Integrals of Interval-valued Measure

近年来,非线性积分在数据挖掘、决策方面起到了越来越重要的作用。本文在区间值测度上建立了上下积分的概念。在论域有限的情况下,上下积分可以看成是目标函数为区间值系数的规划问题。为了求解此规划问题,分别给出了悲观、乐观、折中三种线性规划求解模型,最后通过实例说明了它的有效性。

Recently, nonlinear integrals plays an important role in the data mining, decision-making. Firstly, upper and lower integrals based on the interval-valued measure are built in the paper. If the universal set is finite, upper and lower integral can be regarded as programming problem, which coefficients of object function are interval values measure. Secondly, three kinds of linear programming models, which are pessimistic optimistic and compromise are given. Finally, the efficiency of the models is shown from an example.