广义求和与乘积算子中参数w的影响规律分析

Analysis of Parameter w's Influence Laws in General Summation and Multiplication Operators

广义求和算子与广义乘积算子是基于区间数的证据合成方法得以应用的两个重要参数,实际应用表明两者中参数w对证据合成结果影响较大,掌握参数w的影响规律对其应用将大有裨益。通过对关键函数fu和fi的数学分析,同时依据实例分析的结果,推导出广义求和算子与广义乘积算子中参数w对基于区间数的证据合成结果的三条主要影响规律:1)随着广义求和算子中的参数w增大,证据合成结果变得悲观;2)随着广义乘积算子中的参数w的增大,证据合成结果变得乐观;3)两者中参数w的同时增大或减小可以平衡各自对证据合成结果的悲观或乐观作用。总结出的影响规律可辅助选择适当的参数w,以更好地满足实际工程应用需要。

The general summation and multiplication operators are important in the evidence combination based on interval numbers.And in its applications,their parameter w may influence on the combination,which will result in a certain difficulty for the final decision.Thus,it is very useful to master the influence laws of parameter w.Through analyzing the key functions fu and fi in the two operators,three main influence laws of parameter w is deduced with the help of these illustrations,which are 1） parameter w in the summation operator is pessimistic factor since the combination becomes pessimistic with the increasing w,2） parameter w in the multiplication operator is optimistic factor since the combination becomes optimistic with the increasing w,3） when these two ws increase or decrease similarly,their influence may balance each other.Such these influence laws will be beneficial for its application when ws need to be obtained properly.