概率语言集的随机比较

Stochastic Comparisons of Probabilistic Linguistic Term Sets

本文将随机优势理论引入到概率语言集的比较。基于概率语言集的随机变量表示,首先基于分布函数定义了该集合上的几种偏序关系和严格偏序关系;接着根据期望效用定义了弱序关系和严格弱序关系;并在不同类型的效用函数前提下,证明了偏序(严格偏序)和弱序(严格弱序)的性质与联系;最后讨论了序关系在概率语言集信息下的决策问题中应用的可行性。

The theory of stochastic dominance is introduced to the comparisons of probabilistic linguistic term sets.According to the representation of probabilistic linguistic term sets based on stochastic variables,some partial orders and strict partial orders are defined based on cumulative distributions,then some weak orders and strict weak orders are defined as well,based on expected utilities.The properties and connections of the proposed order relations are proven based on specific classes of utility functions.Finally,the reasonability of using the order relations in decision making is clarified.