犹豫模糊事件的概率及犹豫模糊概率推理方法

Probability of Hesitant Fuzzy Event and Hesitant Fuzzy Probability Reasoning Method

为定量地刻画随机实验中犹豫模糊事件发生的不确定性,结合模糊概率理论与犹豫模糊集理论,定义犹豫模糊事件的概率,并在此基础上给出犹豫模糊事件的条件概率定义。对犹豫模糊事件概率的可列可加性、连续性以及其条件概率的乘法定理、全概率公式和贝叶斯公式等性质进行证明,比较犹豫模糊事件的概率在不同并、交运算下的性质,并给出犹豫模糊事件的概率大小的比较准则和犹豫模糊概率推理方法的步骤。实例分析结果表明,犹豫模糊事件的概率能更好地处理事件发生的不确定性。

In order to quantify the uncertainty of the occurrence of hesitant fuzzy event in random experiment,the probability of hesitant fuzzy event is defined combining fuzzy probability theory and hesitant fuzzy set theory.The definition of conditional probability of hesitant fuzzy event is given on this basis.This paper proves several properties of the probability of hesitant fuzzy event,for instance,the countable additivity and continuity.Properties of the conditional probability of hesitant fuzzy event such as multiplication theorem,the law of total probability and Bayes formula are proved.The properties of the probabilities of hesitant fuzzy events in other union and intersection operations are compared,a comparison criterion for the probabilities of hesitant fuzzy events and the steps of the hesitant fuzzy probability reasoning method are given.Example result shows that the probability of hesitant fuzzy events can better deal with the uncertainty of events.