犹豫模糊语言值事件及其概率

Hesitant Fuzzy Linguistic Term Event and Its Probability

犹豫模糊语言值集采用定性的方法描述了事件的模糊性和人的犹豫性,而事件本身往往还可能包含随机性.因此,本文研究了犹豫模糊语言值事件的概率.首先,以三角模糊数作为语言值,其顶点的横坐标作为语言值的下标,选取一组语言值作为犹豫模糊语言值集的语言值集,并给出了犹豫模糊语言值集的并集、交集和补集运算.其次,提出了犹豫模糊语言值事件的概率和条件概率的定义,证明了犹豫模糊语言值事件的概率的可列可加性、连续性、乘法定理、全概率公式和贝叶斯公式等,并给出了犹豫模糊语言值事件的概率大小比较准则及其概率推理步骤.最后,通过评价球队组训能力的数值例子对犹豫模糊语言值事件的概率进行了说明.犹豫模糊语言值事件的概率采用定性的方法灵活地反映了事件发生的不确定性.

Hesitant fuzzy linguistic term set uses a qualitative method to describe the fuzziness of the event and the hesitation of the human,and the event itself may also contain randomness.Therefore,this paper studies the probability of hesitant fuzzy linguistic term events.First,triangular fuzzy number is used as the linguistic term,the abscissa of the vertex of the triangular fuzzy number is used as the subscript of the linguistic term,and a group of linguistic terms is selected as the linguistic term set of hesitant fuzzy linguistic term set.The union,intersection and complement operation of the hesitant fuzzy linguistic term set are given.Secondly,The definitions of the probability and conditional probability of hesitant fuzzy linguistic term events are proposed.Several properties of the probability of hesitant fuzzy linguistic term events are proved,such as the countable additivity,continuity,multiplication theorem,the law of total probability,Bayes formula and so on.The comparison criteria of the probability of extended hesitant fuzzy linguistic term events and its probabilistic reasoning steps are given.Finally,A numerical example is given to illustrate the application of the probability of extended hesitant fuzzy linguistic term events in basketball team training ability evaluation.The probability of hesitant fuzzy linguistic term events uses a qualitative approach to flexibly reflect the uncertainty of the event.