三维视域下的概率犹豫模糊集及决策应用

PHFS From the 3D Perspective and Its Decision Making Application

在三维视角下定义了概率犹豫模糊集,并在此基础上设置了解决概率犹豫模糊集多属性群决策问题的两种算法.首先将隶属度、概率、决策专家权重看作以三维点坐标形式进行书写的三维变量,建立了计算概率犹豫模糊元的几何距离函数模型、离差程度函数模型以及概率犹豫模糊数的模糊值模型,然后在考虑概率犹豫模糊元的几何距离与离差程度两个因素的基础上计算属性权重.之后,利用加权的几何距离值与离差程度值计算概率犹豫模糊元的综合值,采用Maclaurin对称平均算子对概率犹豫模糊元的综合值进行集结进而对方案排序;计算概率犹豫模糊数的模糊值,以模糊值的上下确界分别作为区间数的右左端点,用区间数来近似表示概率犹豫模糊元的决策信息,同时,使用区间数的积型贴近度公式对各概率犹豫模糊元进行两两测度,通过比较属性的测度结果来鉴定各方案优劣.最后,将两种算法进行了实例验证,决策结果表明了算法的可行性.

This paper redefined the probabilistic hesitant fuzzy sets(PHFS)and established two algorithms for solving multi-attribute group decision making problems with PHFS from the 3D perspective.Firstly,the membership degree,probability and the weight of decision making expert were regarded as 3D variables written in the form of 3D point coordinates.The geometric distance function model of the probability hesitant fuzzy element(PFFE),the deviation degree function model and the probability hesitant fuzzy number(PHFN)fuzzy value model were set up.Secondly,the weight of attributes was calculated based on the geometric distance and deviation degree of PHFE.Thirdly,the comprehensive value of PHFE was calculated by using the weighted geometric distance and deviation degree value,and the Maclaurin symmetric average operator was used to aggregate the comprehensive value of PHFE before sequencing the schemes.Besides,the fuzzy value of PHFN was calculated,the right and left ends of the interval number were represented by the upper and lower bounds of the fuzzy value of PHFN,and the decision making information of PHFE was approximately represented by the interval number.Meanwhile,the product closeness formula of the interval number was used to measure each PHFE in pairs,and the measure results were compared to identify the advantages and disadvantages of each scheme.Finally,the two algorithms were verified by examples,and the decision making results showed the feasibility of the algorithms.