加权概率犹豫模糊集多属性群决策算法及应用

Decision Algorithm for the Multi-Attribute Group of Weighted Probabilistic Hesitant Fuzzy Set and Its Application

对于概率犹豫模糊集中的不同隶属度值赋予了决策专家的综合权重,由此构造出一种蕴含信息量更大、更方便解决决策问题的概率犹豫模糊集合——加权概率犹豫模糊集.针对加权概率犹豫模糊集中的加权概率犹豫模糊元,在使用三维点坐标进行描述的基础上建立加权概率犹豫模糊元的三维得分值模型、三维离差值模型、2个加权概率犹豫模糊元的几何距离模型以及大小判别准则.结合决策专家的综合权重与属性的综合权重提出一种确定正理想方案与负理想方案的方法,基于TOPSIS思想给出一种新的贴近度公式,并利用新的贴近度公式来鉴别各方案优劣.最后,通过一个数值算例说明文中理论与方法的可行性.

The weight for different membership degrees of the probabilistic hesitant fuzzy set is given to the decision expert,and a kind of probabilistic hesitant fuzzy set-weighted probabilistic hesitant fuzzy set,which contains more information and is more convenient to solve the decision problem,is constructed.Aiming at the weighted probabilistic hesitant fuzzy element in the weighted probabilistic hesitant fuzzy set,the three dimensional score value model,the three dimensional deviation model,the geometric distance model of two weighted probabilistic hesitant fuzzy elements and the size criterion are established using three dimensional point coordinates to describe the weighted probabilistic hesitant fuzzy element.A method to determine the positive ideal scheme and the negative ideal scheme is proposed based on the comprehensive weight of decision experts and the comprehensive weight of attributes.A new approximation formula is given based on TOPSIS idea,and the new approximation formula is used to identify the pros and cons of each scheme.Finally,a numerical example is given to illustrate the feasibility of the proposed theory and method.