解决概率犹豫模糊集多属性群决策问题的两种算法  

Two Algorithms for Multi-attribute Group Decision Making with Probabilistic Hesitant Fuzzy Sets

作　　者：朱国成[1] 陈利群[1] 李峰[1] ZHU Guocheng;CHEN Liqun;LI Feng(Science and Technology Association,Guangdong Innovative Technical College,Dongguan 523960,China)

机构地区：[1]广东创新科技职业学院科学技术协会,广东东莞523960

出　　处：《东莞理工学院学报》2022年第5期1-6,共6页Journal of Dongguan University of Technology

基　　金：广东创新科技职业学院特色创新类重点资助项目(2022TSZD05)。

摘　　要：针对概率犹豫模糊集多属性群决策问题,在以点坐标形式描述概率犹豫模糊集的基础上设置了两种算法。算法1:首先将概率犹豫模糊数(PHFN)中的隶属度与之概率以点坐标形式进行描述,建立了概率犹豫模糊元(PHFE)的几何距离模型与离差程度系数模型;其次计算PHFE的综合值并以此建立各方案在单个属性上的比较矩阵,利用Maclaurin对称平均算子集结比较结果,通过比较各方案在所有属性上的集结数值结果大小来鉴定方案优劣。算法2:首先以区间数近似代替PHFE的值,并对由区间数组成的方案属性值进行两两测度来建立积型模糊互补判断矩阵,通过求解所有属性上的积型模糊互补判断矩阵的结果来达到排序方案目的;最后通过一个数值算例验证了两种算法的可行性。In order to solve the problem of multi-attribute group decision making with probabilistic hesitating fuzzy sets,two algorithms are proposed based on the description of probabilistic hesitating fuzzy sets in the form of point coordinates.Algorithm 1:Firstly,the membership degree and probability of PHFN are described in the form of point coordinates.On this basis,the geometric distance model and deviation coefficient model of PHFE are established.Secondly,the PHFE synthesis value was calculated and the comparison matrix of each scheme on a single attribute is established.The Maclaurin symmetric average operator is used to aggregate the comparison results,and the scheme is evaluated by comparing the aggregation values of each scheme on all attributes.Algorithm2:Firstly,the interval number is used to approximate the PHFE value,and the scheme attribute values composed of interval numbers are measured in pairs to establish the product fuzzy complementary judgment matrix,and the sorting scheme is achieved by solving the results of the product fuzzy complementary judgment matrix on all attributes.And then an example is given to verify the feasibility of the two algorithms.

关 键 词：几何距离模型 离差程度系数模型 Maclaurin对称平均算子 积型模糊互补判断矩阵 排序 

分 类 号：O159[理学—数学]