摘要
研究了概率信息完全未知的概率犹豫模糊多属性决策问题.首先,针对概率犹豫模糊元中元素概率完全未知的情形,建立非线性规划模型,确定元素的概率.其次,根据决策者给出的评价值,利用熵权法确定属性权重.然后,将LINMAP方法推广到概率犹豫模糊环境下,提出一种客观确定理想解的方法.并利用折中比率法实现方案的择优排序,这种方法的基本思想是最优方案离正理想解最近并且离负理想解最远,以此得到更为客观合理的决策结果.最后,给出算例说明方法的可行性与有效性.
A problem of probabilistic hesitant fuzzy multi-attribute decision making with completely unknown probability information is studied.Firstly,aiming at the case that the probabilities of probabilistic hesitant fuzzy elements(PHFEs)are completely unknown,a nonlinear programming model is proposed to determine the unknown probabilities of PHFEs.Secondly,according to the evaluation of decisionmakers,the weight of attribute can be determined by entropy weight method.In addition,an approach based on LINMAP method is put forward to determine the probabilistic hesitant fuzzy ideal solutions objectively in the probabilistic hesitant fuzzy environment.Then,the compromise ratio method(CRM),whose basic principle is that the optimal alternative should have the nearest distance from positive ideal solution and the longest distance from negative ideal solution simultaneously,is utilized to rank the alternatives.And more objective and reasonable decision results can be obtained through CRM.Finally,a numerical example is given to illustrate the effectiveness and feasibility of the proposed method.
作者
曹倩
刘小弟
张世涛
吴健
CAO Qian;LIU Xiaodi;ZHANG Shitao;WU Jian(School of Mathematics and Physics,Anhui University of Technology Ma’anshan 243000)
出处
《系统科学与数学》
CSCD
北大核心
2020年第7期1242-1256,共15页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(71601002)
教育部人文社科青年基金(16YJC630077,18YJC630249)
安徽省高校优秀青年人才支持计划项目(gxyqZD2018033)
安徽省自然科学基金(1708085MG168)资助课题。
关键词
概率犹豫模糊集
LINMAP方法
折中比率法
熵权法
Probabilistic hesitant fuzzy set
LINMAP
compromise ratio method
entropy weight method
