阿基米德copula概率对偶犹豫模糊信息集成算子及其在多属性群决策中的应用  

Probabilistic Dual Hesitant Fuzzy Aggregation Operators Based on Archimedean Copula and Its Application to Multiple Attribute Group Decision Making

作　　者：刘兮 陈华友[2,3] 周礼刚[2] LIU Xi;CHEN Huayou;ZHOU Ligang(School of Mathematics and Statistics,Hefei Normal University,Hefei 230601,China;School of Mathematical Sciences,Anhui University,Hefei 230601,China;Stony Brook Institute at Anhui University,Hefei 230039,China)

机构地区：[1]合肥师范学院数学与统计学院,安徽合肥230601 [2]安徽大学数学科学学院,安徽合肥230601 [3]安徽大学纽约石溪学院,安徽合肥230039

出　　处：《运筹与管理》2023年第6期89-96,共8页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(71901088,71901001,71871001);安徽省高校自然科学研究项目(KJ2020A0120);高校优秀青年人才支持计划项目(gxyq2020041,gxbiZD2020056);省级科研平台专项项目(2020PTZD16)。

摘　　要：本文基于阿基米德copula和相应的协copula定义了概率对偶犹豫模糊信息的一些运算法则,为概率对偶犹豫模糊信息的融合提供了一种新思路。这些运算法则不仅可以保持运算的封闭性,而且可以反映出概率对偶犹豫模糊信息之间的关系。在进一步研究运算法则性质的基础上,提出了阿基米德copula加权概率对偶犹豫模糊算术平均算子和几何平均算子,并讨论了其性质。针对概率对偶犹豫模糊信息环境下属性权重信息未知的多属性群决策问题,给出了求解属性权重的公式,并利用上述算子进行信息集结,获得了群决策方法。最后,通过公众生态环境满意度评价的实例说明所提方法的有效性,利用参数对评价结果的影响说明决策方法的灵活性。此外,还将本文方法与现有方法进行了对比分析。Ecological civilization construction theory plays a very important role in the theoretical system of Chinese style socialism.While focusing on economic and social development,China pays more attention to the protection of natural resources and realize the harmonious coexistence of humans and nature.On December 12,2016,the National Development and Reform Commission and other four departments released the Evaluation Index System for Ecological Civilization Construction.The public eco-environment satisfaction has been clearly defined as the main indicator to reflect public satisfaction with the ecological environment quality.Because of the complexity of evaluation and difficulty of quantifying information,probabilistic linguistic information becomes an effective form applied in ecological environment evaluation.Constructing new evaluation models and methods of probabilistic linguistic information turns to be a key scientific problem with both theoretical and practical significance in the evaluation decision-making.When hesitancy fuzzy sets are used for decision evaluation,the importance degree of each membership degree is the same.However,in reality,the importance degree of each membership degree should be different due to the personal preference of decision makers and the difference in the number of decision makers in group decision making.In order to solve this problem,ZHU(2014) combined probabilistic information with hesitant fuzzy set and introduced probabilistic hesitant fuzzy set which consists of several possible membership values associated with their corresponding probabilistic information.To expand information representation dimensions,HAO et al.(2017) proposed the probabilistic dual hesitation fuzzy set,which not only considered multiple membership values of elements and their corresponding probabilistic information,but also paid attention to the non-membership of elements and their respective importance degrees.Operational laws are the core problem of multi-attribute decision making.From the existing lit

关 键 词：多属性群决策 概率对偶犹豫模糊信息 阿基米德COPULA 加权集成算子 信息熵 

分 类 号：C934[经济管理—管理学]