基于毕达哥拉斯模糊信息的多准则决策方法与分类方法研究

How to effectively solve multi-criteria decision making (MCDM) problems in which the decision data is fuzzy information, has become an important and urgent research topic in modern decision science. This project will investigate systematically Pythagorean fuzzy MCDM methods and Pythagorean fuzzy multi-criteria sorting (MCS) methods for solving the decision making problems and the sorting problems where the decision data is Pythagorean fuzzy information. Firstly, this project will develop systematically the aggregating methods, the ranking methods and information measures of Pythagorean fuzzy numbers, which perfect Pythagorean fuzzy theory. Then, this project will study respectively Pythagorean fuzzy behavioral MCDM methods, Pythagorean fuzzy dynamic MCDM methods and Pythagorean fuzzy interactive group MCDM methods, etc., which construct preliminarily Pythagorean fuzzy MCDM methods system. Next, this project will put forward Pythagorean fuzzy MCS methods based on the case that the classification parameters are known in advance, the Pythagorean fuzzy MCS methods based on the situation that the assignment information of alternatives is known in advance, and the group consistency models-based Pythagorean fuzzy MCS methods, which fill the study gaps of Pythagorean fuzzy MCS methods. Afterwards, this project will study respectively heterogeneous Pythagorean fuzzy MCDM problems under the context that the weight information is incomplete, the heterogeneous Pythagorean fuzzy MCDM problems under the circumstance that some of the decision information is missing, and the heterogeneous Pythagorean fuzzy MCDM problems under the case that decision makers have their expectations. And meanwhile this project will propose the corresponding decision making methods to deal with these problems. Additionally, this project will develop the dominance degree function-based heterogeneous Pythagorean fuzzy MCS methods, the weighted distance models-based heterogeneous Pythagorean fuzzy MCS methods, and the outranking relation models-based heterogeneous Pythagorean fuzzy MCS methods. Finally, this project will apply the above research results to construct the risk assessment models of Jiangxi’s strategic emerging industries, and establish the corresponding decision support systems.

如何有效地处理和解决决策数据为模糊信息的多准则决策问题，成为当今决策科学的一项重要且亟需研究的课题。本项目将系统地研究基于毕达哥拉斯模糊信息（PFN）的多准则决策方法与分类方法，首先给出PFN的融合方式、排序方法和信息测度等，形成毕达哥拉斯模糊理论；据此深入研究毕达哥拉斯模糊行为决策方法、动态决策方法及交互式群决策方法等，构建毕达哥拉斯模糊决策方法体系；接着提出基于分类参数已知、基于案例信息已知的毕达哥拉斯模糊分类方法及基于群体一致性的毕达哥拉斯模糊群分类方法，以填补毕达哥拉斯模糊分类方法研究的空白；然后研究权重信息不完备、决策信息存在缺失、带有决策者期望等情形下的混合毕达哥拉斯模糊决策问题并提出相应决策方法；还将研究基于优势度函数、基于加权距离模型和基于级别优先关系模型的混合毕达哥拉斯模糊分类方法；最后将上述研究成果应用于构建江西省战略性新兴产业风险评估模型及研发相应的决策支持系统。

相对于直觉模糊集，毕达哥拉斯模糊集拥有更广阔的赋值空间，能够更加细腻地表征事物的不确定性。项目组对基于毕达哥拉斯模糊信息的多准则决策方法与分类方法进行了系统地研究，并已取得如下研究成果：（1）提出了毕达哥拉斯模糊广义距离测度、信息熵、知识测度以及多种新的毕达哥拉斯模糊排序方法等较好地完善了毕达哥拉斯模糊理论；（2）提出了（区间）毕达哥拉斯模糊多维线性偏好分析方法、三阶段毕达哥拉斯模糊多准则群决策方法、基于毕达哥拉斯模糊规划模型的多准则群决策方法、基于知识测度与相对距离模型的毕达哥拉斯模糊多准则群决策方法等完善了毕达哥拉斯模糊多准则决策方法体系；（3）首次探讨了包含毕达哥拉斯模糊信息和区间毕达哥拉斯模糊信息的多准则聚类问题，提出了毕达哥拉斯模糊层次聚类方法；（4）提出了一种带有心理预期视角下基于概率语言偏差模型的混合型多专家多准则决策方法和一种基于优势度模型的混合型多准则决策方法，进一步充实了混合型多准则决策方法体系。此外，项目组还对基于定性信息的多准则问题以及基于不确定性偏好关系的群决策问题进行了研究，提出了基于概率型语言模型的大群体定性决策方法、基于2-型语言ANP和区间2-型语言ELECTRE II 的定性多准则决策方法、概率型语言VIKOR方法、基于贴近度模型的犹豫梯形模糊多准则群决策方法、犹豫梯形模糊TODIM 多准则群决策方法、犹豫梯形模糊QUALIFLEX 多准则决策方法以及基于几何一致性的区间值模糊偏好关系群决策方法和三阶段区间模糊偏好关系群决策方法等。上述方法被广泛应用于新产品方案的选择、雾霾设备选择、绿色供应商选择等现实决策问题。