基于概率型犹豫模糊集的决策理论与方法研究

Hesitant fuzzy sets (HFSs), which were proposed recently, are a powerful tool of describing uncertainty information. While the new concept allows the membership degree of an element to a set represented by several possible values, the existing representation suggested for HFSs takes the same weight for all these possible evaluation values. Neglecting the difference in the weight of different evaluation values will result in some loss of original evaluation information. The project proposes the concept of probabilistic hesitant fuzzy sets (PHFSs) to fully take into account the difference in the weight for different evaluation values, aiming at providing a more datailed description of people’s hesitancy when they make decision, and hence, it has a greater practical value. The present project includes the following contents: (1) This project defines the basic operations for PHFSs, establishes fusion operators and measure theory and applies them to qualitative and quantitative decision making models; (2) This project establishs the theory for fusing probabilistic hesitant fuzzy information, in which the arguments are correlative each other; (3) This project investigates the fusion methods for dynamic probabilistic hesitant fuzzy information, collected at different periods, and the methods for dynamic decision making with probabilistic hesitant fuzzy information; (4) This project proposes probabilistic hesitant fuzzy decision making methods based on ELECTRE; (5) This project extends all the above results to probabilistic interval-valued hesitant fuzzy sets and applies them to real world issues such as electronic commerce; (6) This project performs sensitive analyses for proposed probabilistic hesitant fuzzy decision making methods in order to provide reliable theory and methods for decision supporting systems.

犹豫模糊集是新近提出的一种描述不确定信息的强有力工具。现有的犹豫模糊信息表达方式虽然允许一个元素属于一个集合的隶属度为几个可能的值，但都赋予这些可能值相同的重要性或权重。忽略不同评价值权重的差异会导致部分原始评价信息的丢失。本项目将提出概率型犹豫模糊集来充分考虑不同评价值可能具有不同权重这种更一般情形，以此来更细致地描述人们在决策时的犹豫状态，因而更加具有实用价值。具体内容包括：定义概率型犹豫模糊集的基本运算、建立其融合算子和测度理论并应用于定性和定量的决策模型中；建立数据之间有关联的概率型犹豫模糊信息融合理论；研究多时段的动态概率型犹豫模糊信息融合方式和决策方法；提出基于ELECTRE等的概率型犹豫模糊决策方法；把上述结果推广到概率型区间犹豫模糊集领域；并运用于电子商务等实际问题；结合决策环境对建议的概率型犹豫模糊决策方法的灵敏性进行分析，为决策支持系统提供可靠的理论与方法支持。

犹豫模糊概念是处理复杂模糊环境下决策问题的有效工具。犹豫模糊集的最初形式没有包含决策者多值评价信息的权重或差异，从而导致评价信息的丢失。本项目通过扩展犹豫模糊集的基本概念，丰富评价信息的不确定表达形式（例如：评价信息的概率表达、人工语言术语的定性表述、对偶犹豫模糊），从而能够充分考虑评价信息之间的差异，完成对多个可能的评价值赋予相应的重要程度。在新的框架下，我们获得以下结果：（1）提出构建犹豫模糊语言信息距离测度的新方法，并将其用于解决多属性决策问题；（2）基于定义的对偶犹豫模糊T模和S模构建一系列优先加权算子，并发展相应的多属性决策方法；（3）提出一个计算模型来处理含弱化修饰词的不确定语言信息的定性决策问题；（4）提出两种一致性过程来解决涉及概率型不确定语言偏好关系的群决策问题；（5）发展了基于优劣排序法的犹豫模糊语言优先决策方法；（6）基于演化博弈论发展了能定量评估专家客观权重确定方法的新途径；（7）提出了复杂语言环境下基于意愿的定性决策方法。