基于概率语言向量术语集的群决策理论与方法

Probabilistic linguistic vector-term set is a brand-new expression to describe the linguistic information in group decision making, whose basic unit is a binary array composed of a linguistic vector-term and its corresponding probability. In decision making process, it can clearly describe and distinguish the different meanings of a linguistic term in different linguistic evaluation scales that have the same granularity, the same linguistic terms and different distributions; thus, the probabilistic linguistic vector-term set has wide application prospects in various fields, such as medical expert consultation, public service evaluation, personalized recommender system, uncertain investment decision making, qualitative portfolio evaluation, etc. In this project, we will systematically investigate the group decision making theory and methods based on probabilistic linguistic vector-term set, which involves the following contents: (1) Study the basic operational laws and aggregation operators of probabilistic linguistic vector-term sets; (2) Construct the measurement theory for probabilistic linguistic vector-term sets, including the distance measures, similarity measures, correlation measures and entropy measures, etc.; (3) Propose the linguistic preference relation theory based on probabilistic linguistic vector-term set, based on this, study the consistency checking criteria, the consistency checking methods, and the inconsistency improving algorithms; (4) Investigate the group consensus problem based on probabilistic linguistic vector-term set, and give the improvement approach to promote reaching a consensus; (5) Introduce the probabilistic linguistic vector-term set in static and dynamic decision making methods, establish the theoretical framework of group decision making based on probabilistic linguistic vector-term set, and develop the corresponding decision support system; (6) implement these research results to practical linguistic group decision making problems to demonstrate the effectiveness of probabilistic linguistic vector-term set in describing linguistic information within group decision making and analyze the performance of group decision making approaches constructed based on Probabilistic linguistic vector-term set.

概率语言向量术语集是一种表达群决策中语言偏好信息的崭新方法，其基本单元是由语言评价向量和相应概率构成的二元数组，在语言群决策过程中能够刻画和区分来自同粒度不同分布标度下相同语言术语的意义。这种信息表示方法在医疗专家会诊、社会公共服务项目评价、个性化推荐系统、金融投资决策、资产组合评价等多方面都有广阔的应用前景。本项目将系统地基于概率语言向量术语集研究群决策理论与方法，具体包括：研究概率语言向量信息的运算法则及融合方式；提出概率语言向量信息的距离测度、相似性测度和熵测度，并在此基础上建立基于概率语言向量术语集的测度理论；基于概率语言向量术语表达式构建偏好关系，研究其一致性检验准则及方法，给出非一致性修正算法；研究基于概率语言向量信息偏好关系的共识达成方法；将概率语言向量术语集引入静动态决策方法，系统地构建基于概率语言向量术语集的决策理论框架和决策支持系统；将上述成果应用到实际的群决策问题中。

概率语言向量术语是一种表达群决策中语言偏好信息的崭新方法，其基本单元是由语言评价向量和相应概率构成的二元数组，在群语言群决策过程中能够刻画和区分来自同粒度但不同分布标度下的相同语言术语的语义。这种信息的表述模型在医疗专家会诊、社会公共服务项目评价以及个性化推荐系统等多个方面都有广阔的应用前景。本项目系统地基于概率语言向量术语的表述模型研究多粒度群语言决策问题的理论与方法，具体包括：研究概率语言向量信息的运算法则及融合方式；提出概率语言向量信息的距离测度和相似性测度等实用测度基础并建立相应的测度理论框架；基于概率语言向量术语的表述模型和特点构建模糊偏好关系，研究其一致性的检验准则，给出非一致性的修正算法；给出基于概率语言向量模糊偏好关系的共识达成方法；将概率语言向量术语引入静、动态决策方法，系统地构建相应的群决策理论和技术框架；将上述成果应用到多个领域的实际的群决策问题。. 本项目完成的重要结果包括：给出了概率语言向量信息的运算法则及融合方式；提出了概率语言向量信息的距离测度和相似性测度等实用测度基础，并在此基础上建立了相应的测度理论框架；对概率语言向量术语的原表述模型进行了改进，解决了其在计算性能方面的缺陷，增强了其应用性能，比如：改进的表述模型能够在多粒度语言群决策问题中一对一地刻画具有个体特征的评价标度，进而刻画个体评价者之间在知识背景或认知水平方面的差异，这对在大群体决策中进行分组决策提供了理论依据和技术支持；基于概率语言向量术语表述模型和特点构建了模糊偏好关系，并研究了其一致性的检验准则，给出了相应的非一致性的修正算法；给出了基于概率语言向量模糊偏好关系的共识达成方法；将概率语言向量术语引入了静、动态决策方法，较为系统地构建了相应的决策理论和技术框架；将上述成果应用到了多个领域的实际的群决策问题，比如：个性化推荐系统、医疗追踪评价和避免过度医疗诊断、政府公共事务决策等。