基于图片模糊集的多准则决策方法及其应用研究

Combined with the decision-makers' risk attitude information, the corresponding membership degree of picture fuzzy sets (PFSs) can be determined by voting, which effectively overcomes the shortcomings that decision-makers should provide the evaluation information by means of precise values. Apparently, PFSs are more suitable for capturing imprecise and uncertain information in actual decision-making problems and improving the accuracy and scientificity of decision-making. Thus, on the basis of the existing theories and methods of intuitionistic fuzzy sets and behavioral preference, this project would systematically research multi-criteria decision-making (MCDM) approaches with PFSs and their applications. Firstly, the reasonable operations and related measures of PFSs would be elaborately developed based on the characteristic of PFSs and voting rules. Subsequently the theories of information fusion, outranking relations and utility function, would be deliberately exploited to solve MCDM problems with PFSs. The evaluation criteria, comparison rules and decision-making models for assessing the given alternatives would be devised and a series of MCDM approaches with PFSs would be further proposed. According to the features of different models, the appropriate intelligence algorithm would be used to obtain the models’ solutions efficiently. On the basis of dynamics of behavioral preference, the final results need to be tested by means of sensitivity analysis. Finally, all approaches being designed theoretically would be applied to the practical decision-making problems, e.g. tourist scenic spot service quality assessment problems, in order to verify their feasibility and effectiveness. The research achievements of this project could enrich the decision theory, provide more technical supports for tourist management and have an explicit significance in both theory and application.

图片模糊集考虑了决策者的风险态度，并以投票的形式描述不同隶属度信息，不仅规避了决策者需对每个隶属度给出精确数值的缺陷，而且更有助于原始评价信息的收集，提高决策的准确性和科学性。因此，本项目拟结合直觉模糊集与行为偏好等理论与方法，对图片模糊多准则决策方法及其应用进行系统研究。首先，结合图片模糊集的特征与投票规则，定义更合理的图片模糊集运算规则与测度等。其次，根据信息融合模型、级别高于关系与效用函数，构建决策方案的比较指标、比较规则与多准则决策模型，提出一系列图片模糊多准则决策方法。同时，考虑决策者行为偏好的动态性，对上述模型中的相关风险参数进行灵敏度分析，并设计相应的智能优化算法。最后，利用所提的多准则决策方法对旅游景点服务质量进行综合评价，验证方法的可行性与有效性。研究成果将发展和完善模糊决策理论与应用，为旅游景点服务质量等现实评价问题提供技术支持，具有重要的理论价值和应用价值。

图片模糊集是将决策者风险态度考虑到决策环境的新型信息表达形式，它能够更全面、有效地收集与描述决策者的原始评价信息，使决策环境更契合实际问题，是当前研究与解决多准则决策问题的重要工具之一。因此，本项目结合已有成果，完成了以下几个方面的研究：（1）考虑了多个准则之间的关联性，定义了图片模糊集结算子，并提出了基于图片模糊集结算子的多准则决策方法；（2）定义了图片模糊距离、相似度与指数熵等测度，探讨了相关性质，并提出了一系列基于图片模糊测度的多准则决策方法；（3）结合在线评论信息，扩展了图片模糊决策方法及其应用；（4）进一步研究了图片模糊集其它相关理论与决策方法。