灰模糊积分在多目标决策中的应用

针对带有大量定性指标且指标间存在大量交互作用的多目标决策问题，提出灰模糊积分决策模型.结合gλ模糊测度和Choquet模糊积分与灰色关联度，将定性指标评价的不确知性和指标间的交互作用很好地体现在评价结果中.专家使用模糊数给被评价对象打分，将模糊数解模糊化为数值并通过灰色关联度法提高打分一致性.使用gλ模糊测度表达指标间的交互作用，通过Choquet模糊积分将各指标评价值进行非线性集成.以某协作制造企业供应商评价与选择问题为例，与灰色综合评价法进行比较，验证了所提模型的可行性和有效性.
Abstract: A novel method called grey fuzzy integral was proposed in order to solve the multi-objective decision making problems that involved a number of qualitative indices and many interactions exist among indices. The λ fuzzy-measures, the Choquet fuzzy integral and the grey correlation degree were combined. Then the uncertainty of qualitative indices and the interaction among all indices can be well expressed in the evaluation results. The experts marked the objects through fuzzy numbers. Then the fuzzy numbers were transformed into numerical values and its consistency was improved through grey correlation method. Interaction among indices were expressed through λ fuzzy measures and integrated through Choquet fuzzy integral. The performance of the proposed method was tested on a practical example about supplier evaluation of collaborative manufacturing enterprise and compared with the grey comprehensive evaluation method. The experimental results validated the feasibility and effectiveness of the proposed method.