三角模糊数型多属性决策灰色优化模型及其在工程设计方案评价中的应用

工程设计方案评价时由于掌握的信息不充分,资料不全,加之问题本身的复杂性、不确定性以及人类思维的模糊性,方案的评价值往往难以精确表达,常用三角模糊数形式表示.针对基于"理想方案"的灰色关联分析评价存在的不足,根据灰色关联度定义,运用扩展的最小二乘方准则构造目标函数,建立了三角模糊数型多属性决策灰色优化模型.模型同时考虑了"理想方案"和"负理想方案",克服了仅考虑一种方案时排序的不相容问题,更具有客观性和合理性.应用实例表明,该模型概念清晰,数学推导严谨,评价值分辨率高,评价结果与实际相符.

Optimal Grey Model for Multi-attribute Decision Making with Triangular Fuzzy Numbers and Its Application in Evaluating of Engineering Design Schemes

Due to inadequate information,incomplete data in evaluating of scheme,and the complicacy and uncertainty of scheme itself and the fuzziness of human thinking,the evaluating value of the schemes is difficult to be expressed,its value is often represented in triangular fuzzy number.Aiming at the shortage of grey correlation analysis based on "ideal scheme",according to the definition of grey correlation degree,an optimal grey model for evaluating scheme is presented by constructing object function with the principle of extended least square.The model has taken into account simultaneously the "ideal scheme" and "negative-ideal scheme",overcome the problem of incompatibilities and it is more objective and reasonable.A practical example indicates the model is clear in concept,vigorous in mathematical deduction,and high resolution in evaluating value,and the result was matched with the fact.