群模糊层次分析法的改进及应用

Improvement and application for group fuzzy analytic hierarchy process

为了解决层次分析法（AHP,Analytic Hierarchy Process）中基于专家主观评价来构造的两两判断矩阵的一致性问题,提出了一种改进的群模糊层次分析法（IGFAHP,Improved Group Fuzzy Analytic Hierarchy Process）.IGFAHP引入了专家的权重系数和三角模糊数,将AHP扩展到群决策和模糊决策领域,设计了一种基于直接模糊判断矩阵的权重计算方法,通过各指标间可能度矩阵转化为实数值求解权重来改进一致性.定义了在模糊集上的一致性函数,并与AHP分别在3~9层指标上进行了对比测试.通过飞行器总体方案风险评价的实例对IGFAHP进行了应用验证.结果表明,IGFAHP相比AHP降低了使用复杂度并提高了一致性.

In order to solve the consistency question of the paired comparison matrix which is constructed based on expert subjective opinion in analytic hierarchy process（AHP）,an improved group fuzzy analytic hierarchy process（IGFAHP） was proposed.The AHP was extended to the field of group decision and fuzzy decision by using expert weight and triangular fuzzy numbers.The index weight counting method was designed based on fuzzy direct comparison matrix,by calculating possible degree matrix and turning it to real numbers,which was an improvement for consistency.The consistency function was defined in fuzzy sets,and tested with index number from three to nine.The method was integrated and applied to evaluate the overall design of aircraft system.The result shows that the new method is effective and alleviates the use complexity.