关键词: 一致性, 几何平均超传递矩阵, 群体决策, 防空预警装备, 体系指标, 效能评估

Abstract:

A group decision-making method based on improved analytic hierarchy process （AHP） was proposed to address the problems of traditional AHP， such as judgment matrices failing consistency checks， long evaluation cycles， and high subjectivity of single expert evaluations. This method approximated the original judgment matrix by constructing a geometric averaging supertransitive matrix. The geometric averaging supertransitive matrix， obtained by geometrically averaging multiple extended matrices constructed from the original judgment matrix， compensated for the lack of good consistency in the original judgment matrix. This method retained expert opinions while passing the AHP consistency checks. At the same time， introducing the consistency ratio into group decision-making to determine the authority of experts maximizes the authenticity of index weights. On the basis of the principles of scientificity， independence， feasibility， and comprehensiveness， a combat effectiveness index system for air defense early warning equipment was constructed. Through the example analysis of the equipment deployment plan using the constructed index system， it was demonstrated that the method was feasible， reasonable， and effective.

Key words: consistency, geometric averaging supertransitive matrix, group decision-making, air defense early warning equipment, index system, effectiveness evaluation