变权综合中的惩罚——激励效用

The Penalty Incentive Utility in Variable Weight Synthesizing

研究分变权综合与效用分析这两大决策分析理论之间的联系并根据分析提出了折衷变权综合模式。主要揭示了均衡函数为综合效用的推广形式和单因素效用的类型与均衡函数类型之间的对应关系。通过折衷型效用函数获得折衷变权，从而扩展了变权方法。

In this paper, the connection between variable weight synthesizing and utility analysis is known as in second order differentiable case. \ \ (1) B(x 1,x 2, ,x m)=mj=1g(x j) is penalty balance function if and only if g(t) is conservative utility function on (0,1); \ \ (2) B(x 1,x 2, ,x m)=mj=1g(x j) is incentive balance function if and only if g(t) is risky utility function on (0,1); \ \ (3) B(x 1,x 2, ,x m)=mj=1g(x j) is the balance function which induce the constant weight synthesizing model if and only if g(t)=t. \ \ (4) B(x 1,x 2, ,x m)=mj=1g(x j)+mj=p+1h(x j) is mixed balance function if and only if g(t) is conservative utility function on (0,1) while h(t) risky utility function on (0,1); \ \ At last, compromise utility is introduced to establish compromise variable weight synthesizing model.