均衡函数及其在变权综合中的应用

Balanced Function and Its Application for Variable Weight Synthesizing

进一步研究了均衡函数，改进了［４］中公理化体系，获得了两大数均衡函数及相应的变权模式并分析了这些模式之间的关系。最后，作为原理说明之用。

In this thesis, balanced function are made a detailed study coming to following aspects: 1) If a elementary function g(t) satisfies g′(t)≥0 and g″(t)≤0 then B 1(x 1,…,x m)=mj=2g(x j) is a balanced function 2) If a elementary function h(t) satisfies ( lnh(t))″≤0 then B 2(x 1,…,x m)=mj=1h(x j) is a balanced function. 3) If B (x 1,…,x m) is a balanced function and the elementary function φ(t) satisfies φ′(t)≥0 on the range of B, then (φB)(x 1,…,x m)+c(c is a constant) is a balanced function and induces the same model of variable weight that B(x 1,…,x m) does. 4) As deduction of the above , we give the balanced functions as ∑ 1(x 1,…,x m)=mj=1x j, ∏ 1(x 1,…,x m)=∏mj=2x α j(α>0) and ∑ α(x 1,…,x m)=mj=2x α j (0≤α≤1), and corresponding weight fomulas. At last, a example is given to note the variable weight principle