系统工程解析结构模型解决电脑选购问题

1、高校生选购电脑 说明结构模型和层次分析法的运用规范分析说明结构模型1、 要素分析找到系统构件电脑的价格电脑的性能操作电脑的寿命电脑的携带电脑的平安性电脑的体积电脑的消遣性售后的修理便利依据上述要素，假设电脑购买系统中共9个要素，其集合为S，则要素组成的集合S=S1,S2,S3,S4,S5,S6,S7,S8,S9。2、要素之间的关联有向图表达3128657943、要素结构的矩阵表达邻接矩阵：依据系统各要素之间的相关关系，可得到邻接矩阵如下： S1 S2 S3 S4 S5 S6 S7 S8 S9 S1 0 1 0 0 0 0 0 0 0 S2 0 0 1 0 0 0 0 1 0 S3 0 0 0

2、0 0 0 0 1 0 S4 0 0 0 0 0 0 0 0 1 A= S5 0 0 0 0 0 1 0 0 0 S6 0 0 0 0 0 0 0 0 0 S7 0 0 0 0 1 0 0 0 0 S8 0 0 0 0 0 0 0 0 0 S9 0 0 0 1 0 0 1 0 0可达矩阵：依据公式M=(A+I)r 得到可达矩阵M S1 S2 S3 S4 S5 S6 S7 S8 S9 S1 1 1 0 0 0 0 0 0 0 S2 0 1 1 0 0 0 0 1 0 S3 0 0 1 0 0 0 0 1 0 S4 0 0 0 1 0 0 0 0 1 A+I= S5 0 0 0 0 1 1 0 0

3、 0 S6 0 0 0 0 0 1 0 0 0 S7 0 0 0 0 1 0 1 0 0 S8 0 0 0 0 0 0 0 1 0 S9 0 0 0 1 0 0 1 0 1 S1 S2 S3 S4 S5 S6 S7 S8 S9 S1 1 1 1 0 0 0 0 1 0 S2 0 1 1 0 0 0 0 1 0 S3 0 0 1 0 0 0 0 1 0 S4 0 0 0 1 0 0 1 0 1 （A+I）2 = S5 0 0 0 0 1 1 0 0 0 S6 0 0 0 0 0 1 0 0 0 S7 0 0 0 0 1 1 1 0 0 S8 0 0 0 0 0 0 0 1 0 S9 0 0 0

4、1 1 0 1 0 1 S1 S2 S3 S4 S5 S6 S7 S8 S9 S1 1 1 1 0 0 0 0 1 0 S2 0 1 1 0 0 0 0 1 0 S3 0 0 1 0 0 0 0 1 0 S4 0 0 0 1 0 0 1 0 1 （A+I）3= S5 0 0 0 0 1 1 0 0 0 S6 0 0 0 0 0 1 0 0 0 S7 0 0 0 0 1 1 1 0 0 S8 0 0 0 0 0 0 0 1 0 S9 0 0 0 1 1 1 1 0 1 S1 S2 S3 S4 S5 S6 S7 S8 S9 S1 1 1 1 0 0 0 0 1 0 S2 0 1 1 0 0 0 0

5、 1 0 S3 0 0 1 0 0 0 0 1 0 S4 0 0 0 1 0 0 1 0 1 （A+I）4 = S5 0 0 0 0 1 1 0 0 0 S6 0 0 0 0 0 1 0 0 0 S7 0 0 0 0 1 1 1 0 0 S8 0 0 0 0 0 0 0 1 0 S9 0 0 0 1 1 1 1 0 1所以，r=34、区域划分SiR(Si)A(Si)C(Si)B(S)11，2，3，811122,3,81,2233,81,2,3,9344，5，6，7，944455,64,5,7,95664,5,6,7,9675,6,74,7,97881,2,3,8195,6,7,94,99 S1

6、 S2 S3 S8 S4 S5 S6 S7 S9 S1 1 1 1 1 S2 0 1 1 1 S3 0 0 1 1 S8 1 0 0 0 M(P)= S4 1 1 1 1 1 S5 0 1 1 0 0 S6 0 0 1 0 0 S7 0 1 1 1 0 S9 0 1 1 1 15、级位划分要素集合SiR(Si)A(Si)C(Si)C(Si)=R(Si)(P1)P1-L011,2,3,811L1=S822,3,81,2233,81,2,3,93881,2,3,88P1-L0-L111,2,311L2=S322,31,22331,2,93P1-L0-L1-L211,211L3=S2221,22P1

7、-L0-L1-L2-L31111L4=S1对该区域进行位级划分的结果为(P1)=S8,S3,S2,S1要素集合SiR(Si)A(Si)C(Si)C(Si)=R(Si)(P2)P1-L044,5,6,7,944L1=S655,65,7,95665,6,7,9675,6,77,9795,6,7,999P1-L0-L144,5,7,944L2=S5555，7，9575,74,7,9795,7,999P0-L0-L1-L244,7,944L3=S7777,979999P0-L0-L1-L2-L344,944L4=S4,S99999对该区域进行位级划分的结果为(P2)=S6,S5,S7,S9,S46、提

8、取骨架 S8 S3 S2 S1 S6 S5 S7 S9 S4 S8 1 0 0 0 S3 1 1 0 0 S2 1 1 1 0 S1 1 1 1 1 M(L)= S6 1 0 0 0 0 S5 1 1 0 0 0 S7 1 1 1 0 0 S9 1 1 1 1 1 S4 1 1 1 1 1 S8 S3 S2 S1 S6 S5 S7 S9 S8 0 0 0 0 S3 1 0 0 0 S2 1 1 0 0 S1 0 1 1 0 M(L)= S6 0 0 0 0 S5 1 0 0 0 S7 1 1 0 0 S9 0 1 1 0 831265794A、合理选购电脑样式B1、价格B2、性能B3、体积B4

9、、修理便利C1、笔记本C2、台式电脑购机评价体系中各要素的推断矩阵及其有关分析计算表AB1B2B3B4WiWi0miB111351.9680.3824.402B211552.2360.4434.068B31/31/5110.5080.0984.067B41/51/5110.4470.0874 (5.159)max4.032 CI=0.011 RL=0.89 CR=0.0120.1B1C1C2WiWi0miC1131.7320.752C21/310.5770.252 (2.309)max2 CI=0 CR=00.1B2C1C2WiWi0miC111/30.5770.252C2311.7320.752 (2.309)max2 CI=0 CR=00.1B3C1C2WiWi0miC1152.2360.8332.002C21/510.4470.1671.998 (2.683)max2 CI=0 CR=00.1B4C1C2WiWi0miC111/50.4470.1671.998C2512.2360.