B题2011年2011第四届一阶段优秀论文1207

1o3/p?0I ?m c?1o3”p?”I?m?m5K ?x 3mm?m?U? )! fe! ? ?)?“! ?mKk?K ? QO?Jm5K?,XJO?Jm? ? )? 7LU5?z?L3? z(? x- m5K ?ym?! 5 Xkm5K ?1 ?n ?m 1207 ?W? m? 1! 2! X= 3! r“ m? m|O ?| F2011c4?22F 数学中国提供（w w w .m a d i o .n e t ） 数学中国教师交流群：70339631数学中国w w w .m a d i o .n e t官方微博：h t t p :/w e i b o .c o m /304456943 数学中国YY网校频道：159214 数学中国w w w .m a d i o .n e t数学中国公众微信平台：s h u x u e z h o n g g u o 1o3/p?0I ?m ?; m?mJcW? 1207 m?dm|”x”c? m?dm”?c?1? 数学中国提供（w w w .m a d i o .n e t ） 数学中国教师交流群：70339631数学中国w w w .m a d i o .n e t官方微博：h t t p :/w e i b o .c o m /304456943 数学中国YY网校频道：159214 数学中国w w w .m a d i o .n e t数学中国公众微信平台：s h u x u e z h o n g g u o ?#1207 2011c1o3/p?0I ?m K8 u?g?)?5dINX c )?5! ?g! ?5?! ?. Xa?uua3?L)?5K% 2y5?o/?)?5?5?a?5?X d?)?5K3n?b?)?e?g ?. d)?5eD?5! ?5! )?X?5! * ?5u?g(?8f?5IAMatlaby?g (f?I?-?L ?9I1-9I ? I?) ?85I?A?-? NX ? /doN)?5?I?1?.?J?A:3 ?YJ?g m 1207 K8 BK m: 数学中国提供（w w w .m a d i o .n e t ） 数学中国教师交流群：70339631数学中国w w w .m a d i o .n e t官方微博：h t t p :/w e i b o .c o m /304456943 数学中国YY网校频道：159214 数学中国w w w .m a d i o .n e t数学中国公众微信平台：s h u x u e z h o n g g u o ?#1207 Abstract While human society continuously developing and civilization moving on, the problems about the biodiversity arise gradually. People of the world begin to show more concern about how to protect the biodiversity.In order to fi nd the method to measure the biodiversity in some areas, based on reasonable assumptions and some knowledge of biology, this paper builds a mathematical model with the method of analytic hierarchy process. Hierarchical structure is set up with four elements-genetical diversity!species diversity!ecosystem diversity!landscape diversity and their sixteen sub elements. Matlab was used to deal with the way of solving the problem. In the process of identifying each sub elements weight, diff erent indexes were used to establish comparative matrix pairs. After getting the corresponding weight of the sub elements, a system was built to quantitatively appraise the biodiversity. The entire error analysis was carried out, and some optional ideas were off ered which can be used in further study. 数学中国提供（w w w .m a d i o .n e t ） 数学中国教师交流群：70339631数学中国w w w .m a d i o .n e t官方微博：h t t p :/w e i b o .c o m /304456943 数学中国YY网校频道：159214 数学中国w w w .m a d i o .n e t数学中国公众微信平台：s h u x u e z h o n g g u o ?#1207 1K?- 2010cI(?IS)?5c?o/?)?5?5 ?a?5?5?Oy?/IS ?6;m?I?)?5)?X?m? IPBES ?8 A?k?Oy?X?(J Xd? ?)?5 D?: ?y3kNk?5 XkJA?qkKJk?5? L,?A?5?y3?U? ?)?5?1? K n?. ?O?k?d)?5?I |u 8?m 2b? 2.1?.?b? (1)Imp6 /?I?z (2)?eZ U?O?%n4723 (3)?5?e 2.2 Z:L)?5o C:LI? Ci:LI?1i D:L5?I? Di:L5?1i T Nj Mk :LIMkekINj|? W Nj Mk :LIMkeINj?A?- 3K dKTK5!?nSK8I K |?gd u?5dNXI? 0,cii= 1,cij= 1 cji 4.2?5u? O ?d?Satty?%nn? I5u? Satty?5n,IOC.I: C.I = C.I R.I 4 数学中国提供（w w w .m a d i o .n e t ） 数学中国教师交流群：70339631数学中国w w w .m a d i o .n e t官方微博：h t t p :/w e i b o .c o m /304456943 数学中国YY网校频道：159214 数学中国w w w .m a d i o .n e t数学中国公众微信平台：s h u x u e z h o n g g u o ?#1207 C.I=y5I,?R.I?g?5I LMatlab? = ?C.IL10% T? K T?5? - c?C.I,?20% 7LN?T-?W 4.2.1)?5o dO IDi?Z?-W Di Z L: W Di Z = W Ck Z W Di Ck ?Z(xi)?5oL Z(xi) = 100 n X i=1 W Di Z Di(xi) Dixi8z 4.2.2I?g I?J?-(W Di Z )?)K ?I?g b?AB4- -5m,Kdak=m?a= k m e ?-5A?3?N? 9-5?4K?9-5?4-5 9? =k?8 ?a = 9 1 8,KIL(XeL) X9I,dMatlabS$,?A?R.Ia,l?1?5u ? 5 数学中国提供（w w w .m a d i o .n e t ） 数学中国教师交流群：70339631数学中国w w w .m a d i o .n e t官方微博：h t t p :/w e i b o .c o m /304456943 数学中国YY网校频道：159214 数学中国w w w .m a d i o .n e t数学中国公众微信平台：s h u x u e z h o n g g u o ?#1207 5?.?) |Matlab O?I9Ie16I?- (1)9I. u?TZ: c11= 1,c21= 3,c22= 1,c31= 3,c32= 1 2,c33 = 1,c41= 2, c42=1 3,c43 = 1 2,c44 = 1 u?TC1: d11= 1,d21= 3,d22= 1,d31= 5,d32= 3,d33= 1 u?TC2: d11= 1,d21= 1,d22= 1,d31= 3,d32= 3,d33= 1,d41= 2, d42=2,d43= 1 2,d44 = 1,d51= 3,d52= 3,d53= 1,d54= 2,d55= 1 u?TC3: d11= 1,d21= 6,d22= 1,d31= 4,d32= 1 4,d33 = 1,d41= 5, d42=1 3,d43 = 2,d44= 1,d51= 3,d52= 1 5,d53 = 1 2,d54 = 1 3,d55 = 1 u?TC4: d11= 1,d21= 3,d22= 1,d31= 4,d32= 3,d33= 1. K?-: w(D1) = 1.11%,w(D2) = 2.74%,w(D3) = 6.75%,w(D4) = 4.41%, w(D5) = 4.41%,w(D6) = 14.02%,w(D7) = 7.89%,w(D8) = 14.02%, w(D9) = 1.32%,w(D10) = 13.69%,w(D11) = 4.12%w(D12) = 6.54%, w(D13) = 2.62%,w(D14) = 1.71%,w(D15) = 4.23%,w(D16) = 10.42%. (2)I. u?TZ: c11= 1,c21= 9 1 8,c22= 1,c31= c21= 9 1 8,c32= 1,c33= 1, c41=1,c42= 9 1 8,c43= 9 1 8,c44= 1 u?TC1: d11= 1,d21= 9 1 8,d22= 1,d31= 9 2 8,d32= 9 1 8,d33= 1 u?TC2: d11= 1,d21= 1,d22= 1,d31= 9 1 8,d32= 9 1 8,d33= 1,d41= 9 2 8, d42= 9 2 8,d43= 1,d44= 1,d51= 9 1 8,d52= 9 1 8,d53= 1,d54= 1,d55= 1 u?TC3: d11= 1,d21= 9 3 8,d22= 1,d31= 9 2 8,d32= 9 1 8,d33= 1, d41=9 3 8,d42= 9 1 8,d43= 1,d44= 1,d51= 9 1 8,d52= 9 2 8,d53= 9 1 8,d54= 9 1 8,d55= 1; u?TC4: d11= 1,d21= 9 1 8,d22= 1,d31= 9 2 8,d32= 9 1 8,d33= 1. K?-: w(D1) = 5.33%,w(D2) = 7.02%,w(D3) = 9.24%,w(D4) = 4.48%, w(D5) = 4.48%,w(D6) = 6.23%,w(D7) = 6.98%,w(D8) = 6.23%, w(D9) = 3.32%,w(D10) = 6.07%,w(D11) = 7.98%w(D12) = 6.43%, w(D13) = 4.61%,w(D14) = 5.33%,w(D15) = 7.02%,w(D16) = 9.24%. l?eL 6 数学中国提供（w w w .m a d i o .n e t ） 数学中国教师交流群：70339631数学中国w w w .m a d i o .n e t官方微博：h t t p :/w e i b o .c o m /304456943 数学中国YY网校频道：159214 数学中国w w w .m a d i o .n e t数学中国公众微信平台：s h u x u e z h o n g g u o ?#1207 dd?I?1D?5r?)?5 dINX,(JXe3 : 6?.?: 6.1?.?: (1)T?.?)?5?o-?I?I (?% ?dIO (2)T?.2?8I?dX (3)d5? ?9p? Nn) 6.2?.? T?.?uX?.?gn?.?5?u?g? n5LS?ucT2? k? l:w;5! n592“)? ?JE?u? l5 1 ? k?I? K?.?- d?.?)w19?I.I?(J? .Ia?JJ(?10g? K-5?( ? XDiDj ?-5?dL ?* ?(JUJ?,?;+N? :?2d;?;9?X |;?1?! !? eZ;z?E? L3?1? n ? 1? ?.z? b? ?.?g?(?4?g(?2 ? .b?gSm3pK|?mvk,? 3) dD?5?5 ?/?|K?)+! )?XD*?512l5w?.CiCjm3pX D?mU3XXJ?.?I 7 数学中国提供（w w w .m a d i o .n e t ） 数学中国教师交流群：70339631数学中国w w w .m a d i o .n e t官方微博：h t t p :/w e i b o .c o m /304456943 数学中国YY网校频道：159214 数学中国w w w .m a d i o .n e t数学中国公众微信平台：s h u x u e z h o n g g u o 2)?5dIO 8 数学中国提供（w w w .m a d i o .n e t ） 数学中国教师交流群：70339631数学中国w w w .m a d i o .n e t官方微博：h t t p :/w e i b o .c o m /304456943 数学中国YY网校频道：159214 数学中国w w w .m a d i o .n e t数学中国公众微信平台：s h u x u e z h o n g g u o ?);?L? ?3?g;+N? ?p23?B?5)?Delphi technique6 ;8N?3?l?%_8l?! ?m pK?;p?)$Eg?1? ?6 u;?! ? ?o?U?N+N“? (J z 1kd(Lucas,W.F)() lX?. :I“E?1996.12 2?7( ?. ?:p?,2003 3 ?9A ?:p?2005.6 4z u )?5?I9Y ?:I?2009.03 51o*?59?ohttp:/ 6F#u*?5?5?)?Vol.18 No.1:76- 81,1998.01 7F#| *?5?a.9)? /n?Vol.51 No.5:454-4621996.09 8Q“#?q?X ?5?dIdIO ?H?EVol.26 No2:26- 29,1999.06 94W?L/)?5d)U9?W/g,?oI) ?Vol.10 No.1:76-782002.03 10?I3AHPIX?%163?I“c+nX 82001c 11 AHP?Id $+nVol.9 No.4:42-452000.12 12x?AHP?I Xn 11990.01 13?7?r?I)?5yGS Vol 35 No.34:111172- 1111742007 14?I3AHPIX?%163?I“c+nX 82001c 15x?AHP?I Xn 11990.01 9 数学中国提供（w w w .m a d i o .n e t ） 数学中国教师交流群：70339631数学中国w w w .m a d i o .n e t官方微博：h t t p :/w e i b o .c o m /304456943 数学中国YY网校频道：159214 数学中国w w w .m a d i o .n e t数学中国公众微信平台：s h u x u e z h o n g g u o ?#1207 16=?Iu?giI?JdXn1n 2005.03 17?L ATEX2?S ? u?,2011,1 18+?Matlabp?E|A:25Y 7N matlabS function W,ahpResult = ahp(C) %?g? %Cn*1?cell.|n+1?u?g?.?C;?g?I?cell|b?1k?km_k?l?mg?1,2,.,m_k, %Ck1,j;?1k+1?1k?j?j=1,2,.,mCk2,j %;?m_k+1*1?6|1L1k+1?A ?1k?j?|?0L %|? %W:Y?8I?- %ahpResult:n*1?cell.|ahpResult;?g?(JahpResultk2,j?Ck1,j %?A?;ahpResultk3,j?A?5C.R. RI=0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 1.51;%5I n = length(C);%?C?nu?n+1 ahpResult = cell(n,1);%;?(J%k? ahpResultk = cell(m_k,1); for kk = 1:m_k %1k+1?1k?kk?A?A? V,D = eig(Ck1,kk); maxD,ind = max(diag(