The method for multi-attribute emergency decision-making considering the interdependence between information sources

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1 ^ 38 *^ 8 fl 6 ß6Jl ^u Vol.38, No fi 8 χ Systems Engineering Theory & Practice Aug., 2018 doi: / (2018) Oßv G7: C934,>μGo: A [dfl 9ο.! ρ!/@wφψfi T1ffi, $2Φ ( fi j 0 m ; w0p, fi ) = ( Ψ8A ± X±`ffi.7v Qß, "S ο-(<^ff, 9F:*ρ Ξ. 6Y, ψ W ffl-(<+k.]`ffi.7v Qca. fl), hwt:a ± ]`ffi.7v Q&!N fi;»z, ψw-(<+kv_]xχcau ffl-(<+k_]a qun@, 4μqA -(; =Z, hwt: Pignistic f C]7vM/cL/?ca, Π[gcLB ]-_R5, 4ρ*` ffi.7v Q] ]. Er, "pχωd'3aeca>`ffi.7v QD]9,.. d'}on, ffl-(<b ]+k.o~ff7v Q}oizΛl, #ßνsflA ± 9k-(<^ff.] ο, Π[fl»>ρy78D]b%.,H 7v; `ffi. Q; A ± ; -(<+k. The method for multi-attribute emergency decision-making considering the interdependence between information sources CHEN Xuelong, WANG Yali (Faculty of Management and Economics, Dalian University of Technology, Dalian , China) Abstract When evidence theory is applied to emergency decision-making, it is often supposed that the information sources are independent which is contrary to the reality. Therefore, we propose the method for multi-attribute emergency decision-making considering the interdependence between information sources. Firstly, the multi-attribute emergency decision-making problem is represented based on evidence theory. Secondly, we put forward the method to compute the interdependent degree between information sources, and the evidence combination rule considering the interdependent degree between information sources to fuse the evidence information. Thirdly, the emergency alternative selection method based on the Pignistic probability, which can expand the difference of alternatives reliability, is discussed. At last, an example analysis on multi-attribute emergency decision-making problem is applied to verify the effectiveness of the proposed method. The analysis results show that considering the interdependence between information sources will make the emergency decision-making more objective and scientific, as well as weaken the independence hypothesis on information sources and expand the application scope of evidence theory. Keywords emergency; multi-attribute decision-making; evidence theory; interdependence of information sources ~'yq: K?GN: Qo3: 0de (1978 ),, 3, [^ΞI<, Λn, fff, gχ F: chenxl dg@ dlut.edu.cn; ψen (1990 ), ffl, 3, >±Π3<, fgχy, gχ F: b&k, wangyali51@163.com. :Oρi: -ke97cyffi ( ); Λοψ<,QS7cgχ(fiYffi (17YJC630014); ZffiZQ7*JYffi (L13DGL061); Om IYffi7gu1 azeπ (DUT18JC01) Foundation item: National Natural Science Foundation of China ( ); Humanities and Social Science Youth Foundation of Ministry of Education of China (17YJC630014); Social Science Planning Foundation of Liaoning Province of China (L13DGL061); The Fundamental Research Funds for the Central Universities (DUT18JC01) Hfi*1( : 0de, ψen. 4hQ5flA#XWqqX b-' v [J]. 7»ρ7Km _v, 2018, 38(8): ,fi*1( : Chen X L, Wang Y L. The method for multi-attribute emergency decision-making considering the interdependence between information sources[j]. Systems Engineering Theory & Practice, 2018, 38(8):

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5 ^ 8 fl 0de, Y: 4hQ5flA#XWqqX b-' v R]E μ,μ vovu#f, c8 vffiusz #FpV@"6j. 7n a,&/6np4fi4dvφ`, o#±<$jln#fpv@"jfi Pj2t, EBJfi4dW3 VP4. md#f cl i h i S#F cl j h j, (#Fp@"jVPj2tC8: ΩI,i mh ih j ({Dep}) =αβh i ih j, ΩI,i mh ih j ({Ind}) =α(1 βh i ih j ), ΩI,i m h ih j ({Dep, Ind}) =1 α. ffin, `ο@o% Ω I ={@" (Dep), iq (Ind)}; m ΩI,i h ih j ({Dep}), m ΩI,i Vz #F cl i h i cl j h j V856j ffffl7de μ,flμ h ih j ({Ind}) νeffp4fi DM i ΛΨff ApV@" iq6j. α %@ VPj2t1>6t, νen#fp@"6jχe fi VP4fi aω`z 0fi ρnxd U#F, D#FpV@"jwΞ[P4fiApV@ "6j. μ$d (7) VUfft P4fiΨffV H #FpV@"j, Λfi#Fp@"jV.CwΞv P4 fi@nffiav P4fiV9ff@"6j, c: ffin, m ΩI,DMi m ΩI,DMi (A) = 1 H H h i=1 (7) ΩI,i mh ih j (A), A 2 ΩI. (8) jp4fi DM i N;4 νeffd (8) VUVP4fi DM i Nz V H #FVhff@"6j. ld, P4fiAp@"6jVPjCApV* ± Pignistic fii]k Vzd UfiKDK, mp4fiapjξ@", Cd (9) (10) Λe. { γ(dmi,dm j )=Betp({Dep}), (9) γ(dm i,dm j )=Betp({Ind}), B A Betp(A) = m(b). (10) B B Ω I,B ffin, Betp( ) %Ξ fii]k2t, ± US@"WiQV Pignistic fiic; γ(dm i,dm j ) γ(dm i, DM j ) ονewp4fiapv@"6j9iq6j. Q γ(dm i,dm j ) > γ(dm i,dm j ) ], 2P4fi DM i DM j j@"v, wa2%iq. ffmr/68vuv P4fi@nffiav P4fiV@"6j. ffffip4fi DM i np4fi DM j V@ "jfivdxffi DM DM i V@"j, Λ vjp4fiv@"jj~n2v. Dfl, FfiQW P4 fi@giq],!ω2p4fiapjiqv, cfqfiv P4fi av P4fi@", (P4fij@"V. D, W P4fiApV9ff@"j/C%W2ANVlKC, c γ(dm i,dm j )=max{γ(dm i,dm j ),γ(dm j,dm i )}. (11) 8 2> γ &fi~ψw ~n2wxφ`. ρ(svπ*a, _P4fi tv*l@"jj~zv, c γ(dm i,dm j ) γ(dm i,dm j,dm t ). % _P4fiV*p, 9ff@"V8ΩWffiH. D, Q,&2% s ], /e WWApV@"j, ρ/lhcn%9ffv@"j [29], Cd (12). γ(dm 1,DM 2,,DM s )=min(γ(dm i,dm j )), i,j =1, 2,,s. (12) μ$mrzu, 8VUfi pwfly8p4fiapv@"j. ffixfl CjXffi,&27n FΞ >Vfi ρnp4e mp4fiv@"j, r+= [29] /e <$pv'h U#F. D, += Ωzu8 G=c,&P4>swΞP4fi@"VflM. Dfl, Ωzuj7nppW a,&p4 fiffiω'p± E»i rvφ`ψ>v, e οlbπ r, Ξk±ffi a,&]pfflfi P4fiffiΩ XΦ`. 3.2 Ybffffl7μ,χ BS4ff ppw a,&/6pffi6ff,&/6, Zq fi P4fiΨffV<$P4 UfiKA;, V/ ß V6ffPjC. Q!, <$V;4)(fipRTd [36 40], p#± Dempster ;4)(ρmRP4fiiQ. 7

6 2050 7»ρ 7 Km _ v ^ 38 * n@"<$v;4, Denoeux [25] Ψ>V V;4)(US(yV?8. PC!Λr, ffip4fiviqw2@ "jμ$b+ mv, cp4fiv@"6j~ 0 c 1, QP4fiV@"6jflffi (0, 1) ](/u m. %Ω, Mr-Ω, flh Ψ>vR<$VT;;4)(, V/ppW a,&-ωn»pwfly8 ßV6ffP j2tc. T;;4)(C8: m Mixed (A) =(1 γ) m (A)+γ m (A), A Ω ' A. (13) ffin, m Mixed (A) νeλpw8 Ω A V6ffPjC; γ νeωpw8p4fiapv@"j; ±6 ονe Dempster ;4)(9 V;4)(. R m 1 m 2 j`ο@o Ω Md}VW BPA 2t, Dempster ;4)(9 V;4)(νeC8: m (A) =m 1 2 (A) = 1 K 1 w(a) = B,C Ω,B C=A m 1 (B) m 2 (C), A Ω, (14) m (A) =m 1 2(A) = 1 K A Ω A w1(a) w2(a), A Ω, (15) 2 B A, B 2N q(b) if A 2N, B A, B 2N q(b), q(b) ( 1) B A +1 = A,B Ω,B A B A, B 2N q(b) (16) otherwise. B A, B 2N q(b), q(b) = m(c), B Ω. (17) C Ω,C B 1 ffin, K 1 1 K 2 νe:μ6j, K 1 =1 B,C Ω,B C= m 1(B) m 2 (C),K 2 =1 m 1 m 2 ( ). A w1(a) A w2(a) j"ffi A VrN>12t (simple basic belief assignment, SBBA). SBBA je m 2tNHp±1W ß, 'Q±1W ß], ffinv ß %`ο@o Ω. vπtdνe%: m(ω) = w, m(a) =1 w, w [0, 1], 8rg% A w[30]. w 1 w 2 jff:) ΩUSV m 1 m 2 V0T, jrn>12t/h b [41]. q(b) j` ο@omvv VPj2t, νe[8ω]ys Ω B VlK"$PjC, $,&*ρnνez B Vl K8Pj. N %d8t];. T;;4)(hqiP4fiffi2iQW2ffi2@"]V*A, PC, md`ο@o% Ω={a, b, c}, W P4fi >Wj BPA 2t m 1 m 2. ν 1 ονe[q γ =0,γ =0.3, γ =0.6 _ γ =1]» ßVA;Φ.. 1 ΞΨ5fi0<» fiν2λz5 2 Ω m 1 m 2 m m m Mixed γ =0 m Mixed γ =0.3 m Mixed γ =0.6 m Mixed γ =1 {a} {b} {a, b} {c} {a, c} {b, c} Ω ffν 1 8 2>, QP4fijffi2iQ] (γ =0),A;Φ. Dempster )(@ ; QP4fijffi2@ "] (γ =1),A;Φ. V;4)(@ ; Q@"jflffi (0, 1) Ap], A;Φ.(jWRj;)(Vl 0DVΦ Pignistic %ff -> $ffiz $; ffffi M2thjd}$ Ω N= b]m, bu>v ß6ffPjCnΛ &ffz Ez@I$?K Vfi4dW,?ΦX4 az V,& w. Pignistic fiil%ff Smith [42] Ψ>, ΞVjΩ,P4fi4d]V6,&-Ω. Smets [43] vffi 2 [ Pignistic fiivjlx$, ρ<~ffi$fi4dρj`μv,&fikw. Smets?%PjI$ffi 2 fi (

7 ^ 8 fl 0de, Y: 4hQ5flA#XWqqX b-' v 2051 y: Credal(9 Pignistic (. $ Credal (, Ω8 /»RρJ R (D-S R 8C_JP R JPp R 8ΩW RX) VUPjρn; $ Pignistic (, ΩVPjfi]P4fiiVTd ffi,&. C VN(,&@ffl, w(,&&fi~;vφi. XffiPjVN(,&zu@ffl, Pignistic fiivνjtd ο±;;fvb+, ρωfikdk» ΩApVPj*,?οpVZffi,&uCVC`Ξ ; BΠX ffifiivzupcy$ Bayes zu@ffl, Pignistic fiififfipj, fizq:lfii, ρ8$fi (EMn< $ Uj;. ΩffiQ6 VC`Ξ fi!d, 8Ω ]*s], Pignistic fiivφiοl~; [44]. D, fl H #± Pignistic fii (wd (10)), DK 3.2 H ΛU»z 6ffPjV*, ffilq,&. Dfl, nffippwfly8v a,&-ω, Z3g»pWV0T.»z Vl0f; Pignistic fiicc d (18) Λe. Beptg=(A) = n λ j Bept(A). (18) j=1 ffin, Beptg=(A) νez A Vf; Pignistic fiic; λ j %»pw0t, ff(e 2uVU. ffmd,>» z V Pignistic fiic, rnω`z U ], &filkf; Pignistic fiicvz %l8ωvz. 4 Ξ_$ffi μ$+= [18], H,&[j DM 1 DM 2 _ DM 3 % a,&-ω`'lφz. ρχ az VΦ ]vπfi 8 4 ρnpw: AΩΩT (C 1 ) ψffωt (C 2 ) QΦΩT (C 3 ) _D ]p (C 4 ). #±οav (E 2u (AHP) /WWnffl m"8vupw C j (j =1, 2, 3, 4) V0T λ j, Cν 2 Λe.,&2n 5 aω`z (A 1, A 2,, A 5 ) U Eρn, >=c»}ν4"8, Cν 3 Λe, ffin»}ν4x K"8Cν 4 Λe. 2 ψß kοq@ qx C 1 C 2 C 3 C 4 λ j C 1 1 1/2 1/ C / C C 4 1/2 1/2 1/ C.R= ΞΨ ψ»)v?ß.?}%χ Ξw 4&pDQ@ Λ C 1 C 2 C 3 C 4 DM 1 DM 2 DM 3 DM 1 DM 2 DM 3 DM 1 DM 2 DM 3 DM 1 DM 2 DM 3 A 2 * [ OY OY OY * OY OY OY * [ OY A 3 OY [ [ OY * [ OY [ OY * A OY OY A 5 OY OY OY [ OY * OY 4 4)o3`6G ~ s 2 [ 3 OY 4 6 cb,&"8nλlp4j3 V, μ$d ß. C,&2 DM 1 $ pw C 1 8 ß% E 1 11 = {A 1,A 4 } E 1 12 = {A 3} E 1 13 = {A 5} E 1 14 = {Ω}. μ$ν 4 U> E1 11 E1 12 E1 13 E1 14

8 2052 7»ρ 7 Km _ v ^ 38 * n V,&ν4XKC ο% 6, 4, 5, 1. ffd (2) U>pW C 1 8,&2 DM 1 >V ßfii %: ˆm 1 11 ({A 6λ 1 1,A 4 })= 6λ 1 +4λ 1 +5λ 1 +1 =0.2846, ˆm1 12 ({A 4λ 1 3}) = 6λ 1 +4λ 1 +5λ 1 +1 =0.1897, ˆm 1 13({A 5 })= 5λ 1 6λ 1 +4λ 1 +5λ 1 +1 =0.2372, ˆm1 14({Ω}) = 1 6λ 1 +4λ 1 +5λ 1 +1 = ffin, λ 1 = jpw C 1 V0T. J, fi fi pw8fi,&2 >V ß_ffiXflfii C, C ν 5 Λe. 5 ΞΨ ψ»)v?*ffl L6=s: &g#m (BPA) qx -'3 ρ`χo W BPA C 1 DM 2 {A 1, A 4, A 5}: ; {A 2, A 3}: DM 1 {A 1, A 4}: ; {A 3}: ; {A 5}: ; Ω: DM 3 {A 1}: ; {A 2, A 4, A 5}: ; {A 3}: C 2 DM 2 {A 1, A 4}: ; {A 2, A 5}: ; Ω: DM 1 {A 1, A 4}: ; {A 2, A 3, A 5}: DM 3 {A 1}: ; {A 3, A 5}: ; {A 4}: ; Ω: C 3 DM 2 {A 1}: ; {A 2}: ; {A 3, A 4}: ; Ω: DM 1 {A 1, A 4}: ; {A 2, A 3, A 5}: DM 3 {A 1, A 4}: ; {A 2, A 5}: ; {A 3}: C 4 DM 2 {A 1, A 5}: ; {A 2}: ; {A 4}: ; Ω: DM 1 {A 1}: ; {A 3}: ; {A 4, A 5}: ; Ω: DM 3 {A 1, A 3, A 5}: ; {A 2, A 4}: ffffifi,&2v0t -fi, mr w 1j =0.36, w 2j =0.34, w 3j =0.3 (j =1, 2, 3, 4), /b 6 t η j =0.95. (ffd (3) U,&2 DM 1 DM 2 9 DM 3 n V85j ο%: v 1j =0.95, v 2j =0.8972, v 3j = (j =1, 2, 3, 4). ffd (4), ßV BPA s@ VfiοN, USl0DV BPA. Cν 6 Λe. 6 ZcV?vJ Cv BPA qx -'3 ρ`χo BPA C 1 DM 2 {A 1, A 4, A 5}: ; {A 2, A 3}: ; Ω: DM 1 {A 1, A 4}: ; {A 3}: ; {A 5}: ; Ω: DM 3 {A 1}: ; {A 2, A 4, A 5}: ; {A 3}: ; Ω: C 2 DM 2 {A 1, A 4}: ; {A 2, A 5}: ; Ω: DM 1 {A 1, A 4}: ; {A 2, A 3, A 5}: ; Ω: DM 3 {A 1}: ; {A 3, A 5}: ; {A 4}: ; Ω: C 3 DM 2 {A 1}: ; {A 2}: ; {A 3, A 4}: ; Ω: DM 1 {A 1, A 4}: ; {A 2, A 3, A 5}: ; Ω: DM 3 {A 1, A 4}: ; {A 2, A 5}: ; Ω: C 4 DM 2 {A 1, A 5}: ; {A 2}: ; {A 4}: ; Ω: DM 1 {A 1}: ; {A 3}: ; {A 4, A 5}: ; Ω: DM 3 {A 1, A 3, A 5}: ; {A 2, A 4}: ; Ω: F vffiv/n pw8 ßV6ffPj2tC, Zq3gP4fiV@"W, nfi,&2 (cp4fi) UP4;4. μ$ 3.1 Ψ>VP4fi@"je zu, m:μ$ν 3 V=c m"8, c,&2 >V aω`z ρnp4 U#F. C$pW C 1 8,,&2 DM 1 DM 2 >V aω`z #FI %: DM 1 = {cl3(a 1 3 ),cl4(a 1 5 ),cl5(a 1 1,A 4 )} DM 2 = {cl2(a 2 2,A 3 ),cl4(a 2 1,A 4,A 5 )}. ffd (5), V/ ο@nffip 4fi DM 1 DM 2 V#Fp@}j"8 M 1 M 2 : M 1 = , M 2 = / /3 2/

9 ^ 8 fl 0de, Y: 4hQ5flA#XWqqX b-' v 2053 ff u 1 nw"8 U#F, US ο@nffip4fi DM 1 DM 2 Vz #Fp@}j: DM 1 : β32 1 =1,β54 1 =1;DM 2 : β45 2 =2/3, β23 2 =1/2. $D, n#fpv@"j±d (7) U:H. ff`ο@o Ω =5,ρmR#F±1VPj2ttXiffiK, / α =0.75 [29], U: m 1 32 ({Dep}) =0.75 m 1 54 ({Dep}) =0.75 DM 1 : m 1 32({Ind}) =0, m 1 54({Ind}) =0, m 1 32 ({Dep, Ind}) =0.25 m 1 54 ({Dep, Ind}) =0.25 m 2 45 ({Dep}) =0.5 m 2 23 ({Dep}) =0.375 DM 2 : m 2 45({Ind}) =0.25, m 2 23({Ind}) = m 2 45 ({Dep, Ind}) =0.25 m 2 23 ({Dep, Ind}) P4fiVz #FpV@"6jwΞ[P4fiApV@"j. ffd (8) (10) VUP4fi ApV@"j: { γ(dm1,dm 2 )=0.875 γ(dm 1,DM 2 )=0.125, { γ(dm2,dm 1 )= γ(dm 2,DM 1 )= ffffiffiqw P4fi@GiQ],!Ω?%P4fiApjiQV. Λ, ffd (11) UP4fiApV9 ff@"j% γ(dm 1,DM 2 )=max{γ(dm 1,DM 2 ),γ(dm 2,DM 1 )} = J, V/$fi pwfly8 P4fiApV9ff@"6j, Cν 7 Λe. O±d (13) A;»pW83gP4fi@"jV ß6ffPjC, Cν 8 Λe. 7 ΞΨ ψ»fi 8EF A±ν-ffiν qx C 1 C 2 C 3 C 4 γ(dm 1,DM 2,DM 3) ΞΨ ψ»l6x±fiνg C 1 C 2 C 3 C 4 ρ BPA ρ BPA ρ BPA ρ BPA {A 1} {A 1} {A 1} {A 1} {A 4} {A 4} {A 1, A 4} {A 3} {A 2} {A 2, A 5} {A 2, A 5} {A 4, A 5} {A 2, A 3} {A 2, A 3, A 5} {A 2, A 3, A 5} {A 1, A 5} {A 1, A 4, A 5} {A 3, A 5} {A 2} {A 2} {A 5} {A 5} {A 3,A 4} {A 4} {A 4, A 5} {A 1, A 4} {A 4} {A 1, A 3, A 5} {A 3} Ω {A 3} {A 2, A 4} {A 1, A 4} Ω {A 5} {A 2, A 4, A 5} Ω Ω ld, % ffi,&, ffd (18) nfi 0TpW8V ß Ul0, ßV6PjC U Pignistic fii ]K, nz U ], ρ += [18] (Dempster ;4) 9Xffi V;4)(ΛUz V Pignistic fiic_ z Φ]y] UfflΞ, Cν 9 Λe. fffflξφ.8?, lφz % A 1 8fi. PXffi Dempster ;4 )(US aω`z ] A 5 >A 2, rxffifl+t;;4)(vφ. Xffi V;4)(VΦ.vI, c A 2 >A 5. 4jffffiT;;4)(j Dempster ;4)( ffi ;4Φ.flffiO±WR;4)(USVΦ.Ap; 'ffe 8?P4fi$»pWfly8j@"V'@"j?, Λ fl+zu;4vφ.ξπ ffiff V)(;4VΦ., Cο 1 Λe. Pffν V;4 )(, T;;4)(fiKDK[ ]' ]@_V»z pv Pignistic *C, ο ffiz V/N, vd6 jmff<[fl+zuvφi. afl, Gν 3 NV=c,&P48 2>,»P4fin aω`z A 2 V»i ρn9ffzffiz A 5. D, 3gP4fiV@"WΩGGff Dempster ;4)(8ΩUSVfitffiB$,& P4VΦ., b a,&φ.οl6b ;$.

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