The method for multi-attribute emergency decision-making considering the interdependence between information sources
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- ῬαΧάβ Παπαϊωάννου
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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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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 ;$.
10 2054 7»ρ 7 Km _ v ^ 38 * 9 ΞΨ5fi0<» ).?}%χ Pignistic &gg=χ j# ffa Λ U<<5*) Dempster <5*) W<5*) Bept(A i) Λ ^ Bept(A i) Λ ^ Bept(A i) Λ ^ A A A A A Mh Bept(A i ) A 1 A 2 A 3 A 4 A 5 Dempster Ω 1 ΞΨ5fi0<» χ Pignistic &gg fi=P 5fi0<»)j#νa.?}%χ Pignistic &gω Pignistic flj+ U<<5*) W<5*) Bept(A 1) Bept(A 4) Bept(A 4) Bept(A 3) Bept(A 3) Bept(A 5) Bept(A 5) Bept(A 2) appw,&jμsgy a%jv"x-ωav, &fi]pfflfi P4Φ ffi2v/_ppwf; ρnxφ`. <$JlΩ?4 BJP4fi4dV-Ω, Pffi<$A;/6NVP4fiiQWmR$^i ±NfiΩfi<^. Dfl+Ψ>3gP4fi@"WVppW a,&zu. m:, 7nppW a,&-ω NP4fi4dV-Ω, >Xffi<$JlV-Ωνe. ffie, nffip4fi@"v-ω, nfi P4fi >Vz ρnp4 U#F, /#F e #FpV@"j, rv/p4fiapv@"j, $ x@"p4 VTΦe V ], sff<[<$jl$bj3 P4]VΦi. #E, Ψ>3gP4fi@"jV<$T; ;4)(, A;fi P4fi<$P4; r >Xffi Pignistic fiicv aω`z V`', ^<pp W a,&vξv. ld, / P,r[zuV ±/6, ρ ffiξ@"zu U[nffl 2. 2Φ.ν ~, fl+ψ>vzufi ΩbppW a,&v/6οlfik Φ.οl6b, ]GG[<$Jlfi"P 4fiiQWVmR, DK[ffi$^i ±NVx#. ΠYff [1] cq, ', %v, Y. νthz b&k vgχ»+ ^j [J]. &Kffm, 2016, 28(8): 3 5. Liu Y, Xu W, Qiao H, et al. A preface to the progress of research on emergency management of emergencies[j]. Management Review, 2016, 28(8): 3 5. [2] PΠ', roν,.,-, Y..*νthz b&kgχ»+ [J]. 7»ρ7Km _v, 2012, 32(5):
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