Vấn đề kết nhập thông tin biểu diễn bằng bộ 4 với ngữ nghĩa dựa trên đại số gia tử

T^p chi Tin hqc vk Diiu kliiSn hpc, T.27, S.3 (2011), 241-252 VAN DE KET NHAP THONG TIN BIEU DIEN BANG BO vdl NGur NGHTA DLTA TREN DAI S6 GIA TCT NGUYfiN VAN LONG, H O A N G VAN THONG Dai hoc Giao thong van tdi Tdm tat Bai toan k^t nh$,p thong tin ndi chung ddng vai tro quan trgng qu4 trinh lay quylt dinh va do no cd y nghia ufng dung r0ng ldn, d^c biet la bki todn ket nh?Lp thong tin md vi ngudi thudng quyet dinh thong qua thong tin md ngon ngii Cho den cdc phudng phdp gidi bai todn chu yeu d\ta tren cdc tap md Trong [8] va [7] cdc tdc gia da nghien ciiu giai bai todn ling dung ngii nghia ngon ngii dvra tren d^\ so gia tijf (DSGT) vdi bieu diin ngfl nghia tUcJng iing bang do; lieu bo va bp Trong bai bdo nay, thong tin md cua thang ddnh gid duoc bieu diin bang bo dl khac phuc mot so thigu sdt [7] No cho phep biiu thi thong tin md day dii hdn va cho phep tinh todn tren cdc thong tin ngon ngii thang ddnh gid triic tiep hdn va do kgt qua ket nhap tu nhign va chinh xdc hdn Abstract The role of information aggregation problems is in general very important in the decision process and hence they can find applications in many fields, particularly, for the fuzzy information aggregation problem since human makes decisions by means of vague linguistic terms So far there are many methods have been exploited to solve these problems but mainly based on fuzzy sets The works [8] and [7] were devpted to solve this problem, applying hedge-algebra-based semantics of linguistic terms to representing linguistic data by 2-tuples or 3-tuples In this paper we introduce 4-tuple representation exploiting more deeply hedge-algebra-based semantics of linguistic terms for solving this problem This allows represent the semantics of linguistic symbols in rating scale more completely and hence it produces output results more exactly and naturaly M DAU Rat nhieu van de cua viec lay quy^t dinh hang cua ngiidi deu dua tren cac thdng tin khdng chinh xac cd ban chat md, khdng chac chdn Ly thuyet tap md da tao cac md hinh toan hoc va cac cdng cu cho phep diia cac each tiep can khac de giai cac bai toan lay quyet dinh nhiing Hnh viic khac Nhiing tilu ilng dung cua ly thuyet tap md lai thdc day sii phat trien ciia chinh ly thuyet dd va vay da ddi cac chuyen nganh nhii cdng nghe logic md (Fuzzy logics technology), cdng nghg ket nhap (Aggregation technology), tinh toan vdi cac txt ngdn ngii (Computing with Words-CW) Tinh toan vdi cac tii ngdn ngii la mot ly thuyet cho phep thao tac tren cac tii de giai quyet cac bai toan ma dii lieu dau vao va dau can bieu thi bang cac tii ngdn ngii, dac biet ddi vdi cac bai toan lay quyet dinh Mdt bai toan quan trgng cua qua trinh lay quyet dinh la tdng hop, ket gdp cac thong tin, dii heu ngdn ngii tii cac ngudn khac (tii cac chuyen gia chang han), de cd mot thong tin danh gia dai dien chung, diidc goi la bdi todn kit nhdp tren cac tii ngon ngii Bai toan cd t h i diidc md ta nhii sau: 242 NGUY&N VAN LONG, H O A N G VAN T H O N G Gia si'r ngiidi (luyet djnh phai lay (luyet djnh chgn mOt phiidng dn "tdt nhat" m phudng 4n Igfa cliMii Ai, i = 1, ,m, tren cd sd lay ^ kien d4nh gid cua n chuyen gia Cj, j = I, 11 Trong mdi triidng tiidng tin ngdn ngii, eae chuyen gia bilu thj danh gia cua minh bang eae tfr ngdn ngii (thang danh gia, ngdn ngii) liy t9.p S = SQ,- • - ,Sg Ky hi?u Xij la y kien danh gux eiia eliuyen gia j ve phiidng An AiMgt >eii can tt.r nhien la can djnh gia y kien tong hgp cua cdc chuyen gia ddi vdi tiing phiTdng an nghia la ta can sir di^ng mgt phep toan ket nh^p f(« tfch hgp cac f kien {xij : j = 1, ., 7)} eua eae elmyen gia Mgt each hinh thiic todn hgc, toan tuf ket nhdp Id mgt dnh x?i (J* : {so Sg}" —> {soi • • • ^ Sg} Anh x^ ndy phai dirge xdc djnh cho ket qua ciia phep todn @(sti, .s,„) eo the'' xem Id bien thj y kien tdp the ciia n chuyen gia Nhir vdy, l)ai todn ket nhdp Id mgt bdi t.oaii cdt yeu qud trinh lay quyet dinh, va vi gid tri ciia todn ti'r cung la mgt tir ngdn ngfi, nen ngiidi ta can sii dting cdng cu tfnh todn tren cdc tfr ngdn ngfr Cd nhifMi phiidng phdp ti^p can tfnh todn khdc [1-5, 7, 8, 10] de giai quyet van de De ldm rd ngi dung nghign cutu cua bdi bdo, ta se phan tfch tong quan mgt vdi phudng phdp 1.1 Phi:fdng p h a p t i n h t o a n ngon ngU diia t r e n n g u y e n ly m d r o n g cua t a p md Y tudng chinh cua phUdng phdp Id cdc phep tfnh ket nhdp kinh dign nhu phep trung binh so hgc, trung binh cd trgng so , cd the chuyen cdc phep tfnh tUdng iing tren cac tap md, ching ban phep lay trung binh cgng md, trung binh cdng md cd trgng so tren cac tap md Khi dd, cdc tii ngdn ngii tap S dUdc xem la cdc nhdn cua cac tdp md Cac phep ket nhap md thuc hien trgn cdc tap md ciia cdc nhdn tap S se cho ket qua la tap md Ndi chung tap md ket qua khdc vdi cdc tap md cua cdc nhan, hay nd khdng bigu thi cho mdt nhan ngdn ngii nao S Dieu dan den sii cdn thiet phai phdt triln cdc phuong phdp xdp xi ngon ngit, tiic la tim mgt nhan ngdn ngii S cd tdp md xap xi tdp md ket qua nhat 1.2 Phi/cTng p h a p t i n h t o a n t r e n cac ky hieu n g o n ngi? Gia sut y kien ddnh gid theo mgt tigu chf dugc bilu thi bdng cdc tii ngdn ngii tap S = {SQ, - ,Sg} dugc sdp tuyen tfnh theo ngii nghia cua chung cho: Sj < Sj neu va chi nlu i < j.Vi khdng thi tfnh true tiep trgn cdc tii ngn ngUdi ta mugn ckn triic tfnh todn cua doan [0, g] bao hdm cac chi so di thi;c hi?n vi?c ket nhdp so hgc Y tudng the hien nhU sau [3-5] Gia sut ta lay ket nhdp tdp cdc tii ngdn ngii A = {ai, ., Op}, Oi E S.Ta thiic hign mgt hodn vi cdc chi sd cua tdp A, A = { a ^ i , , a,rp}, cho a,ri > a-irj neu i < j - Xet mdt phep kit nhap so hgc g nao dd, g se cdm sinh mOt phep ket nhdp 9* trgn tap S dUdc dinh nghia nhu sau: Tfnh g{'Ki, , TTp) E [0, p], vdi TFI, , Tfp la cdc chi so cua cdc phan tut A Ddt i* = round(5'(7ri, , TTp)), dd round la phep lam tron so hgc Khi dd phan tut Si* dugc xem la kit qua ket nhdp g*{aT,^, ., a^rp) Phep kit nhap g* dudc dinh nghia nhu tren la mdt han che, yi nd chiu mgt rang bugc ft tu nhien va mat mat nhilu thong tin Hiln nhign, thay vi dung chi so cdc tii nhu tren, neu ta sut dung ngii nghia dinh lugng cua cdc tut ngdn ngii thang ddnh gid thi dinh nghia phep ket nhap g* cd cd sd hdp ly hdn (xem [10]) VAN D ^ KET NHAP THONG 1.3 TIN Bifiu DI6N BANG BO 243 Phtfdng p h a p t i n h t o a n ngon ngiJ di^a t r e n bieu d i i n ddf lieu b o ^Trong phUdng phdp tren ta can lam trdn bdng bilu thiic i* = round(p(7ri, • •, TTp)) de kit qua la mgt tii ngdn ngii Oi* tdp S Tuy nhien vi?c ldm trdn ldm m4t mdt thdng tin vd cac tdc gia [4] da dUa cdch bieu diln dii li?u bO de khdc phuc si; mat mdt thdng tin ndy k-1 \—h-\ k I tj I I b, g Hinh 1.1 Bilu diln bg Y tudng ciia phUdng phdp nhu sau: gid tri g{ni, , TTp) chUa ldm trdn se Id mgt so thuc b E[0,g] k-0.5 ton tQ,i m0t khodng Sk{C) cho gid tri dinh lucfng v{y) nam Sk{C) cimg vdi hai khodng tinh md mite k + ki vdi no Viec chiing minh menh de trgn la rat ddn gidn -".hiing tdi khdng trinh bay d ddy VAN D E K E T NHAP THONG TIN BI^U DifiN BANG BO 245 D i n h n g h i a Vdi mgi y E X^k), khodng (2.4) cd tfnh chit v{y) E Sk{C), va nd Id dilm cua khoang Sk{C) vdi tdpd tu nhign trgn mien so th^c, dUdc ggi Id ldn cdn ngii nghia miic fc cua tut ngdn ngii y 2.2 Bieu d i i n tuf n g o n ngu? b a n g b o ngi? nghia Cho mgt DSGT tuyin tfnh vd diy du A X = {X, G, C, H, [0,1] Phep p-ngdi g*,g* : {Ts)^ -^ Ts, dugc ggi la phdp kit nhdp md rdng cua phep kit nhdp thdng thudng g sang miln cdc bg chiia cdc tut ngdn ngii nlu nd dUdc dinh nghia nhu sau: Vdi vectd dii lifu {{sik, v{sik), rik, S{sik)) : fc = 1, ,p), g*{{sii, v{sii), m, S{sii)), , {sip, v{sip), rip, S{sip))) = A{g{rii, , g{rip)) (3.9) Dinh nghia phep kit nhdp trfn tut dua trgn bilu diln bg ngii nghia ciia chiing mang nhilu thdng tin ngii nghia ciia tut hdn so vdi vifc thUc hifn phep kit nhdp tren cdc chi so vi nhiing ly sau: (i) Cac khoang ldn can S{si) cua cdc tur mang ngii nghia dinh lUdng cua cdc tut vdi miic tinh md I Chiing dugc xdc dinh dua tren dg dg tinh md cua cdc tut ngdn ngii Vi vdy, gid tri thuc rj cung mang nhilu thdng tin ngii nghia cua tut nhilu hdn cdc chi so ciia chiing; VAN Dfe K^T NHAP THONG TIN Bifiu DifiN BANG BO 249 (ii) Theo dinh nghia cua bg ngii nghia, gid tri ngii nghia dinh lugng v{si) cua Si cd the dugc xem Id gid tri thuc mang thdng tin ngii nghia phii hgp vdi si nhat va hieu so {ri* - v{si*)) cho ta thdng tin vl df lech cua vifc chuyen doi gid tri thuc vo gid tri ngdn ngii Sau day ta chi mgt so phep kit nhdp thdng dung 1) Phep trung binh cong so hgc Cho cac bg ngii nghia tren thang dilm Ts, {sik, v{sik), rik, S{sik)), k=l, ,p Dinh nghia 3.1, phep ket nhdp trung binh so hgc 9anth{0'l^ ,ap) = p Theo y ak ^-^ i