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`eu khiˆe’n ho.c, T.23, S.2 (2007), 110–121 Ta.p ch´ı Tin ho.c v` a Diˆ ˆ T CACH ´ ˆ´P CA ˆ N DE ˆ U ˆ’ XA ˆ´P XI’ DU ˜ LIE MO TIE ’ ˜ ˆ ` TRONG CO SO DU LIE.U MO ˜ˆ N CAT ˜ˆ N CONG ´ HO ˆ`1 , NGUYE ˆ ` NGUYE HAO Viˆ en Cˆ ong nghˆe thˆ ong tin, Viˆe.n Khoa ho.c v` a Cˆ ong nghˆe Viˆe.t Nam Tru.`o.ng Da.i ho.c Khoa ho.c Huˆe´ Abstract In this paper, we introduced a method to approximate data on domain of fuzzy attributes in relation of fuzzy databases based hedge algebra Because, domain of fuzzy attributes can except values are number, linguistic values, thus we have to effect and simply on method to approximate data ´t B` `en tri thuˆ T´ om t˘ a b´ ao tr`ınh b` ay mˆ o.t phu.o.ng ph´ ap xˆ a´p xı’ d˜ u liˆe.u trˆen miˆ o.c t´ınh m` o cu’a mˆ o.t `en tri cu’a thuˆ o du a trˆen da.i sˆ a u liˆe.u m` o.c t´ınh m` o c´o thˆe’ l` quan hˆe co so’ d˜ o´ gia tu’ Bo’.i v`ı miˆ `an c´o mˆ o ch´ ung ta cˆ o.t phu o ng ph´ gi´ a tri sˆ o´, gi´ a tri ngˆ on ng˜ u , d´ ap xˆ a´p xı’ d˜ u liˆe.u mˆ o.t c´ach n gia’n v` a hiˆe.u qua’ ˘ T VA ˆ´N D`E ˆ DA `eu t´ac gia’ v`a ngo`ai nu.´o.c quan tˆam nghiˆen c´ u.u v`a d˜a u liˆe.u m`o d˜a du.o c nhiˆ Co so’ d˜ `eu c´ach tiˆe´p cˆa.n kh´ac nhu c´ach tiˆe´p c´o nh˜ u ng kˆe´t qua’ d´ang kˆe’ ([1–5, 10, 12]) C´o nhiˆ y thuyˆe´t kha’ n˘ang ([4]) Prade v`a Testemale n˘am 1983, cˆa.n theo l´ y thuyˆe´t tˆa.p m`o ([1]), theo l´ quan hˆe tu.o.ng du.o.ng ([2, 3, 5]) Tˆa´t ca’ c´ac c´ach tiˆe´p cˆa.n trˆen nh˘`a m mu.c d´ıch n˘a´m b˘a´t v`a xu’ l´ y mˆo.t c´ach tho’a d´ang trˆen mˆo.t luˆa.n diˆe’m n`ao d´o c´ac thˆong tin khˆong ch´ınh x´ac (unexact), `ay du’ (incomplete) Do su da khˆong ch˘a´c ch˘a´n (uncertainty) hay nh˜ u.ng thˆong tin khˆong dˆ u ngh˜ıa v`a thao da.ng cu’a nh˜ u.ng loa.i thˆong tin n`ay nˆen ta g˘a.p rˆa´t kh´o kh˘an biˆe’u thi ng˜ t´ac v´o i ch´ ung `eu t´ac gia’ nghiˆen c´ u.u [6–8] v`a d˜a c´o Trong th`o.i gian qua, da.i sˆo´ gia tu’ du.o c nhiˆ `eu khiˆe’n ´.ng du.ng d´ang kˆe’, d˘a.c biˆe.t lˆa.p luˆa.n xˆa´p xı’ v`a mˆo.t sˆo´ b`ai to´an diˆ nh˜ u.ng u `e co so’ d˜ V`ı vˆa.y, viˆe.c nghiˆen c´ u u vˆ u liˆe.u m`o theo c´ach tiˆe´p cˆa.n da.i sˆo´ gia tu’ l`a mˆo.t hu.´o.ng `an quan tˆam gia’i quyˆe´t m´o.i cˆ ˆ´ GIA TU’ DA I SO `an n`ay s˜e tr`ınh b`ay tˆo’ng quan vˆ `e mˆo.t Dˆe’ xˆay du ng c´ach tiˆe´p cˆa.n da.i sˆo´ gia tu’., phˆ u ngh˜ıa du a v`ao cˆa´u tr´ uc cu’a da.i sˆo´ sˆo´ n´et co ba’n cu’a da.i sˆo´ gia tu’ v`a kha’ n˘ang biˆe’u thi ng˜ ´ ´ ´ ’ ’ ’ gia tu , h`am di.nh lu o ng ng˜ u ngh˜ıa v`a mˆo.t sˆo t´ınh chˆa t cua da.i sˆo gia tu ` y TRUTH gˆo`m c´ac t` u sau: Ta x´et miˆen ngˆon ng˜ u cu’a biˆe´n chˆan l´ dom(TRUTH) = {true, false, very true, very false, more-or-less true, more-or-less false, ˆ T CACH ´ ˆ´P CA ˆ N DE ˆ’ XA ˆ´P XI’ DU ˜ LIE ˆ U MO TIE 111 possibly true, possibly false, approximately true, approximately false, little true, little false,very u nguyˆen thuy’, c´ac t` possibly true,very possibly false }, d´o true, false l`a c´ac t` u nhˆa´n (mordifier hay intensifier) very, more-or-less, possibly, approximately, little go.i l`a c´ac gia tu’ `en ngˆon ng˜ (hedges) Khi d´o miˆ u T = dom(TRUTH) c´o thˆe’ biˆe’u thi nhu mˆo.t da.i sˆo´ AH = `an tu’ sinh H l`a tˆa.p (X, G, H, ), d´o G l`a tˆa.p c´ac t` u nguyˆen thuy’ du.o c xem l`a c´ac phˆ u (c´ac kh´ai niˆe.m m`o.) c´ac gia tu’ du.o c xem nhu l`a c´ac ph´ep to´an mˆo.t ngˆoi, quan hˆe (trˆen c´ac t` l`a quan hˆe th´ u tu du.o c “ca’m sinh” t` u ng˜ u ngh˜ıa tu nhiˆen V´ı du du a trˆen ng˜ u ngh˜ıa, c´ac quan hˆe th´ u tu sau l`a d´ ung: false true, more true very true nhu ngvery false more false, possibly true true nhu.ng false possibly false Tˆa.p X du.o c sinh t` u G bo’.i c´ac ph´ep `an tu’ cu’a X s˜e c´o da.ng biˆe’u diˆ˜en x = hn hn−1 h1x, x ∈ G t´ınh H Nhu vˆa.y mˆo˜i phˆ `an tu’ du o c sinh t` `an tu’ x du.o c k´ Tˆa.p tˆa´t ca’ c´ac phˆ u mˆo.t phˆ y hiˆe.u l`a H(x) Nˆe´u G c´o d´ ung + `an tu’ sinh du o ng k´ y hiˆe.u l`a c , mˆo.t go.i l`a hai t` u nguyˆen thuy’ m`o , th`ı mˆo.t du o c go.i l`a phˆ − − + `an tu’ sinh ˆam k´ phˆ y hiˆe.u l`a c v`a ta c´o c < c Trong v´ı du trˆen true l`a du.o.ng c`on false ´.ng l`a ˆam Cho da.i sˆo´ gia tu’ X = (X, G, H, ), v´o.i G = {c+ , c− }, d´o c+ v`a c− tu.o.ng u + − − `an tu’ sinh du o ng v`a ˆam, X l`a tˆa.p nˆ `en H = H ∪ H v´o i H = {h1 , h2 , , hp} v`a l`a phˆ + H = {hp+1 , , hp+q}, h1 > h2 > > hp v`a hp+1 < < hp+q u ngh˜ıa cu’a X nˆe´u ∀h, ∈ H + Di.nh ngh˜ıa 2.1 ([9]) f : X → [0, 1] go.i l`a h`am di.nh lu.o ng ng˜ − ho˘a.c ∀h, k ∈ H v`a ∀x, y ∈ X, ta c´o: f (hx) − f (x) f (hy) − f (y) = f (kx) − f (x) f (ky) − f (y) V´o.i da.i sˆo´ gia tu’ v`a h`am di.nh lu.o ng ng˜ u ngh˜ıa ta c´o thˆe’ di.nh ngh˜ıa t´ınh m`o cu’a mˆo.t kh´ai niˆe.m m`o Cho tru.´o.c h`am di.nh lu.o ng ng˜ u ngh˜ıa f cu’a X X´et bˆa´t k` y x ∈ X T´ınh m`o cu’a x d´o du.o c b˘`a ng du.`o.ng k´ınh cu’a tˆa.p f (H(x)) ⊆ [0, 1] H`ınh T´ınh m`o cu’a gi´a tri True Di.nh ngh˜ıa 2.2 [9] H`am f m : X → [0, 1] du.o c go.i l`a dˆ o t´ınh m` o trˆen X nˆe´u thoa’ m˜an `eu kiˆe.n sau: c´ac diˆ (1) f m(c− ) = W > v`a f m(c+ ) = − W > (2) V´o.i c ∈ {c− , c+} th`ı p+q f m(hi c) = f m(c) i=1 f m(hy) f m(hc) f m(hx) (3) V´o.i mo.i x, y ∈ X, ∀h ∈ H, = = , v´o.i c ∈ {c− , c+ } f m(x) f m(y) f m(c) ˜ ˜ ˆ N CAT ´ HO ˆ`, NGUYE ˆ N CONG ˆ ` NGUYE HAO 112 ngh˜ıa l`a tı’ sˆo´ n`ay khˆong phu thuˆo.c v`ao x v`a y , du.o c k´ı hiˆe.u l`a µ(h) go.i l`a dˆo t´ınh m`o (fuzziness measure) cu’a gia tu’ h `e 2.1 [9] Mˆ e.nh dˆ (1) f m(hx) = µ(h)f m(x), v´o.i mo.i x ∈ X p+q (2) f m(hi c) = f m(c), d´o c ∈ {c− , c+ } i=1 p+q f m(hi x) = f m(x), ∀x ∈ X (3) i=1 p p+q µ(hi ) = α v`a (4) µ(hi ) = β , v´o.i α, β > v`a α + β = i=p+1 i=1 Di.nh ngh˜ıa 2.3 [9] H`am Sign : X → {−1, 0, 1} l`a mˆo.t ´anh xa du.o c di.nh ngh˜ıa mˆo.t c´ach dˆe qui nhu sau, v´o.i mo.i h, h ∈ H : (1) Sign(c−) = −1 v`a Sign(hc−) = +Sign(c−) nˆe´u hc− < c− Sign(hc−) = −Sign(c−) nˆe´u hc− > c− Sign(c+) = +1 v`a Sign(hc+) = +Sign(c+) nˆe´u hc+ > c+ Sign(hc+) = −Sign(c+) nˆe´u hc+ < c+ (2) Sign(h hx) = −Sign(hx) nˆe´u h l`a negative dˆo´i v´o.i h v`a h hx = hx (3) Sign(h hx) = +Sign(hx) nˆe´u h l`a positive dˆo´i v´o.i h v`a h hx = hx (4) Sign(h hx) = nˆe´u h hx = hx Di.nh ngh˜ıa 2.4 [9] Gia’ su’ cho tru.´o.c dˆo t´ınh m`o cu’a c´ac gia tu’ µ(h), v`a c´ac gi´a tri `an tu’ sinh f m(c− ), f m(c+) v`a w l`a phˆ `an tu’ trung h`oa H`am di.nh dˆo t´ınh m`o cu’a c´ac phˆ u ngh˜ıa (quantitatively semantic function) ν cu’a X du.o c xˆay du ng nhu sau v´o.i lu.o ng ng˜ x = him hi2 hi1 c: (1) ν(c− ) = W − α.f m(c− ) v`a ν(c+ ) = W + α.f m(c+) (2) ν(hj x) = p f m(hi x)− 1−Sign(hj x)Sign(h1hj x)(β −α) f m(hj x) ν(x)+Sign(hj x)× i=j v´o.i j p, v`a j ν(hj x) = ν(x)+Sign(hj x)× f m(hi x)− i=p+1 1−Sign(hj x)Sign(h1hj x)(β−α) f m(hj x) v´o.i j > p ˆ T CACH ´ ˆ´P CA ˆ N DE ˆ U MO ` ˆ’ XA ˆ´P XI’ DU ˜ LIE MO TIE `en tri cu’a Trong mu.c n`ay, s˜e tr`ınh b`ay mˆo.t phu.o.ng ph´ap m´o.i dˆe’ xˆa´p xı’ d˜ u liˆe.u trˆen miˆ `en tri thuˆo.c thuˆo.c t´ınh m`o quan hˆe cu’a co so’ d˜ u liˆe.u m`o Viˆe.c d´anh gi´a d˜ u liˆe.u trˆen miˆ ´ ´ ’ ’ ’ t´ınh m`o cua quan hˆe co so d˜ u liˆe.u m`o theo c´ach tiˆep cˆa.n da.i sˆo gia tu du o c xˆay du ng u.) Nhu vˆa.y, du a trˆen phˆan hoa.ch t´ınh m`o cu’a c´ac gi´a tri da.i sˆo´ gia tu’ (gi´a tri ngˆon ng˜ `en tri tu.o.ng u nˆe´u go.i Dom(Ai ) l`a miˆ ´.ng v´o.i thuˆo.c t´ınh m`o Ai v`a xem nhu mˆo.t da.i sˆo´ gia tu’ th`ı d´o Dom(Ai ) = Num(Ai) ∪ LV (Ai), v´o.i Num(Ai ) l`a tˆa.p c´ac gi´a tri sˆo´ cu’a Ai v`a u liˆe.u, ta x´et hai tru.`o.ng ho p sau LV (Ai ) l`a tˆa.p c´ac gi´a tri ngˆon ng˜ u cu’a Ai Dˆe’ xˆa´p xı’ d˜ ˆ T CACH ´ ˆ´P CA ˆ N DE ˆ’ XA ˆ´P XI’ DU ˜ LIE ˆ U MO TIE 113 `en tri cu’a thuˆ 3.1 Miˆ o.c t´ınh quan hˆ e l` a gi´ a tri ngˆ on ng˜ u Trong tru.`o.ng ho p n`ay, ch´ ung ta di xˆay du ng c´ac phˆan hoa.ch du a v`ao t´ınh m`o cu’a c´ac gi´a tri ngˆon ng˜ u V`ı t´ınh m`o cu’a c´ac gi´a tri da.i sˆo´ gia tu’ l`a mˆo.t doa.n cu’a [0,1] cho nˆen ho c´ac ung dˆo d`ai s˜e ta.o th`anh phˆan hoa.ch cu’a [0,1] Phˆan doa.n nhu vˆa.y cu’a c´ac gi´a tri c´o c` hoa.ch u ´ ng v´o i c´ac gi´a tri c´o dˆo d`ai t` u l´o.n ho.n s˜e mi.n ho.n v`a dˆo d`ai l´o.n vˆo ha.n th`ı dˆo `an vˆ `e d`ai cu’a c´ac doa.n phˆan hoa.ch gia’m dˆ y hiˆe.u Di.nh ngh˜ıa 3.1 Go.i f m l`a dˆo t´ınh m`o trˆen DSGT X V´o.i mˆo˜i x ∈ X, ta k´ I(x) ⊆ [0, 1] v`a |I(x)| l`a dˆo d`ai cu’a I(x) Mˆo.t ho c´ac ξ = {I(x) : x ∈ X} du.o c go.i l`a phˆan hoa.ch cu’a [0,1] g˘a´n v´o.i x nˆe´u: (1) {I(c+), I(c−)} l`a phˆan hoa.ch cu’a [0,1] cho|I(c)| = f m(c), v´o.i c ∈ {c+ , c−} (2) Nˆe´u doa.n I(x) d˜a du.o c di.nh ngh˜ıa v`a |I(x)| = f m(x) th`ı {I(hix) : i = p + q} du.o c `eu kiˆe.n |I(hix)| = f m(hi x) v`a |I(hix)| di.nh ngh˜ıa l`a phˆan hoa.ch cu’a I(x) cho thoa’ m˜an diˆ l`a tˆa.p s˘a´p th´ u tu tuyˆe´n t´ınh `an tu’ x Ta c´o Tˆa.p {I(hix)} du.o c go.i l`a phˆan hoa.ch g˘a´n v´o.i phˆ p+q |I(hix)| = |I(x)| = i=1 f m(x) Di.nh ngh˜ıa 3.2 Cho P k = {I(x) : x ∈ X k } v´o.i X k = {x ∈ X : |x| = k} l`a mˆo.t phˆan hoa.ch Ta n´oi r˘`a ng u xˆa´p xı’ ν theo m´ u.c k P k du.o c k´ y hiˆe.u u ≈k ν v`a chı’ I(u) v`a I(v) k c` ung thuˆo.c mˆo.t khoa’ng P C´o ngh˜ıa l`a ∀u, v ∈ X , u ≈k v ⇔ ∃∆k ∈ P k : I(u) ⊆ ∆k v`a I(v) ⊆ ∆k X , G, H, ), d´o H = H + ∪ H − , H + = {ho.n, V´ı du 3.1 Cho da.i sˆo´ gia tu’ X = (X rˆ a´t}, ho.n < rˆ a´t, H − = {´ıt, kha’ n˘ang}, ´ıt > kha’ n˘ang, G = { tre’ , gi` a} Ta c´o P = {I (tre’), I (gi`a)} l`a mˆo.t phˆan hoa.ch cu’a [0, 1] Tu o ng tu , P = {I (ho n tre’ ), I (rˆ a´t tre’ ), I (´ıt tre’ ), I (kha’ a), I (rˆ a´t gi` a), I (´ıt gi` a), I (kha’ n˘ang gi` a)} l`a phˆan hoa.ch cu’a [0, 1] n˘ang tre’ ), I (ho n gi` V´ı du 3.2 Theo V´ı du 3.1, P l`a phˆan hoa.ch cu’a [0, 1] Ta c´o ho.n tre’ ≈1 rˆ a´t tre’ v`ı 1 1 a´t tre’ ) ⊆ ∆ P l`a phˆan hoa.ch cu’a [0, 1], ta ∃∆ = I (tre’ ) ∈ P m`a I (ho n tre’ ) ⊆ ∆ v`a I (rˆ c´o ´ıt gi` a ≈2 rˆ a´t ´ıt gi` a v`ı ∃∆2 = I (´ıt gi` a )∈ P m`a I (´ıt gi` a) ⊆ ∆2 v`a I (rˆ a´t ´ıt gi` a) ⊆ ∆2 Di.nh ngh˜ıa 3.3 X´et P k = {I(x) : x ∈ X k } v´o.i X k = {x ∈ X : |x| = k} l`a mˆo.t phˆan hoa.ch Ta n´oi r˘`a ng u khˆong xˆa´p xı’ v m´ u.c k P k du.o c k´ y hiˆe.u u =k v v`a chı’ I(u) v`a k I(v) khˆong c` ung thuˆo.c mˆo.t khoa’ng P C´o ngh˜ıa l`a ∀u, v ∈ X , u =k v ⇔ ∀∆k ∈ P k : I(u) ⊂ ∆k ho˘a.c I(v) ⊂ ∆k V´ı du 3.3 Theo V´ı du 3.1, P = {I (ho.n tre’ ), I (rˆ a´t tre’ ), I (´ıt tre’ ), I (kha’ n˘ang tre’ ), I (ho.n gi` a), I (rˆ a´t gi` a), I (´ıt gi` a), I (kha’ n˘ang gi` a)} l`a phˆan hoa.ch cu’a [0, 1] Cho.n ∆2 = I (rˆ a´t 2 2 tre’ )∈ P , ta c´ o I (´ıt tre’ ) ⊂ ∆ v`a I (rˆ a´t tre’ ) ⊆ ∆ (1’) M˘a.c kh´ac v´o i mo.i ∆ = I (´ıt tre’ ) 2 ∈ P ta c´ o I (´ıt tre’ ) ⊂ ∆ v`a I (rˆ a´t tre’ ) ⊂ ∆2 (2’) T` u (1’) v`a (2’) ta suy ´ıt tre’ =2 rˆ a´t tre’ Di.nh ngh˜ıa 3.4 X´et P k = {I(x) : x ∈ X k } v´o.i X k = {x ∈ X : |x| = k} l`a mˆo.t phˆan hoa.ch Go.i ν l`a h`am di.nh lu.o ng ng˜ u ngh˜ıa trˆen X Ta n´oi r˘`a ng u nho’ ho.n v m´ u.c k P k du o c k´ y hiˆe.u u kha’ n˘ang, G = {nho’, l´ o.n} Gia’ su’ cho W = 0, 6, f m(ho.n) = 0, 2, f m(rˆ a´t) = 0, 3, f m(´ıt) = 0, 3, f m(kha’ n˘ang) = 0, 2 Ta c´o P = {I (ho.n l´ o.n), I (rˆ a´t l´ o.n), I (´ıt l´ o.n), I (kha’ n˘ang l´ o.n), I (ho.n nho’), I (rˆ a´t nho’), ’ ’ ’ ’ ’ I (´ıt nho), I (kha n˘ ang nho)} l`a phˆan hoa.ch cua [0, 1] f m(nho) = 0, 6, f m(l´ o n) =0, 4, f m(rˆ a´t o n) = 0, 08 Ta c´o |I (rˆ a´t l´ o n)| = f m(rˆ a´t l´ o n) = 0, 12, hay I (rˆ a´t l´ o n) = 0, 12, f m(kha’ n˘ang l´ l´ o n) = [0, 88, 1] Do d´o theo di.nh ngh˜ıa Φ2(0, 9) = rˆ a´t l´ o n) a´t l´ o n v`ı 0, ∈ I (rˆ Tu o ng tu ta c´o |I (kha’ n˘ang l´ o n)| = f m(kha’ n˘ang l´ o n) = 0, 08, hay I (kha’ n˘ang l´ o.n) = ang l´ o n v`ı 0, 75 ∈ I (kha’ n˘ang l´ [0, 72, 0, 8] Do d´o theo di.nh ngh˜ıa Φ2 (0, 75) = kha’ n˘ o n) ˆ T CACH ´ ˆ´P CA ˆ N DE ˆ’ XA ˆ´P XI’ DU ˜ LIE ˆ U MO TIE 117 `an n`ay, gia’ su’ ch´ `an tu’ du.o c sinh t` `an tu’ l´ Trong phˆ ung tˆoi chı’ x´et c´ac phˆ u phˆ o.n `an tu’ sinh l´o.n H`ınh 3.1 T´ınh m`o cu’a phˆ X , G, H, ), v l` Di.nh l´ y 3.4 Cho da.i sˆo´ gia tu’ X = (X a h` am di.nh lu.o ng ng˜u ngh˜ıa cu’a o X , Φk l` a h` am ngu.o c cu’a v , ta c´ k k k (1) ∀x ∈ X , Φk (v(x )) = xk (2) ∀a ∈ I(xk ), ∀b ∈ I(y k ), xk =k y k , nˆe´u a < b th`ı Φk (a) kha’ n˘ang ho n}, Hsuckhoe = {kha’ n˘ang, ´ıt}, rˆ Wsuckhoe = 0, 6, f m(xˆ a´u) = 0, 6, f m(tˆ o´t) = 0, 4, f m(rˆ a´t) = 0, 3, f m(kh´ a) = 0, 2, f m(kha’ n˘ang) = 0, 2, f m(´ıt) = 0, − X tuoi , Gtuoi, Htuoi, ), v´o.i Gtuoi = {tre’ , gi` a}, Ht+ uoi = {rˆ a´t, ho.n}, Htuoi = X T uoi = (X {kha’ n˘ ang, ´ıt}, rˆ a´t > ho.n v`a ´ıt > kha’ n˘ang Wtuoi = 0, 4, f m(tre’ ) = 0, 4, f m(gi` a) = 0, 6, f m(rˆ a´t) = 0, 3, f m(kh´ a) =0, 15, f m(kha’ n˘ang) = 0, 25, f m(´ıt) = 0, + X luong , Gluong , Hluong , ), v´o.i Gluong = {cao, thˆ X Luong = (X a´p}, Hluong = {rˆ a´t, ho.n}, − a´p) = Hluong = {kha’ n˘ ang, ´ıt}, rˆ a´t > ho.n v`a ´ıt > kha’ n˘ang Wluong = 0, 6, f m(thˆ 0, 6, f m (cao) = 0, 4, f m(rˆ a´t) = 0, 25, f m(kh´ a) = 0, 25, f m(kha’ n˘ang) = 0, 25, f m(´ıt) = 0, 25 Dˆ o´i v´ o.i thuˆ o.c t´ınh TUOI: Ta c´o f m(rˆ a´t tre’ ) = 0, 12, f m(ho.n tre’ ) = 0, 06, f m(´ıt tre’ ) = 0, 12, f m(kha’ n˘ ang tre’ ) = 0, V`ı rˆ a´t tre’ < ho.n tre’ < tre’ < kha’ n˘ang tre’ < ´ıt tre’ nˆen I (rˆ a´t tre’ ) = [0, 0, 12], I (ho.n tre’ ) = [0, 12, 0, 18], I (kha’ n˘ang tre’ ) = [0, 18, 0, 3], I (´ıt tre’ ) = [0, 3, 0, 4] Ta c´o f m(rˆ a´t gi` a) = 0, 18, f m(ho.n gi` a) = 0, 09, f m(´ıt gi` a) = 0, 18, f m(kha’ n˘ang gi` a) = 0, 15 V`ı ´ıt gi` a < kha’ n˘ang gi` a < gi` a < ho.n gi` a < rˆ a´t gi` a nˆen I (´ıt gi` a) = [0, 4, 0, 58], I (kha’ a) = [0, 73, 0, 82], I (rˆ a´t gi` a) = [0, 82, 1] n˘ang gi` a) = [0, 58, 0, 73], I(ho n gi` ´ ’ X Nˆeu cho.n ψ1 = 100 ∈ tuoi d´o ∀ω ∈ N um(T U OI), su du.ng IC(ω) ta c´o N um(T U OI) = {0, 31, 0, 85, 0, 32, 0, 45, 0, 41, 0, 61, 0, 59, 0, 75, 0, 25} a´t gi` a, Φ2(0, 32) = Do d´o Φ2(0, 31) = ´ıt tre’ v`ı 0, 31 ∈ I (´ıt tre’ ), tu.o.ng tu Φ2 (0, 85) = rˆ ´ıt tre’ , Φ2 (0, 45) = ´ıt gi` a, Φ2 (0, 41) = ´ıt gi` a, Φ2 (0, 61) = kha’ n˘ang gi` a, Φ2 (0, 59) = kha’ n˘ang gi` a, Φ2 (0, 75) = ho.n gi` a, Φ2 (0, 25) = kha’ n˘ang tre’ Dˆ o´i v´ o.i thuˆ o.c t´ınh LUONG: Ta c´of m(rˆ a´t thˆ a´p) = 0, 15, f m(kh´ a thˆ a´p) = 0, 15, f m(´ıt thˆ a´p) = 0, 15, f m(kha’ n˘ang thˆ a´p) = 0, 15 ´ ´ ´ a p < thˆ a´p < kha’ n˘ang thˆ a´p < ´ıt thˆ a´p nˆen I (rˆ a´t thˆ a´p) = [0, 0, 15], I (ho.n V`ı rˆ a t thˆ a p < ho n thˆ thˆ a´p) = [0, 15, 0, 3], I (kha’ n˘ang thˆ a´p) = [0, 3, 0, 45], I (´ıt thˆ a´p) = [0, 45, 0, 6] ˜ ˜ ˆ N CAT ´ HO ˆ`, NGUYE ˆ N CONG ˆ ` NGUYE HAO 120 Ta c´o f m(rˆ a´t cao) = 0, 1, f m(ho.n cao) = 0, 1, f m(´ıt cao) = 0, 1, f m(kha’ n˘ang cao) = 0, a´t cao nˆen I (´ıt cao) = [0, 6, 0, 7], I (kha’ V`ı ´ıt cao < kha’ n˘ang cao < cao < ho.n cao < rˆ n˘ang cao) = [0, 7, 0, 8], I (ho n cao) = [0, 8, 0, 9], I (rˆ a´t cao) = [0, 9, 1] Nˆe´u cho.n ψ2 =rˆ a´t rˆ a´t cao ∈ X luong v`a ψ1 = 3.000.000, ta c´o v (rˆ a´t rˆ a´t cao) = 0, 985 d´o ∀ω ∈ N um(LU ON G) = {2.800.000, 2.000.000, 500.000, 1.500.000}, su’ du.ng IC(ω) = {ω × v(ψ2 )}/ψ1, ta c´o N um(LU ON G) = {0, 92, 0, 65, 0, 16, 0, 49} a´t cao, Φ2 (0, 65) = ´ıt cao, Φ2 (0, 16) = ho.n thˆ Do d´o Φ2 (0, 92)= rˆ a´p, Φ2 (0, 49) = ´ıt cao Vˆa.y, nh˜ u ng c´an bˆo c´o T U OI ≈2 ho n gi` a v`a SU CKHOE ≈2 kha’ n˘ang tˆ o´t l`a: Ba’ng 3.2 Kˆe´t qua’ t`ım kiˆe´m cu’a v´ı du (a) Socm Hoten Suckhoe Tuoi Luong 88888 Thanh T` ung kha’ n˘ang tˆo´t 75 1.500.000 v`a nh˜ u.ng c´an bˆo c´o T U OI ≈1 tre’ ho˘a.c c´o LU ON G =1 cao Ba’ng 3.2 Kˆe´t qua’ t`ım kiˆe´m cu’a v´ı du (b) Socm 11111 33333 44444 66666 99999 Hoten `au Pha.m Tro.ng Cˆ `an Tiˆe´n Trˆ V˜ u Ho`ang Thuˆa.n Yˆe´n Nguyˆ˜en Cu.`o.ng Suckhoe rˆa´t rˆa´t tˆo´t xˆa´u kh´a xˆa´u kha’ n˘ang xˆa´u ´ıt tˆo´t Tuoi 31 32 45 61 25 Luong 2.800.000 2.000.000 500.000 thˆa´p kh´a thˆa´p ˆ´T LUA ˆ N KE `en tri thuˆo.c B`ai b´ao xem x´et mˆo.t c´ach tro.n ve.n viˆe.c d´anh gi´a dˆe’ dˆo´i s´anh c´ac gi´a tri miˆ t´ınh cu’a mˆo.t quan hˆe co so’ d˜ u liˆe.u m`o nhˆa.n gi´a tri da da.ng.Viˆe.c d´anh gi´a n`ay l`a ph` u ´ ´ ’ ’ ’ u l`a tu o ng dˆoi ph´ ho p v´o i thu c tˆe, bo i v`ı gi´a tri cua ngˆon ng˜ u c ta.p Trˆen co so n`ay, b`ai b´ao d˜a phˆan t´ıch c´ac quan hˆe dˆo´i s´anh gi˜ u.a hai gi´a tri theo ng˜ u ngh˜ıa m´o.i 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di xˆay du ng c´ac phˆan hoa.ch du a v`ao t´ınh m`o cu’a c´ac