王瑛+蔣曉東+張璐

文章編號(hào)：16742974(2014)04011807

收稿日期：20131030

基金項(xiàng)目：國家自然科學(xué)基金資助項(xiàng)目(71340003)

作者簡介：王 瑛（1964-），女，湖南漢壽人，湖南大學(xué)副教授

通訊聯(lián)系人，E-mail:wangying31106@163.com

摘 要：針對(duì)科技獎(jiǎng)勵(lì)評(píng)價(jià)問題，用標(biāo)準(zhǔn)差系數(shù)改進(jìn)CRITIC法對(duì)專家評(píng)分進(jìn)行動(dòng)態(tài)賦權(quán)，結(jié)合云模型用逆向云發(fā)生器構(gòu)造模糊評(píng)價(jià)矩陣，用虛擬云計(jì)算出評(píng)價(jià)項(xiàng)目的期望、熵和超熵，得出評(píng)價(jià)結(jié)果并排序．既考慮了科技獎(jiǎng)勵(lì)評(píng)價(jià)過程中專家評(píng)分的模糊性和隨機(jī)性，又實(shí)現(xiàn)了定性語言與定量數(shù)值之間的轉(zhuǎn)換，減少了專家主觀因素的干擾，使評(píng)價(jià)結(jié)果更加準(zhǔn)確、客觀.

關(guān)鍵詞：云；改進(jìn)的CRITIC法；科技獎(jiǎng)勵(lì)評(píng)價(jià)

中圖分類號(hào)：G311 文獻(xiàn)標(biāo)識(shí)碼：A

Research on the Evaluation of Science and Technological Awards

Based on Improved CRITIC Method and Cloud Model



WANG Ying，JIANG Xiaodong，ZHANG Lu

(College of Finance and Statistics, Hunan Univ, Changsha, Hunan 410079, China)

Abstract: To address theproblems in the evaluation of science and technology awards, this paper proposed an improved CRITIC method, which was modified by coefficient of standard deviation to carry on the dynamic empowerment. And combined withcloud model, the method used reverse cloud generator to construct a fuzzy evaluation matrix and usedthe virtual cloud to calculate the expectation entropy and hyper entropy of evaluated project to get and sort the evaluation results. This method can consider the fuzziness and the randomness of expert score in the evaluation of science and technology awards, and realize the conversion between the qualitative linguistic and the quantitative numerical value, thus reducing the interference of expert subjective factors and making the results more accurate and objective.



Key words: clouds; improved CRITIC method; the evaluation of science and technology awards



科技獎(jiǎng)勵(lì)制度是中國科技工作的一個(gè)重要組成部分，也是國家促進(jìn)科技創(chuàng)新和發(fā)展的一種舉措，它對(duì)于激發(fā)科技工作者的工作積極性，鼓舞科技工作者的創(chuàng)造熱情，促進(jìn)科技工作與經(jīng)濟(jì)發(fā)展相結(jié)合等各方面都有重要作用.如何公正、客觀、有效地評(píng)價(jià)科技成果，為指導(dǎo)科技獎(jiǎng)勵(lì)評(píng)價(jià)提供理論和方法依據(jù)，顯得尤為重要.因此，研究和完善科學(xué)的科技獎(jiǎng)勵(lì)評(píng)估機(jī)制，并將科學(xué)評(píng)價(jià)理論、方法和技術(shù)運(yùn)用到科技獎(jiǎng)勵(lì)評(píng)審工作中成為新時(shí)期科技獎(jiǎng)勵(lì)研究的重點(diǎn)內(nèi)容.

對(duì)于科技獎(jiǎng)勵(lì)綜合評(píng)價(jià)方法的探索，不少專家在這方面都進(jìn)行過研究.如：石磊等[1]用模糊決策理論對(duì)科技獎(jiǎng)勵(lì)評(píng)價(jià)建立數(shù)學(xué)模型，并探討用該模型進(jìn)行科技獎(jiǎng)勵(lì)評(píng)價(jià)的步驟．李茹等[2]在分析傳統(tǒng)綜合評(píng)價(jià)方法的基礎(chǔ)上，將主觀評(píng)價(jià)與客觀評(píng)價(jià)相整合，提出了一種基于模糊集理論的組合賦權(quán)模糊綜合評(píng)價(jià)方法，對(duì)項(xiàng)目完成情況進(jìn)行橫向與縱向的比較后采用組合賦權(quán)法進(jìn)行評(píng)價(jià)．劉業(yè)政等[3]提出根據(jù)專家個(gè)體決策與群體決策之間的偏離度計(jì)算專家權(quán)重，并用熵值法計(jì)算屬性權(quán)重，以新的權(quán)重計(jì)算出專家個(gè)體決策與群體決策的差異，保證項(xiàng)目評(píng)價(jià)的客觀性．張立軍等[4]建立信度系數(shù)分析模型，計(jì)算單個(gè)專家評(píng)分的信度系數(shù)，根據(jù)單個(gè)專家對(duì)項(xiàng)目的排序與綜合排序之間的一致性，測(cè)量專家評(píng)議的質(zhì)量．王瑛等[5-7]提出了EBP科技獎(jiǎng)勵(lì)綜合評(píng)價(jià)智能模型、最小二乘支持向量機(jī)模型和基于改進(jìn)DS證據(jù)理論的TOPSIS模型．金聰?shù)泉8]采用定性定量相結(jié)合的方法，將人工神經(jīng)網(wǎng)絡(luò)模型與模糊系統(tǒng)的理論和方法相結(jié)合實(shí)現(xiàn)對(duì)科技成果獎(jiǎng)勵(lì)的智能評(píng)審.

湖南大學(xué)學(xué)報(bào)(自然科學(xué)版)2014年

第4期王 瑛等：基于改進(jìn)的CRITIC法和云模型的科技獎(jiǎng)勵(lì)評(píng)價(jià)研究

針對(duì)科技獎(jiǎng)勵(lì)評(píng)價(jià)涉及多個(gè)指標(biāo)、多個(gè)專家、多個(gè)項(xiàng)目的特點(diǎn)，本文提出了一種新的評(píng)價(jià)方法, 采用改進(jìn)的CRITIC法對(duì)專家進(jìn)行動(dòng)態(tài)賦權(quán)，結(jié)合云模型對(duì)科技獎(jiǎng)勵(lì)進(jìn)行綜合評(píng)價(jià).該方法既考慮了專家動(dòng)態(tài)權(quán)重，又考慮了指標(biāo)權(quán)重，將專家評(píng)分的模糊性和隨機(jī)性相結(jié)合，實(shí)現(xiàn)了定性語言與定量數(shù)值之間的轉(zhuǎn)換，降低了專家評(píng)分主觀性影響，使評(píng)價(jià)結(jié)果更加科學(xué)、準(zhǔn)確和客觀.

1 基于改進(jìn)CRITIC法的專家動(dòng)態(tài)權(quán)重

在綜合評(píng)價(jià)中，各個(gè)專家受其自身知識(shí)結(jié)構(gòu)、對(duì)評(píng)判項(xiàng)目熟悉程度以及個(gè)人偏好等因素的影響，對(duì)評(píng)判項(xiàng)目的評(píng)分存在差異，因此，在綜合評(píng)價(jià)中有必要考慮到不同專家意見的重要性，有必要對(duì)專家賦權(quán).

根據(jù)專家賦權(quán)所考慮的因素劃分，專家賦權(quán)方法可以分為兩類：一類是根據(jù)專家有關(guān)的先驗(yàn)信息為專家賦權(quán)，此時(shí)賦予的權(quán)重是對(duì)專家知識(shí)、經(jīng)驗(yàn)、水平等的綜合數(shù)量表示，據(jù)此確定的專家權(quán)重被稱為主觀權(quán)重[9]；另一類是根據(jù)專家提供的判斷信息質(zhì)量對(duì)專家進(jìn)行賦權(quán)，據(jù)此確定的專家權(quán)重被稱為客觀權(quán)重[10].一般情況下，專家的主觀權(quán)重是事先賦予的，不隨專家給出的評(píng)判信息的質(zhì)量而改變，故主觀權(quán)重其實(shí)是一種靜態(tài)權(quán)重，而專家的客觀權(quán)重隨其給出的評(píng)判信息質(zhì)量改變，因而客觀權(quán)重是動(dòng)態(tài)的，稱之為專家動(dòng)態(tài)權(quán)重.本文根據(jù)各個(gè)專家對(duì)各項(xiàng)目的各項(xiàng)指標(biāo)的評(píng)分對(duì)專家進(jìn)行動(dòng)態(tài)賦權(quán).

1.1 CRITIC法的基本原理

CRITIC法是由Diakoulaki于1995年提出的一種新的客觀賦權(quán)方法，它是以特征的對(duì)比強(qiáng)度和特征的沖突性兩方面來綜合確定特征的客觀權(quán)重[11].用CRITIC法對(duì)專家動(dòng)態(tài)賦權(quán)，對(duì)比強(qiáng)度表示同一個(gè)項(xiàng)目各專家評(píng)分差距的大小，用標(biāo)準(zhǔn)差來表示，標(biāo)準(zhǔn)差的大小表明了各專家評(píng)分方案差距的大小，標(biāo)準(zhǔn)差越小說明各專家評(píng)分差距越小，所賦權(quán)重應(yīng)越大，反之則越??；沖突性則是用專家評(píng)分間的相關(guān)性來衡量，如果2個(gè)專家評(píng)分之間具有較強(qiáng)的正相關(guān)則說明沖突性較低，所賦權(quán)重應(yīng)較大，反之則越小.

1.2 基于改進(jìn)的CRITIC法的專家動(dòng)態(tài)權(quán)重

設(shè)有n個(gè)評(píng)價(jià)項(xiàng)目A1,A2,…，Ai,…，An，m個(gè)評(píng)價(jià)指標(biāo)P1,P2,…，Pj,…，Pm以及r個(gè)評(píng)分專家C1,C2,…，Ck,…，Cr，組成評(píng)價(jià)指標(biāo)的樣本集xkij如表1所示.

表1 專家評(píng)分的原始數(shù)據(jù)

Tab.1 The original data of expert score

C1

…

Cr

P1

P2

…

Pm

…

P1

P2

…

Pm

A1

x111

x112

…

x11m

…

xr11

xr12

…

xr1m

A2

x111

x112

…

x11m

…

xr11

xr12

…

xr1m



An

x1n1

x1n2

…

x1nm

…

xrn1

xrn2

…

xrnm



CRITIC法是用標(biāo)準(zhǔn)差來衡量對(duì)比強(qiáng)度絕對(duì)變動(dòng)的方法，用標(biāo)準(zhǔn)差系數(shù)這一相對(duì)變動(dòng)來進(jìn)行改進(jìn)［12］，以減少專家評(píng)分差異程度的影響．

對(duì)于特定評(píng)審項(xiàng)目Ai，用f(k)ij表示第k個(gè)專家Ck對(duì)指標(biāo)Pj評(píng)分所包含的信息量和獨(dú)立性的綜合度量，用標(biāo)準(zhǔn)差系數(shù)uij來反映對(duì)比強(qiáng)度，用∑rl=1γkl來反映專家Ck與其他專家間的沖突性，其中γkl表示第k個(gè)專家與第l個(gè)專家之間的相關(guān)系數(shù)，則f(k)ij表示為：

f(k)ij=1uij∑rl=1γkl. (1)

式中：uij=σijij，xij=1r∑rk=1x(k)ij，σ2ij=1r∑rk=1(x(k)ij－xij)2.

因此，f(k)ij越大表示第k個(gè)專家Ck評(píng)分所包含的綜合信息量越多，即該專家的相對(duì)重要程度越大，所賦權(quán)重也應(yīng)該越大，所以第k個(gè)專家Ck的客觀權(quán)重w(k)ij應(yīng)該為：

w(k)ij=f(k)ij∑rk=1f(k)ij，j=1,2,…,m.(2) 

由于專家對(duì)每個(gè)項(xiàng)目中的每個(gè)指標(biāo)的判斷和評(píng)分情況都不同，因此對(duì)于每個(gè)項(xiàng)目中每個(gè)指標(biāo)的各位專家的動(dòng)態(tài)權(quán)重可用以下向量來表示：

Wij=(W1ij,W2ij,…,Wkij,…,Wrij) .

從表1可知，對(duì)于特定項(xiàng)目Ai，專家Ck的第j個(gè)指標(biāo)值為xkij.專家Ck的第j個(gè)指標(biāo)Pj的客觀權(quán)重為w(k)ij，則考慮專家權(quán)重后第j個(gè)指標(biāo)Pj的得分可以表示為：

ykij=w(k)ijx(k)ij，i=1,2,…，n.(3)

2 云模型

2.1 云的概念及其數(shù)字特征

云模型由中國李德毅在90年代初期提出的，它是在隨機(jī)數(shù)學(xué)和模糊數(shù)學(xué)的基礎(chǔ)上，用于刻畫語言值隨機(jī)性、模糊性及二者間的關(guān)聯(lián)性的一種方法.云模型綜合考慮了不確定概念的隨機(jī)性和模糊性，實(shí)現(xiàn)了不確定語言與定量數(shù)值之間自然轉(zhuǎn)化[13].

設(shè)U為一論域，U={X}，T為與U相聯(lián)系的定性語言，GT(X)是U中的元素X對(duì)于T所表達(dá)的定性概念的隸屬度，它是一個(gè)具有穩(wěn)定傾向的隨機(jī)數(shù)，其在論域上的分布稱為隸屬云，簡稱為云，每個(gè)X稱為一個(gè)云滴(X,GT(x))[14].GT(X)在［0,1］中取值，云是從論域U到區(qū)間［0,1］的映射，即GT(X):U→［0,1］,x∈U,x→GT(X).

云的數(shù)字特征用期望Ex,熵En,超熵He 3個(gè)數(shù)值來表征[15],如圖1所示.

云滴

圖1云的數(shù)字特征示意圖

Fig.1 Schematic diagram of the cloud

digital characteristics



期望Ex：云滴在論域空間分布的期望，是論域空間中最能代表定性概率的值，其確定度是1.

熵En：定性概念的不確定性度量，熵既度量了定性概念的亦此亦彼性,又度量了定性概念隨機(jī)性,它反映了論域空間中可被語言值接受云滴的取值范圍,同時(shí)代表定性概念云滴的離散程度.

超熵He：熵的不確定性度量，也就是熵的熵，反映了在論域空間代表該語言值的所有點(diǎn)的不確定度的凝聚性.

2.2 云發(fā)生器

云發(fā)生器，即云模型的生成算法，它是構(gòu)造不確定性推理的基礎(chǔ)，是建立定性和定量之間相互聯(lián)系、相互依存、量中有性、性中有量的映射關(guān)系.

正向云發(fā)生器是由云的3個(gè)數(shù)字特征產(chǎn)生云滴，積累到一定數(shù)量匯聚為云，是從定性到定量的映射，它是一個(gè)直接、前向的過程，具體來說是從語言值的定性信息中獲取定量數(shù)據(jù)的范圍及分布規(guī)律.

逆向云發(fā)生器是由云滴產(chǎn)生云的3個(gè)數(shù)字特征，是從定量到定性的映射，它是一個(gè)間接、逆向的過程，具體來說是將一定數(shù)量的精確數(shù)據(jù)有效轉(zhuǎn)換為恰當(dāng)?shù)亩ㄐ哉Z言(Ex,En,He)表示的概念，并據(jù)此代表這些精確數(shù)據(jù)所反映的云滴的整體，如圖2所示.



圖2 逆向云發(fā)生器

Fig.2 Reverse cloud generator

逆向云發(fā)生器是以統(tǒng)計(jì)理論為基礎(chǔ)，其有2種基本運(yùn)算方式：一種是包含確定度信息的運(yùn)算，另一種是不包含確定度信息的運(yùn)算.本文采用不含確定度信息的算法，算法如下[16]：

輸入：樣本點(diǎn)xi，其中i=1,2,…，n.

輸出：這n個(gè)云滴所表示的定性概念的數(shù)字特征(Ex,En,He).

算法步驟：

1) 根據(jù)xi計(jì)算樣本均值=1n∑ni=1xi，一階樣本絕對(duì)中心距1n∑ni=1xi-,樣本方差S2=1n－1∑ni=1(xi－)2；

2) 期望Ex=；

3) 熵En=π2×1n∑ni=1xi－Ex；

4) 超熵He=S2－E2n.

2.3 虛擬云算法

虛擬云[17]是按照某種應(yīng)用目標(biāo)，對(duì)各個(gè)基云的數(shù)字特征進(jìn)行計(jì)算，將得到的結(jié)果作為新的數(shù)字特征所構(gòu)造的云，對(duì)于一個(gè)語言變量T,可通過基云定義為：

T{T1(Ex1,En1,He1),T2(Ex2,En2,He2),…，Tn(Exn,Enn,Hen)}.對(duì)各個(gè)基云進(jìn)行邏輯運(yùn)算——軟“AND”或軟“OR”得到的新云就是虛擬元T(Ex,En,He).

采用虛擬云理論中的一種綜合算法，計(jì)算公式如下：

Ex=w1Ex1+w2Ex2+…+wnExnw1+w2+…+wn,

En=w21w21+w22+…+w2nEn1+w22w21+w22+…+w2nEn2+

…+w2nw21+w22+…+w2nEnn，

He=w21w21+w22+…+w2nHe1+w22w21+w22+…+w2nHe2+

…+w2nw21+w22+…+w2nHen．

式中：wi為第i個(gè)指標(biāo)的權(quán)重；(Exi,Eni,Hei)為第i個(gè)指標(biāo)的云模型參數(shù)；n為指標(biāo)的個(gè)數(shù).

3 改進(jìn)的CRITIC法和云模型結(jié)合的科技

獎(jiǎng)勵(lì)綜合評(píng)價(jià)步驟

假設(shè)在科技獎(jiǎng)勵(lì)中有n個(gè)評(píng)價(jià)項(xiàng)目{A1,A2,…，Ai,…，An}，m個(gè)評(píng)價(jià)指標(biāo){P1,P2,…，Pj,…，Pm}以及r個(gè)評(píng)分專家{C1,C2,…，Ck,…，Cr}，實(shí)施步驟如下：

1) 確定科技獎(jiǎng)勵(lì)評(píng)價(jià)的指標(biāo)論域.目前，國家科學(xué)技術(shù)進(jìn)步獎(jiǎng)(社會(huì)公益項(xiàng)目)的評(píng)價(jià)設(shè)定了5個(gè)指標(biāo)，其評(píng)價(jià)依據(jù)主要是技術(shù)創(chuàng)新程度P1，技術(shù)經(jīng)濟(jì)指標(biāo)的先進(jìn)程度P2，推廣應(yīng)用程度P3，已獲社會(huì)、生態(tài)、環(huán)境效益P4和對(duì)科技進(jìn)步的推動(dòng)作用P5這5個(gè)指標(biāo)，則評(píng)價(jià)指標(biāo)論域?yàn)椋邯?/p>

P=P1,P2,P3,P4,P5.

2) 確定評(píng)價(jià)指標(biāo)的權(quán)重.權(quán)重是表征因子相對(duì)重要性大小的表征量度值,是為了使綜合評(píng)價(jià)能夠考慮各影響因素對(duì)總體影響程度的不一致性.引入P上的一個(gè)模糊子集S，稱為權(quán)重分配集，S=(s1,s2,…，sm)，其中si>0,∑mi=1si=1. 

3) 確定考慮專家動(dòng)態(tài)權(quán)重的模糊評(píng)價(jià)矩陣.以項(xiàng)目Ai為例，根據(jù)式(1)和式(2)計(jì)算專家Ck的第j個(gè)指標(biāo)Pj的客觀權(quán)重為wkij，根據(jù)公式(3)計(jì)算考慮專家動(dòng)態(tài)權(quán)重后指標(biāo)Pj的得分ykij.采用逆向云發(fā)生器計(jì)算模糊評(píng)價(jià)矩陣，得到對(duì)于特定項(xiàng)目Ai的評(píng)價(jià)矩陣：

Ri=r1r2rm=(Ey1,En1,He1)(Ey2,En2,He2)(Eym,Enm,Hem).

項(xiàng)目Ai的評(píng)價(jià)指標(biāo)Pj(j=1,2,…，m)的專家評(píng)價(jià)結(jié)果云rj(Eyj,Enj,Hej)，每個(gè)專家對(duì)每個(gè)指標(biāo)的評(píng)分都具有一定的隨機(jī)性和模糊性，對(duì)于評(píng)價(jià)指標(biāo)Pj可以打分為Eyj，則不同專家對(duì)于這個(gè)分?jǐn)?shù)的評(píng)定一般在［Eyj－3Enj,Exj+3Enj］范圍內(nèi)，而Hej則進(jìn)一步體現(xiàn)了主觀評(píng)定的隨機(jī)性.

4)利用虛擬云算法，計(jì)算項(xiàng)目Ai的綜合評(píng)價(jià)結(jié)果：

Bi=S?Ri=s1,s2,…，sm?r1r2rm=s1,s2,…，sm?(Ey1,En1,He1)(Ey2,En2,He2) (Eym,Enm,Hem)=

s1Ey1+s2Ey2+…+smEyms1+s2+…+sms21s21+s22+…+s2mEn1+s22s21+s22+…+s2nEn2+…+s2ms21+s22+…+s2mEnms2ms21+s22+…+s2mHe1+s2ms21+s22+…+s2mHe2+…+s2ms21+s22+…+s2mHemT=(Ex,En,He)．

5) 計(jì)算n個(gè)項(xiàng)目的綜合評(píng)價(jià)結(jié)果并排序. 同理，可以得到n個(gè)評(píng)價(jià)項(xiàng)目的綜合評(píng)價(jià)結(jié)果為：

B=B1B2BnT=(Ex1,En1,He1)(Ex2,En2,He2)(Exn,Enn,Hen)T.(4)

由公式(4)得到每個(gè)項(xiàng)目的綜合評(píng)價(jià)結(jié)果，再結(jié)合期望Ex、熵En、超熵He的大小排序，期望值越大排名越靠前，若兩者期望相同，再比較熵En的大小，熵值越小(即穩(wěn)定性越好)排名越好；若兩者期望、熵都相同，則再比較超熵He的大小，超熵值越小(即隨機(jī)性越小)排名越好.

4 實(shí)證分析

選取25位專家對(duì)中國國家科技進(jìn)步獎(jiǎng)(社會(huì)公益項(xiàng)目)24項(xiàng)科技成果的等級(jí)評(píng)價(jià)數(shù)據(jù)(數(shù)據(jù)來源: 科技部國家科學(xué)技術(shù)獎(jiǎng)勵(lì)工作辦公室，原始數(shù)據(jù)略)，運(yùn)用Matlab7.0軟件進(jìn)行實(shí)證分析.

1) 確定科技獎(jiǎng)勵(lì)評(píng)價(jià)的指標(biāo)論域.根據(jù)原始數(shù)據(jù)確定科技獎(jiǎng)勵(lì)的評(píng)價(jià)指標(biāo)論域?yàn)椋邯?/p>

P=P1,P2,P3,P4,P5.

2) 確定評(píng)價(jià)指標(biāo)的權(quán)重.根據(jù)給定指標(biāo)的權(quán)重，得到與評(píng)價(jià)指標(biāo)論域相對(duì)應(yīng)的模糊子集S=(0.2,0.2,0.2,0.25,0.15).

3) 確定考慮專家動(dòng)態(tài)權(quán)重的模糊評(píng)價(jià)矩陣.以項(xiàng)目A1為例，根據(jù)公式(1)和(2)求得25位專家的動(dòng)態(tài)權(quán)重，如表2所示.

表2 25位專家的動(dòng)態(tài)權(quán)重計(jì)算結(jié)果

Tab.2 The dynamic weights calculation results of 25 experts

[BHDFG2,WK7，WK5，WK5。4W]P1

P2

P3

P4

P5

C1

0.375 3

0.377 7

0.334 0

0.373 0

0.300 2

C2

0.121 2

0.172 7

0.235 7

0.236 4

0.182 3



C25

0.314 0

0.265 9

0.294 9

0.301 2

0.343 3 

根據(jù)公式(3)，得到考慮專家動(dòng)態(tài)權(quán)重后項(xiàng)目A1各指標(biāo)的得分，如表3所示.

表3 考慮專家動(dòng)態(tài)權(quán)重后項(xiàng)目A1各指標(biāo)的得分

Tab.3 Each index score table of projects A1 after 

considering experts dynamic weights

指標(biāo)



P1

P2

P3

P4

P5

A1

0.750 5

0.242 5



0.942 0

0.755 40.518 0

0.797 7

0.668 1

0.707 1 

0.884 7

0.746 0

0.709 2

1.204 7

0.600 4

0.547 0

1.029 9

采用逆向云發(fā)生器計(jì)算模糊評(píng)價(jià)矩陣，根據(jù)逆向云發(fā)生器計(jì)算指標(biāo)的評(píng)價(jià)云滴為(0.720 7,0.27 1,0.013 6)．

同理，計(jì)算項(xiàng)目A1其他4個(gè)指標(biāo)的評(píng)價(jià)云滴，得到項(xiàng)目A1的評(píng)價(jià)矩陣為：

R1=r1r2r3r4r5=(Ey1,En1,He1)(Ey2,En2,He2)(Ey3,En3,He3)(Ey4,En4,He4)(Ey5,En5,He5)=

(0.720 7,0.271 0,0.013 6)(0.685 6,0.259 3,0.088 6)(0.793 5,0.249 0,0.134 5)(0.896 4,0.319 4,0.073 9)(0.800 4,0.423 1,0.103 2)

4)利用虛擬云算法，計(jì)算項(xiàng)目A1的綜合評(píng)價(jià)結(jié)果.

B1=S?R1=s1,s2,…，s5?

r1r2r5=0.2,0.2,0.2,0.25,0.15?

(0.720 7,0.271 0,0.013 6)(0.685 6,0.259 3,0.088 6)(0.793 5,0.249 0,0.134 5)(0.896 4,0.319 4,0.073 9)(0.800 4,0.423 1,0.103 2)=

(0.781 4,0.295 9,0.080 0)．

5) 確定24個(gè)項(xiàng)目的綜合評(píng)價(jià)結(jié)果并排序.同理，可計(jì)算出24個(gè)評(píng)價(jià)項(xiàng)目的綜合評(píng)價(jià)結(jié)果，如表4所示.

表4 24個(gè)項(xiàng)目的綜合評(píng)價(jià)結(jié)果

Tab.4 Comprehensive evaluation results of 24 projects

項(xiàng)目

綜合評(píng)價(jià)結(jié)果

項(xiàng)目

綜合評(píng)價(jià)結(jié)果

A1

(0.781 4,0.295 9,0.080 0)

A13

(0.696 0,0.695 4,0.113 9)

A2

(0.645 1,0.645 3,0.073 2)

A14

(0.856 6,0.863 4,0.081 8)

A3

(0.702 5,0.700 4,0.149 9)

A15

(0.948 1,0.949 6,0.061 4)

A4

(0.625 2,0.622 9,0.042 6)

A16

(0.829 6,0.622 9,0.042 6)

A5

(0.630 8,0.640 8,0.065 9)

A17

(1.075 6,1.084 9,0.074 0)

A6

(0.899 8,0.907 5,0.058 7)

A18

(0.964 4,0.971 3,0.048 4)

A7

(0.801 5,0.807 6,0.087 6)

A19

(0.824 6,0.830 7,0.099 8)

A8

(1.018 4,1.027 1,0.078 4)

A20

(0.758 2,0.761 4,0.065 2)

A9

(1.063 0,1.071 2,0.104 4)

A21

(0.781 0,0.779 0,0.042 0)

A10

(0.934 3,0.944 9,0.059 5)

A22

(0.846 0,0.846 8,0.067 8)

A11

(0.837 5,0.839 5,0.118 1)

A23

(0.687 8,0.688 1,0.098 0)

A12

(0.963 4,0.967 4,0.109 9)

A24

(0.879 9,0.884 9,0.064 0)

以項(xiàng)目A1～A4為例進(jìn)行排序，得到項(xiàng)目A1～A4的綜合評(píng)價(jià)結(jié)果云模型圖如圖3所示.

評(píng)價(jià)云滴

圖3 項(xiàng)目A1～A4的綜合評(píng)價(jià)云模型圖

Fig.3 Comprehensive evaluation cloud model

diagram of project A1～A4



由圖3可知，項(xiàng)目A1的Ex較大，綜合評(píng)價(jià)結(jié)果較好，En較小，離散程度較小，穩(wěn)定性較好，項(xiàng)目A4的He在4個(gè)項(xiàng)目中最小，云滴較薄，確定度的隨機(jī)性最小.由排序規(guī)則，項(xiàng)目A1～A4的排序依次為A1，A3，A2，A4.

同理，可以得到24個(gè)評(píng)價(jià)項(xiàng)目的排序結(jié)果，如表5所示.

表5 24個(gè)項(xiàng)目的排序結(jié)果

Tab.5 Sorting result of 24 projects

項(xiàng)目

排序

項(xiàng)目

排序

項(xiàng)目

排序

A1

16

A9

2

A17

1

A2

22

A10

7

A18

4

A3

19

A11

12

A19

14

A4

24

A12

5

A20

18

A5

23

A13

20

A21

17

A6

8

A14

10

A22

11

A7

15

A15

6

A23

21

A8

3

A16

13

A24

9

5 結(jié) 論

1)利用標(biāo)準(zhǔn)差系數(shù)衡量CRITIC法中專家的對(duì)比強(qiáng)度，將其與專家間的沖突性相結(jié)合確定專家動(dòng)態(tài)權(quán)重，計(jì)算各項(xiàng)目每個(gè)指標(biāo)的得分，提高了樣本數(shù)據(jù)的代表性.

2)采用逆向云發(fā)生器確定評(píng)價(jià)項(xiàng)目的模糊評(píng)價(jià)矩陣，考慮了每個(gè)專家的評(píng)分具有一定的模糊性及隨機(jī)性，降低了專家評(píng)分受主觀因素影響的程度.

3)改進(jìn)的CRITIC法和云模型相結(jié)合對(duì)科技獎(jiǎng)勵(lì)進(jìn)行綜合評(píng)價(jià)，得出各個(gè)項(xiàng)目的評(píng)價(jià)結(jié)果并排序，實(shí)現(xiàn)了定性語言與定量數(shù)值之間的轉(zhuǎn)換，與傳統(tǒng)的評(píng)價(jià)方法相比，評(píng)價(jià)結(jié)果更加科學(xué)、準(zhǔn)確和客觀.

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