蔣艷君謝悅波黃旻
摘要:針對傳統(tǒng)TOPSIS法權重計算的強主觀性、相對接近度計算過程中出現(xiàn)與理想點及負理想點等距的問題,通過基于博弈論的組合賦權法將主觀權重與客觀權重組合對監(jiān)測指標進行賦權,并定義“虛擬負理想點”代替?zhèn)鹘y(tǒng)負理想點,采用改進的距離計算公式計算各樣本與理想點及“虛擬負理想點”之間的距離,對傳統(tǒng)TOPSIS法進行改進并將其用于水質(zhì)斷面優(yōu)化設計。以浦陽江干流9個水質(zhì)監(jiān)測斷面2012年監(jiān)測數(shù)據(jù)為實例,以相對貼近度為基礎,將原有9個斷面優(yōu)化為7個斷面,并對優(yōu)化結果進行一致性檢驗,結果顯示,改進的TOPSIS法優(yōu)化結果準確、有效,因此對環(huán)境監(jiān)測布點及斷面優(yōu)化工作具有一定的應用價值。
關鍵詞:博弈論;主觀權重;客觀權重;TOPSIS;斷面優(yōu)化
中圖分類號:TV213.4;X832 文獻標志碼:A 文章編號:
16721683(2016)05007805
Optimization of water quality monitoring sections based on improved TOPSIS method
JIANG Yanjun1,XIE Yuebo1,HUANG Min2
(1.College of Hydrology and Water Resources of Hohai University,Nanjing 210098,China;2.Environmental Monitoring Station in Pujiang County,Jinhua 322200,China)
Abstract: This work aimed to solve the irrationality of traditional TOPSIS,such as the strong subjective of weight calculation,the equal distance to the ideal point and the negative ideal point.The subjective weight and objective weight were combined by combining weights method based on Game Theory,"virtual negative ideal point" was defined to replace the traditional negative ideal point and used to improve formula to calculate the distance between each sample and the ideal point or negative ideal point.An improved TOPSIS method was built to optimize water quality sections.Based on the monitoring data of 9 water quality monitoring sections in Puyang River in 2012,water quality monitoring sections were optimized by the improved TOPSIS.As a result,the original 9 sections were optimized to 7 sections,which was proved to be scientific and effective by F test and t test method.Therefore,it will provide a great reference for layout of the environmental monitoring sites and section optimization.
Key words: game theory;subjective weight;objective weight;TOPSIS;section optimization
水質(zhì)監(jiān)測斷面的布設是水質(zhì)監(jiān)測工作的基礎,斷面優(yōu)化布設體現(xiàn)了監(jiān)測工作的科學性、合理性。水質(zhì)監(jiān)測斷面布設的總原則為以最少的斷面、測點數(shù),取得最全面、科學合理的水質(zhì)監(jiān)測信息[1]。為科學合理地取得斷面最優(yōu)布設方案,消除傳統(tǒng)水質(zhì)監(jiān)測斷面布設中存在的主觀成分,常采用數(shù)理統(tǒng)計的方法如物元分析法[23]、歷史數(shù)據(jù)相關分析法[4]、模糊聚類分析法[5]、人工神經(jīng)網(wǎng)絡模型[6]等對已有監(jiān)測斷面進一步優(yōu)化。
TOPSIS法是系統(tǒng)工程中有限方案多目標決策分析的一種常用技術[7],常被用于多種方案評價優(yōu)選,近年來TOPSIS在水環(huán)境監(jiān)測方面的應用逐漸增多,如張先起等[8]用熵權改進TOPSIS權重計算用于邯鄲市地下水水質(zhì)評價、張倩等[9]將AHP與TOPSIS模型結合用于污染場地修復技術的篩選、馮光文等[10]運用熵權法改進TOPSIS模型對新疆輻射環(huán)境監(jiān)測點進行優(yōu)化、張苗云等[11]運用TOPSIS模型對某市水質(zhì)監(jiān)測點進行優(yōu)化等。傳統(tǒng)TOPSIS法的賦權常采用主觀權重法[12]如專家評分法、Delphi法等進行指標賦權,近年來不少專家學者[13]對賦權法進行改進,如使用熵權法等客觀賦權法代替主觀賦權法增加權重系數(shù)的客觀性與合理性,但主觀權重與客觀權重都存在各自的優(yōu)缺點,不能全面地反應各指標對方案優(yōu)選結果的重要程度。另外,傳統(tǒng)TOPSIS法在計算相對貼近度時,常出現(xiàn)各待選方案與理想點與負理想點歐氏距離都近的現(xiàn)象,致使優(yōu)選結果出現(xiàn)誤差。本文針對以上傳統(tǒng)TOPSIS法中不合理處進行改進,并將其用于水質(zhì)斷面優(yōu)化分析實例中,得到較為理想的分析結果。
1 改進的TOPSIS法基本原理
針對傳統(tǒng)TOPSIS法存在的某些不合理的計算方法,本文根據(jù)相關理論基礎,對傳統(tǒng)TOPSIS法的指標權重計算及相對接近度算法進行改進,使TOPSIS理論得到拓展與完善。
1.1 構造優(yōu)化矩陣及其規(guī)范化
以個水質(zhì)監(jiān)測斷面,個監(jiān)測指標監(jiān)測數(shù)據(jù)為基礎[14],構造優(yōu)化矩陣:
1.2 確定指標權重
本文采用主觀權重的層次分析法與客觀權重的熵權法構成組合權重法對TOPSIS法的賦權進行改進[15]。組合權重法能很好地表達監(jiān)測指標對優(yōu)選結果的作用,同時反映出各指標之間的相互作用,形成互補,使權重系數(shù)更具合理性。
1.2.1 層次分析法
根據(jù)水質(zhì)監(jiān)測指標與地表水環(huán)境質(zhì)量標準的五級水質(zhì)類別[16],構建水質(zhì)的遞階層次結構[17],層次分析法步驟如下[18]:
1.2.2 熵權法
1.2.3 基于博弈論的組合賦權
基于博弈論的組合賦權基本思想是不同層次評價指標體系賦權的集成,其集成過程不是簡單的物理過程,而是相互比較、相互協(xié)調(diào)的過程,故適宜于用博弈論合理組合主觀賦權法和客觀賦權法。計算步驟如下[21]:
1.3 構造規(guī)范化加權矩陣
根據(jù)各指標權重計算結果與規(guī)范化矩陣,構造規(guī)范化加權矩陣:
1.4 相對接近度計算
首先構造理想點、負理想點為參考點,規(guī)范化后的指標均為正向指標,則理想點cj+與負理想點cj-的表達式如下:
Ri越接近于1表示待選方案越接近理想點,越接近于0表示待選方案越接近“虛擬負理想點”。“虛擬負理想點”相比于傳統(tǒng)負理想點的優(yōu)點在于通過延長待選方案與傳統(tǒng)負理想點的距離從而避免出現(xiàn)位于理想點與“虛擬負理想點”連線的中垂線上的點其貼近度相等而無法排序的情況。
2 實例分析
本文實例數(shù)據(jù)為浦陽江干流9個水質(zhì)監(jiān)測斷面的高猛酸鹽指數(shù)、COD、TP、氨氮及氟化物等指標的2012年年均值數(shù)據(jù)(由該年逐日水質(zhì)監(jiān)測數(shù)據(jù)計算得出,每日監(jiān)測數(shù)據(jù)為上午8點左右水質(zhì)情況見表2),上游至下游斷面依次編號1~9號。監(jiān)測斷面分布見圖1。
根據(jù)相對接近度計算結果,將水質(zhì)監(jiān)測斷面分為以下3類。
第一類包括1號、6號、7號監(jiān)測斷面,其中6號、7號監(jiān)測斷面相對接近度為均大于0.9,且僅相差0.009,與理想點的距離遠小于與“虛擬負理想點”的距離,根據(jù)斷面實際地理位置及監(jiān)測功能分析,6號、7號斷面相距較近且監(jiān)測功能一致,可歸為一類,6號監(jiān)測斷面的相對貼近度大于7號,故保留6號;1號監(jiān)測斷面相對貼近度接近于1,距離理想點距離最近,且位于流域入口且為監(jiān)測飲用水水源地之用,可作為保留斷面。綜上,第一類保留1號、6號監(jiān)測斷面。
第二類只有2號監(jiān)測斷面,其相對接近度小于0.9而大于0.65,與其他斷面的相對貼近度相差較大,故作為保留斷面。
第三類包括8號、3號、4號、9號、5號等5個監(jiān)測斷面,其相對貼近度較為接近,且均大于0.5, 其中3號、8號斷面相對貼近度較大相距較遠且與其他斷面監(jiān)測功能不同,故都作為保留。4號、5號監(jiān)測斷面相距較近檢測功能一致且相對貼近度相差僅為0.016,9號監(jiān)測斷面支流與干流匯流處監(jiān)測斷面,故保留5號、9號監(jiān)測斷面。
將優(yōu)化前水質(zhì)監(jiān)測數(shù)據(jù)與優(yōu)化后水質(zhì)監(jiān)測數(shù)據(jù)作為兩個樣本,采用F檢驗與t檢驗對兩個樣本的均值做一致性檢驗,檢驗結果見表5。
綜上所述,結合斷面實際分布規(guī)律,通過改進的TOPSIS法對浦江縣9個水質(zhì)監(jiān)測斷面進行優(yōu)化分析,將9個監(jiān)測斷面最終優(yōu)化為7個監(jiān)測斷面,可為浦江縣環(huán)境監(jiān)測站的水質(zhì)監(jiān)測工作節(jié)省大量人力、物力資源。
3 結論
傳統(tǒng)TOPSIS模型的賦權方法一般采用主觀賦權法,權重計算結果主觀性較強,本文提出基于博弈論的組合賦權法將主觀權重與客觀權重組合對各指標進行賦權,主客觀權重的結合可以減少傳統(tǒng)TOPSIS法的主觀權重計算方法的主觀性同時對權重進行主觀控制,避免出現(xiàn)不實的想象,同時以實際監(jiān)測數(shù)據(jù)為依據(jù)又能減少單一客觀權重計算法因監(jiān)測數(shù)據(jù)偶然誤差所產(chǎn)生的影響,并定義“虛擬負理想點”對待選方案相對接近度計算公式進行改進,避免傳統(tǒng)TOPSIS法中出現(xiàn)與理想點及負理想點等距的矛盾現(xiàn)象,使TOPSIS法得到改進與拓展。
將改進的TOPSIS法用于浦陽江干流水質(zhì)監(jiān)測斷面優(yōu)化計算中,結果將9個監(jiān)測斷面優(yōu)化為7個,優(yōu)化前后水質(zhì)檢測結果通過一致性檢驗,改進的TOPSIS法理論成立,計算結果準確有效,可為后期斷面優(yōu)化工作提供相應參考。
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