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TOPSIS法
TOPSIS法(Technique for Order Preferenceby Similarity to Ideal Solution,)逼近理想解排序法、理想點法 TOPSIS法概述 TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution )法是C.L.Hwang和K.Yoon於1981年首次提出,TOPSIS法根據有限個評價對象與理想化目標的接近程度進行排序的方法,是在現有的對象中進行相對優劣的評價。理想化目標(Ideal Solution)有兩個,一個是肯定的理想目標(positive ideal solution)或稱最優目標,一個是否定的理想目標(negative ideal solution)或稱最劣目標,評價最好的對象應該是與最優目標的距離最近,而與最劣目標最遠,距離的計算可採用明考斯基距離,常用的歐幾里德幾何距離是明考斯基距離的特殊情況。 TOPSIS法是一種理想目標相似性的順序選優技術,在多目標決策分析中是一種非常有效的方法。它通過歸一化後的數據規範化矩陣,找出多個目標中最優目標和最劣目標(分別用理想解和反理想解表示) ,分別計算各評價目標與理想解和反理想解的距離,獲得各目標與理想解的貼近度,按理想解貼近度的大小排序,以此作為評價目標優劣的依據。貼近度取值在0~1 之間,該值愈接近1,表示相應的評價目標越接近最優水平;反之,該值愈接近0,表示評價目標越接近最劣水平。該方法已經在土地利用規劃、物料選擇評估、項目投資、醫療衛生等眾多領域得到成功的應用,明顯提高了多目標決策分析的科學性、準確性和可操作性。 TOPSIS法的基本原理 其基本原理,是通過檢測評價對象與最優解、最劣解的距離來進行排序,若評價對象最靠近最優解同時又最遠離最劣解,則為最好;否則為最差。其中最優解的各指標值都達到各評價指標的最優值。最劣解的各指標值都達到各評價指標的最差值。 TOPSIS法中“理想解”和“負理想解”是TOPSIS法的兩個基本概念。所謂理想解是一設想的最優的解(方案),它的各個屬性值都達到各備選方案中的最好的值;而負理想解是一設想的最劣的解(方案),它的各個屬性值都達到各備選方案中的最壞的值。方案排序的規則是把各備選方案與理想解和負理想解做比較,若其中有一個方案最接近理想解,而同時又遠離負理想解,則該方案是備選方案中最好的方案。 |
TOPSIS
The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a multi-criteria decision analysis method, which was originally developed by Hwang and Yoon in 1981 with further developments by Yoon in 1987, and Hwang, Lai and Liu in 1993. TOPSIS is based on the concept that the chosen alternative should have the shortest geometric distance from the positive ideal solution and the longest geometric distance from the negative ideal solution. It is a method of compensatory aggregation that compares a set of alternatives by identifying weights for each criterion, normalising scores for each criterion and calculating the geometric distance between each alternative and the ideal alternative, which is the best score in each criterion. An assumption of TOPSIS is that the criteria are monotonically increasing or decreasing. Normalisation is usually required as the parameters or criteria are often of incongruous dimensions in multi-criteria problems. Compensatory methods such as TOPSIS allow trade-offs between criteria, where a poor result in one criterion can be negated by a good result in another criterion. This provides a more realistic form of modelling than non-compensatory methods, which include or exclude alternative solutions based on hard cut-offs. |