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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク TOPSIS ： ウィキペディア英語版 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. ==TOPSIS method== The TOPSIS process is carried out as follows: ;Step 1: Create an evaluation matrix consisting of m alternatives and n criteria, with the intersection of each alternative and criteria given as $x\_$, we therefore have a matrix $(\; x\_\; )\_$. ;Step 2: The matrix $(\; x\_\; )\_$ is then normalised to form the matrix $R\; =\; (\; r\_\; )\_$, using the normalisation method $r\_\; =\; \backslash frac\; ^\; x\_^2\; \}\},\; i\; =\; 1,\; 2,\; .\; .\; .,\; m,\; j\; =\; 1,\; 2,\; .\; .\; .,\; n$ ;Step 3: Calculate the weighted normalised decision matrix $T\; =(t\_)\_\; =\; (\; w\_jr\_\; )\_,\; i\; =\; 1,\; 2,\; .\; .\; .,\; m$ :Where $w\_j\; =\; W\_j\; /\; \backslash sum\_^W\_j,\; j\; =\; 1,\; 2,\; .\; .\; .,\; n$ so that $\backslash sum\_^\; w\_j\; =\; 1$, and $W\_j$ is the original weight given to the indicator $v\_j,\; j\; =\; 1,\; 2,\; .\; .\; .,\; n.$ ;Step 4: Determine the worst alternative $(A\_w)$ and the best alternative $(A\_b)$: $A\_w\; =\; \backslash \; |\; i\; =\; 1,2,...,m)|\; j\; \backslash in\; J\_+\; \backslash rangle\; \backslash rbrace\; \backslash equiv\; \backslash \; |\; i\; =\; 1,2,...,m)|\; j\; \backslash in\; J\_-\; \backslash rangle,\; \backslash langle\; max(t\_\; |\; i\; =\; 1,2,...,m)|\; j\; \backslash in\; J\_+\; \backslash rangle\; \backslash rbrace\; \backslash equiv\; \backslash \; =\; \backslash sqrt(t\_\; -\; t\_)^2\},\; i\; =\; 1,\; 2,\; .\; .\; .,\; m$, and the distance between the alternative $i$ and the best condition $A\_b$ :$d\_\; =\; \backslash sqrt(t\_\; -\; t\_)^2\},\; i\; =\; 1,\; 2,\; .\; .\; .,\; m$ :where $d\_$ and $d\_$ are L2-norm distances from the target alternative $i$ to the worst and best conditions, respectively. ;Step 6: Calculate the similarity to the worst condition: $s\_=\; d\_\; /\; (d\_\; +\; d\_),\; 0\; \backslash le\; s\_\; \backslash le\; 1,\; i\; =\; 1,\; 2,\; .\; .\; .,\; m$. $s\_\; =\; 1$ if and only if the alternative solution has the best condition; and $s\_\; =\; 0$ if and only if the alternative solution has the worst condition. ; Step 7: Rank the alternatives according to $s\_\; (i\; =\; 1,\; 2,\; .\; .\; .,\; m)$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「TOPSIS」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.