Forecasting Analysis by Fuzzy Grey Model GM(1,1)

模糊灰色GM(1,1)預測模式

10.29977/JCIIE.200609.0006

曹銳勤(Ruey-Chyn Tsaur)

預測 ； 灰色模式GM(1,1) ； 模糊集合 ； 模糊灰色模式GM(1,1) ； 稀少資料 ； forecasting, grey model GM(1,1) ； fuzzy set ； fuzzy grey model GM(1,1) ； limited data

工業工程學刊

23卷5期（2006 / 09 / 01）

415 - 422

英文

儘管在資料量稀少如四筆的條件下，灰色模式GM(1,1)已成功的被應用於解決工程及管理的相關問題；然而，也由於資料量稀少，決策者從預測值上所獲得的資訊量不足而使得決策品質不佳。由於許多研究結果顯示模糊廻歸、模糊時間序列等模糊預測模式，在資料量稀少及資料為語意資料等不確定的環境下具有良好的預測結果。因此，對於輸入值為實數值且環境存在不確定的條件下，本研究提出映射累加AGO值及模糊參數而求得模糊輸出的預測值。採用此模式，決策者可以獲得一個可能的外插預測區間而得到較充分的預測資訊，減少資訊不充分下的決策損失。最後，以一範例作為說明。

The grey model GM(1,1) has been successfully applied in management and engineering problems with as little as four data. Because of lack of sufficient data, a decision maker obtained too little information from the extrapolative value to make an ineffective decision in grey model GM(1,1). A considerable amount of research has shown that fuzzy forecasting tools such as fuzzy regression and fuzzy time series are powerful forecasting models under an uncertain environment. Therefore, by crisp-input value to obtain AGO value, we propose fuzzy grey model GM(1,1) by mapping AGO value with the fuzzy parameter to forecast fuzzy-output extrapolative value under uncertain and limited data. By the crisp-input and fuzzy-output fuzzy grey model GM(1,1)model, a decision making can obtain more information from the obtained possible forecasting interval and so reduce the possible loss in decision making under uncertainty with limited data. Finally, an example is given for illustration.

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