قارن الطرق

	نموذج التنبؤ الرمادي GM(1,1)	نموذج ARIMA (الانحدار الذاتي المتكامل للمتوسط المتحرك)	الاستدلال القائم على الحالات (CBR)
المجال	الحوسبة المرنة	الاقتصاد القياسي	الحوسبة المرنة
العائلة	Regression model	Regression model	Machine learning
سنة النشأة	1982	2015	1994
صاحب الطريقة	Julong Deng	Box & Jenkins (Box-Jenkins methodology)	Janet Kolodner; Agnar Aamodt & Enric Plaza (R4 cycle)
النوع	Small-sample grey forecasting model	Univariate time-series model	Experience-based (analogical) problem solving
المصدر التأسيسي	Deng, J. L. (1982). Control problems of grey systems. Systems & Control Letters, 1(5), 288–294.	Box, G. E. P., Jenkins, G. M., Reinsel, G. C. & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021	Aamodt, A., & Plaza, E. (1994). Case-based reasoning: Foundational issues, methodological variations, and system approaches. AI Communications, 7(1), 39–59.
الأسماء البديلة	GM(1,1), grey prediction model, grey forecasting, gri tahmin modeli	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	CBR, case-based reasoning cycle, analogy-based reasoning, vaka tabanlı akıl yürütme
ذات صلة	2	5	2
الملخص	GM(1,1) is the core forecasting model of grey system theory, introduced by Julong Deng in 1982, designed to predict from very few observations and incomplete information — situations where classical time-series models like ARIMA need far more data. It accumulates the raw series to expose a hidden exponential trend, fits a first-order grey differential equation, and projects future values, making it popular in engineering, energy, and management forecasting with short data records.	ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins methodology set out in Box, Jenkins, Reinsel & Ljung's Time Series Analysis (5th ed., 2015).	Case-based reasoning solves a new problem by retrieving similar problems solved in the past and adapting their solutions, rather than reasoning from first principles or a trained statistical model. Formalized as the Retrieve-Reuse-Revise-Retain cycle by Aamodt and Plaza in 1994 and popularized by Janet Kolodner, CBR mirrors how human experts in medicine, law, and engineering reason by analogy from remembered cases, and it learns simply by storing each newly solved case.