離散型小樣本資料之分析

Resolution of Discrete Small Sample Problems

張婉吟(Wan-Yin Chang)

指導教授 ： 王小璠

國立清華大學/工學院/工業工程與工程管理學系/碩士(2013年)

摘要

隨著全球化與科技快速發展，產品的生命週期越來越短，在資料量不足的情況之下，提供管理者正確的預測訊息是很困難的；除此之外，現實生活也有許多稀有事件，例如：地震、金融風暴、颱風…等，這些事件雖然很少發生，但總是伴隨著嚴重的生命財產損失，這類缺乏資料量的問題，我們稱之為「小樣本問題」或「稀有事件」。
目前大多研究僅考慮連續空間的資料，鮮少探討離散型的小樣本問題。然而，許多社會經濟問題皆為離散型的資料，如何解決資料不足的問題更形重要。本研究根據多重集合除法，在原始樣本所給定的數值範圍內產生額外的有效資料，並以乏晰理論為基礎，將資料型態轉換成為離散型的數據資料，再根據擴充理論(Extension Principle)推導出隸屬函數作為分析之用。所以本研究結合資料建構法（Data Construction Method）與乏晰理論（Fuzzy Set Theory），提出一套直觀、正確、且有效率的資料產生法，稱之為「乏晰資料建構法（Fuzzy Data Construction Method）」以克服因為資料量太少而無法顯現的離散型小樣本問題，並減少因缺乏資料所造成的損失。

關鍵字

稀有事件 ； 離散小樣本 ； 資料建構法 ； 乏晰理論 ； 乏晰資料建構法

並列摘要

With the rapid changes in the global marketplace, using available data to build a management model has become increasingly difficult because the necessary information is often insufficient and incomplete. In the real world, the occurrence of some rare events may have a widespread socioeconomic impact and may cause significant losses. The data type of these rare events is mostly discrete. Thus, this study proposes a systematic way of filling information gaps and recognizing their underlying patterns accurately.
An intuitive method based on the concept of analysis is presented to generate virtual samples. Moreover, by applying the extension principle in the fuzzy set theory, the degree of belonging of a generated datum to the discrete sample set can be described. The proposed method is therefore called fuzzy data construction method. Numerical example is provided to illustrate the procedure.

並列關鍵字

rare events ； discrete small sample ； data construction method ； fuzzy set theory ； fuzzy data construction method

參考文獻

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