粗化數據之統計分析

Abstract

本文討論在抽樣調查中被視為隨機集合模型的樣本，並試著架構基於模糊統計邏輯的粗化數據(coarse data)之理論與特性。因為有些抽樣調查中的數據可以視為隨機集合模型所得出的新數據。如何應用數學分析方法，配合軟計算技術以達到有效之資料處理與統計分析就是本研究之重點。我們將隨機抽樣樣本當作隨機實驗所做出來的結果，而這個論點可以幫助我們分析粗化數據。在探索抽樣調查的隨機集合和分佈的時候，機率測度論提供了很多種非精確數據給予統計學推測結論(statistical inference)，我們推廣傳統理論，以模糊集合及隸屬度為基礎，作為集合元素運算之依據。 \n關鍵字：粗化數據、隨機集合、隸屬度函數

In this paper we discuss the sample in the random set model for the sampling survey. Since the data from sampling survey can be treated as a new type of data from the random set model. How to apply the mathematical analyzing methods as well as soft computing techniques to reach an efficient propose is our main goal. We treat random sampling data as the result of random experimental design. And this concept will help us to analyze the coarse data. Finally, in investigating the random set and its distributions for the random sampling survey, traditional probability measure theory serves an important role in the statistical inference, while we use the membership function and fuzzy operations to extend traditional concept into a more general case.\nKeywords： Coarse data, Random set, Membership function