On Fuzzy Random Variables upon Crisp Random Variables

關於明確隨機變數之模糊隨機變數

林德成(Der-Chen Lin) ； 傅清芬(Ching-Fen Fuh)

《智慧科技與應用統計學報》 9卷2期 (2011/12) Pp. 17-29

https://doi.org/10.29807/JTITAS.201112.0002

摘要

在一般現象中可分為兩種型式，一為確定現象與不確定現象。在確定現象中通常可用二元邏輯之明確集合理論來處理，而不確定現象又可分為隨機現象與模糊現象。在一般現實情形中，使用二元邏輯做推理基礎並不符合實務狀況，此時需要用不同的角度來看待問題，可考慮使用模糊觀點加上隨機變數之概念來探討相關問題，在本文中將討論到由模糊集合之基本運算來推論多變量模糊隨機變數的相關性質，並舉例說明。在本文將使用不同於Yao文中之方法來推論相關性質。

關鍵字

隨機變數 ； 模糊隨機變數 ； 模糊獨立隨機變數

並列摘要

A General phenomenon could be divided into two types, that one is the determinacy phenomenon and the other is the indeterminacy phenomenon. The determinacy phenomenon could be handled by crisp set theory of binary logics, while the indeterminacy phenomenon could be further divided into a random phenomenon and a fuzzy phenomenon. In reality, using binary logics as the basis of reasoning does not fit the actual situation and thus different perspectives should be used to treat problems. Fuzzy perspectives and the concept of random variables could be used to discuss related problems. This paper uses basic algorithm of fuzzy set to deduce the related features of multivariate fuzzy random variables, and presents examples for demonstration. A method that is different from Yao's is used to infer related features.

並列關鍵字

random variables ； fuzzy random variables ； independency of fuzzy random variables