Random fuzzy location-scale family with linear fuzzy location function

Abstract

Coexistence of fuzziness and the randomness has become an intrinsic character in modern manufacturing environments. Accordingly, it is necessary to introduce a new random fuzzy reliability concept and regression models to facilitate the random and fuzzy uncertainties. In this article, we propose the average chance reliability as a measure of quality index under random fuzzy uncertainty, which can be regarded as a counterpart of conventional reliability under probability theory. Furthermore, we extend the probabilistic location-scale family, which is actually a non-normal regression model, into a random fuzzy location-scale family, which is developed for the facilitation of the covariate modeling under random fuzzy environments. We will particularly focus our development on a random fuzzy location-scale family, in which the location function is a fuzzy regression model with each fuzzy exploratory variable being piecewise linear credibility distributed.

隨機性和模糊性的共存已成為現代製造產業環境之固有的特徵。 因此, 為了提供隨機模糊不確定性模型框架, 有必要引入新的隨機模糊可靠性概念及回歸模型。 在本文中, 我們建議以平均機會可靠性作為在隨機模糊不確定性下質量指標之測度, 它可以被視為概率理論下常規可靠性的對應概念。 此外， 我們把概率理論中的位置-尺度分佈族擴展為隨機模糊的位置-尺度分佈族， 這實際上是一種非正態的回歸模型。 該發展為了提供隨機模糊環境下伴隨(共) 變量的建模框架。 我們的推導將特別集中於其位置函數是模糊回歸模型,而模糊自變量則服從分段線性可信性分佈函數的隨機模糊位置-尺度分佈族。

(*聯絡人: [email protected])

Keywords:

• random fuzzy variable
• location-scale family
• piecewise linear credibility distribution function

Keywords:

• 關鍵詞： 隨機模糊變數 ， 分段線性可信性分佈函數 ， 位置-尺度分佈族

Notes

(*聯絡人: [email protected])