Fuzzy Cumulative Distribution Function and its Properties

The statistical methods based on cumulative distribution function is a start point for many parametric or nonparametric statistical inferences. However, there are many practical problems that require dealing with observations/ parameters that represent inherently imprecise. However, Hesamian and Taheri (2013) was extended a concept of fuzzy cumulative distribution function. Applying a common notion of fuzzy random variables, they extended a vague concept of fuzzy cumulative distribution function. However, the main properties of the proposed method has not yet been considered in fuzzy environment. This paper aims to extend the classical properties of the fuzzy cumulative distribution function in fuzzy environment.