An Algebraic Approach for Neutrosophic Random Variables by the Refined Ah-Isometry

In this article, we are going to extend the definition of literal neutrosophic random variables to literal refined neutrosophic random variables and we will study its new properties. We derive and present various concepts including refined neutrosophic probability distribution function in the continuous case, refined neutrosophic cumulative distribution function of continuous refined neutrosophic random variables, refined neutrosophic expected value, refined neutrosophic variance, refined neutrosophic standard deviation, refined neutrosophic mean deviation, refined neutrosophic rth quartiles, refined neutrosophic moments generating function, and refined neutrosophic characteristic function. Additionally, the paper includes many solved examples and applications. This paper opens the road to generalizing many concepts in neutrosophic probability theory specially neutrosophic reliability theory, neutrosophic stochastic processes, and neutrosophic queuing theory.