Fundamentals of Neutrosophical Simulation for Generating Random Numbers Associated with Uniform Probability Distribution

Abstract

The simulation process depends on generating a series of random numbers subject to the uniform probability distribution in the interval [0, 1]. The generation of these numbers is starting from the cumulative distribution function of the uniform distribution. Through previous studies in classical logic, we found any random number R0, met with a cumulative distribution function value equal to R0, but these specific numbers may not have sufficient accuracy, which leads to obtaining results that are not sufficiently accurate when doing the simulation. To bypass this case, in this paper, we present a study that enables us to generate as accurate as possible random numbers, using neutrosophic logic ' this Logic given by American mathematician Florentin Smarandache in 1995'. The first step in the study is, define the cumulative distribution function of the neutrosophic uniform distribution, depending on definition of the neutrosophic integral and definition of the neutrosophic uniform distribution. We used the new definition to generate random numbers subject to a neutrosophic uniform distribution on the interval [0, 1]. The result was that each random number R0 corresponds to a interval of the distribution function related to R0, So that it preserves enough precision for the random numbers, and thus we get a more accurate simulation of any system we want to simulate.